Pharmaceutical Sciences, Faculty of
DSpace
UBCV
Moein, Anita
Doctor of Philosophy - PhD
University of British Columbia
Phosphatidylinositol-3-kinase (PI3K)/AKT/mammalian target of rapamycin (mTOR) signaling is one of the most important intracellular pathways, and a master regulator for many cancer types. Massive efforts dedicated to the development of drugs targeting PI3K signaling, however, the number of approved inhibitors remains limited. Thesis objectives were to acquire a better understanding of the PI3K/AKT/mTOR pathway dynamic response by developing mechanistic preclinical and clinical pharmacokinetic (PK)-pharmacodynamic (PD) models. Conducted a retrospective assessment of the translational PK-PD modeling performance with apitolisib, a dual PI3K/mTOR inhibitor. Integrated PK-PD-Efficacy models developed for xenografts bearing human renal cell adenocarcinoma (RCC) and patients with solid tumors show a steep sigmoid curve linking pAkt inhibition to tumor growth inhibition and quantified that a minimum of 35% to 45% pAkt modulation is needed for tumor shrinkage in patients based on platelet-rich plasma surrogate matrix and in xenografts based on tumor tissue matrix. Based on this relationship, constant pAkt inhibition of 61% and 65% would be necessary to achieve tumor stasis in xenografts and patients, respectably. Developed a longitudinal exposure-tumor growth inhibition (TGI) model to characterize and compare everolimus (mTORC1 inhibitor) vs apitolisib’s (dual PI3K/mTORC1/2 inhibitor) ability to inhibit tumor growth, and quantitated each drug’s efficacy decay caused by emergence of tumor resistance over time in patients with metastatic-RCC. The estimated on-treatment tumor growth rate constant was 1.7-fold higher for apitolisib compared to everolimus. Half-life for loss of treatment effect over time for everolimus was 16.1 weeks compared to 7.72 weeks for apitolisib suggesting a faster rate of tumor re-growth for apitolisib patients likely due to the emergence of resistance. Developed longitudinal TGI models to characterize tumor response in women with ER+/HER2- advanced/metastatic breast cancer undergoing treatment with fulvestrant alone or in combination with the PI3K inhibitor, taselisib. Assessed impact of clinically relevant covariates on TGI metrics and identified patient subsets most likely to benefit from these treatments. Based on results, additive/potentially synergistic anti-tumor effects were observed in patients treated with the taselisib-fulvestrant combination. In conclusion, these methods and results underscore the significance of model informed drug development for targeted cancer therapy throughout the drug development lifecycle.
QUANTITATIVE PHARMACOKINETIC-PHARMACODYNAMIC MODELING TO OPTIMIZE TARGETED PI3K-AKT-MTOR ONCOLOGY THERAPEUTICS DEVELOPMENT by Anita Moein M.S., Pharmaceutical Sciences, University at Buffalo, 2014 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Pharmaceutical Sciences) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) July 2024 © Anita Moein, 2024 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled: Quantitative Pharmacokinetic-Pharmacodynamic Modeling to Optimize Targeted PI3K-AKT-mTOR Oncology Therapeutics Development Submitted by Anita Moein in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Pharmaceutical Sciences Examining Committee: Dr. Harvey Wong, Associate Professor, Pharmaceutical Sciences, UBC Supervisor Dr. Matthew Wright, Executive Director, Drug Metabolism & Pharmacokinetics, Genentech Supervisory Committee Member Dr. Karla Williams, Associate Professor, Pharmaceutical Sciences, UBC University Examiner Dr. Anotida Madzvamuse, Professor, Mathematics, UBC University Examiner Additional Supervisory Committee Members: Dr. Thomas Chang, Professor and Associate Dean, Pharmaceutical Sciences, UBC Supervisory Committee Member Dr. Jin Y. Jin, Executive Director, Global Head of Modeling and Simulation, Genentech Supervisory Committee Member Dr. Shyh-Dar Li, Professor, Pharmaceutical Sciences, UBC Supervisory Committee Member iii Abstract Phosphatidylinositol-3-kinase (PI3K)/AKT/mammalian target of rapamycin (mTOR) signaling is one of the most important intracellular pathways, and a master regulator for many cancer types. Massive efforts dedicated to the development of drugs targeting PI3K signaling, however, the number of approved inhibitors remains limited. Thesis objectives were to acquire a better understanding of the PI3K/AKT/mTOR pathway dynamic response by developing mechanistic preclinical and clinical pharmacokinetic (PK)-pharmacodynamic (PD) models. Conducted a retrospective assessment of the translational PK-PD modeling performance with apitolisib, a dual PI3K/mTOR inhibitor. Integrated PK-PD-Efficacy models developed for xenografts bearing human renal cell adenocarcinoma (RCC) and patients with solid tumors show a steep sigmoid curve linking pAkt inhibition to tumor growth inhibition and quantified that a minimum of 35% to 45% pAkt modulation is needed for tumor shrinkage in patients based on platelet-rich plasma surrogate matrix and in xenografts based on tumor tissue matrix. Based on this relationship, constant pAkt inhibition of 61% and 65% would be necessary to achieve tumor stasis in xenografts and patients, respectably. Developed a longitudinal exposure-tumor growth inhibition (TGI) model to characterize and compare everolimus (mTORC1 inhibitor) vs apitolisib’s (dual PI3K/mTORC1/2 inhibitor) ability to inhibit tumor growth, and quantitated each drug’s efficacy decay caused by emergence of tumor resistance over time in patients with metastatic-RCC. The estimated on-treatment tumor growth rate constant was 1.7-fold higher for apitolisib compared to everolimus. Half-life for loss of treatment effect over time for everolimus was 16.1 weeks compared to 7.72 weeks for apitolisib suggesting a faster rate of tumor re-growth for apitolisib patients likely due to the emergence of resistance. Developed longitudinal TGI models to characterize tumor response in women with ER+/HER2- advanced/metastatic breast cancer iv undergoing treatment with fulvestrant alone or in combination with the PI3K inhibitor, taselisib. Assessed impact of clinically relevant covariates on TGI metrics and identified patient subsets most likely to benefit from these treatments. Based on results, additive/potentially synergistic anti-tumor effects were observed in patients treated with the taselisib-fulvestrant combination. In conclusion, these methods and results underscore the significance of model informed drug development for targeted cancer therapy throughout the drug development lifecycle. v Lay Summary PI3K/AKT/mTOR signaling is considered as a master intracellular regulator for many cancer types. Massive efforts have been dedicated to the development of drugs targeting PI3K signaling, however, the number of approved inhibitors remains limited. The overall aim of this thesis was to acquire a better understanding of the PI3K/AKT/mTOR pathway response by developing mechanistic PK-PD models to integrate and characterize dynamic relationship between exposure of targeted drugs, modulation of PD biomarkers/tumor triggered by inhibition of PI3K/AKT/mTOR pathway and estimation of longitudinal response including emergence of tumor resistance. Thesis results evaluated the translatability of the preclinical analysis to patients and provides information that will enhance the value of future preclinical translational dose-finding and dose optimization studies to accelerate clinical drug development. Additionally, results highlight the differences in efficacy of targeted drugs with different mechanisms of action and provides insights into the impact of combination therapies and individualize responses to these treatments. vi Preface This dissertation comprises my research to develop quantitative pharmacokinetic-pharmacodynamic modeling framework for evaluating time-varying treatment effects of targeted PI3K-AKT-mTOR oncology therapeutics during drug development. I conducted comprehensive literature reviews, designed the studies, performed data cleaning, formatting, and compiling, conducted rigorous data analysis, interpreted, and presented the results. Studies were designed and conducted under supervision and guidance of Dr. Harvey Wong. Advice and suggestions on the studies’ design, analytic approaches and methodologies was provided from Dr. Jin Y. Jin, Dr. Matthew R. Wright, and Dr. Shyh-Dar Li. Data Source The pre-clinical experimental raw data and clinical trials raw data used in this thesis were provided by Genentech Inc., a member of the Roche group. Clinical Trials Registry NCT00854152; NCT00854126; NCT01442090; NCT02340221; NCT01296555 All clinical trials were conducted in accordance with Good Clinical Practice guidelines and the Declaration of Helsinki. Prior to enrollment, written informed consent was acquired from all patients, in alignment with the approved protocols from the ethics committees at each study site. All clinical trials information can be accessed through the following website. https://clinicaltrials.gov/. vii Chapter 1: “Introduction”, I conducted literature reviews and wrote the chapter, Dr. Harvey Wong edited and provided comments. Chapter 2: “Retrospective Assessment of the Translational Pharmacokinetic-Pharmacodynamic Modeling Performance: A Case Study with Apitolisib, A Dual PI3K/mTOR inhibitor” has been accepted for publication at the Drugs in R&D journal. I was the primary author, conducted comprehensive literature reviews, designed the study, performed data cleaning, formatting, and compiling, conducted rigorous data analysis, interpreted, and presented the results. This study was designed and conducted under supervision and guidance of Dr. Harvey Wong. Comments and revisions for the manuscript was provided by Dr. Harvey Wong. Advice and suggestions on the study design, analytic approaches and methodologies was provided from Dr. Jin Y. Jin, Dr. Matthew R. Wright, and Dr. Shyh-Dar Li. This chapter (manuscript) has been improved through the peer-review process at the Drugs in R&D journal. Chapter 3: “Quantitative Assessment of Drug Efficacy and Emergence of Resistance in Patients with Metastatic Renal Cell Carcinoma Using a Longitudinal Exposure-Tumor Growth Inhibition Model: Apitolisib (dual PI3K/mTORC1/2 inhibitor) versus Everolimus (mTORC1 inhibitor)” has been improved through the peer-review process at the Journal of Clinical Pharmacology where it has been accepted for publication. I was the primary author, conducted comprehensive literature reviews, designed the study, performed data cleaning, formatting, and compiling, conducted rigorous data analysis, interpreted, and presented the results. This study was designed and conducted under supervision viii and guidance of Dr. Harvey Wong. Comments and revisions for the manuscript was provided by Dr. Harvey Wong. Advice and suggestions on the study design, analytic approaches and methodologies was provided from Dr. Jin Y. Jin, Dr. Matthew R. Wright, and Dr. Shyh-Dar Li. Chapter 4: “Quantitative Characterization of the Effects of Fulvestrant Alone or in Combination with Taselisib (PI3Kinase Inhibitor) on Longitudinal Tumor Growth in Patients with Estrogen Receptor-positive, HER2-negative, PIK3CA-mutant, Advanced or Metastatic Breast Cancer” has been improved through the peer-review process at the Cancer Chemotherapy and Pharmacology journal, where it has been accepted for publication. I was the primary author, conducted comprehensive literature reviews, designed the study, performed data cleaning, formatting, and compiling, conducted rigorous data analysis, interpreted, and presented the results. This study was designed and conducted under supervision and guidance of Dr. Harvey Wong. Comments and revisions for the manuscript was provided by Dr. Harvey Wong. Advice and suggestions on the study design, analytic approaches and methodologies was provided from Dr. Jin Y. Jin, Dr. Matthew R. Wright, and Dr. Shyh-Dar Li. ix Table of Contents Abstract ........................................................................................................................................................ iii Lay Summary ................................................................................................................................................. v Preface ......................................................................................................................................................... vi Table of Contents ......................................................................................................................................... ix List of Tables ............................................................................................................................................... xii List of Figures ..............................................................................................................................................xiii Acknowledgements ..................................................................................................................................... xvi Dedication .................................................................................................................................................. xvii Chapter 1: Introduction ................................................................................................................................ 1 1.1 Background ......................................................................................................................................... 1 1.1.1 PI3K/AKT/mTOR Pathway ............................................................................................................ 2 1.1.2 PI3K Function and Isoforms ......................................................................................................... 5 1.1.3 Approved PI3K Inhibitors ............................................................................................................. 6 1.2 Model-Informed Drug Development .................................................................................................. 8 1.2.1 Pharmacokinetics and Pharmacodynamics Models .................................................................... 9 1.2.2 Translational Pharmacokinetics-Pharmacodynamics Xenografts Models ................................. 11 1.2.3 Clinical Exposure-Tumor Growth Inhibition Models .................................................................. 13 1.3 Research Aim and Specific Objectives .............................................................................................. 14 Chapter 2: Retrospective Assessment of the Translational Pharmacokinetic-Pharmacodynamic Modeling Performance: A Case Study with Apitolisib, A Dual PI3K/mTOR inhibitor .................................................. 16 2.1 Introduction ...................................................................................................................................... 17 2.2 Methods ............................................................................................................................................ 20 2.2.1 Xenograft Dataset ...................................................................................................................... 20 2.2.2 Clinical Trials Dataset ................................................................................................................. 22 2.2.3 Pharmacokinetic Models ........................................................................................................... 23 2.2.4 Pharmacokinetic-Pharmacodynamic (PK-PD) Models Describing pAkt Modulation ................. 24 2.2.5 Integrated PK-PD-Efficacy Models ............................................................................................. 26 2.2.6 Models Evaluation...................................................................................................................... 29 2.2.7 Models Assumptions and Limitations ........................................................................................ 29 2.2.8 Software ..................................................................................................................................... 30 2.3 Results ............................................................................................................................................... 30 2.3.1 Pharmacokinetic Models ........................................................................................................... 30 x 2.3.2 PK-PD Models Describing pAkt Modulation .............................................................................. 34 2.3.3 Integrated PK-PD-Efficacy Models ............................................................................................. 37 2.4 Discussion .......................................................................................................................................... 48 2.5 Conclusions ....................................................................................................................................... 54 Chapter 3: Quantitative Assessment of Drug Efficacy and Emergence of Resistance in Patients with Metastatic Renal Cell Carcinoma Using a Longitudinal Exposure-Tumor Growth Inhibition Model: Apitolisib (dual PI3K/mTORC1/2 inhibitor) versus Everolimus (mTORC1 inhibitor) ................................... 56 3.1 Introduction ...................................................................................................................................... 57 3.2 Methods ............................................................................................................................................ 60 3.2.1 Clinical Trial ................................................................................................................................ 60 3.2.2 Study Design and Data ............................................................................................................... 60 3.2.3 Population Longitudinal Exposure-Tumor Growth Inhibition Model ........................................ 61 3.2.4 Software ..................................................................................................................................... 65 3.3 Results ............................................................................................................................................... 65 3.3.1 Population Longitudinal Exposure-Tumor Growth Inhibition Model ........................................ 65 3.4 Discussion .......................................................................................................................................... 82 3.5 Conclusions ....................................................................................................................................... 88 Chapter 4: Quantitative Characterization of the Effects of Fulvestrant Alone or in Combination with Taselisib (PI3Kinase Inhibitor) on Longitudinal Tumor Growth in Patients with Estrogen Receptor-positive, HER2-negative, PIK3CA-mutant, Advanced or Metastatic Breast Cancer .................................... 90 4.1 Introduction ...................................................................................................................................... 91 4.2 Methods ............................................................................................................................................ 94 4.2.1 Clinical Trial ................................................................................................................................ 94 4.2.2 Study Design and Data ............................................................................................................... 95 4.2.3 Longitudinal Tumor Growth Inhibition Models ......................................................................... 96 4.2.4 Software ................................................................................................................................... 108 4.3 Results ............................................................................................................................................. 108 4.3.1 Data .......................................................................................................................................... 108 4.3.2 Longitudinal Tumor Growth Inhibition Models ....................................................................... 110 4.4 Discussion ........................................................................................................................................ 139 4.5 Conclusion ....................................................................................................................................... 145 Chapter 5: Conclusions ............................................................................................................................. 146 5.1 Summary of Research Findings ....................................................................................................... 146 5.2 PI3K/AKT/mTOR Pathway Significance ........................................................................................... 147 xi 5.3 PI3K/AKT/mTOR Drug Development Challenges ............................................................................ 147 5.4 Research Contributions and Impact................................................................................................ 149 5.4.1 Significance of Research Findings ............................................................................................ 149 5.4.2 Translational Pharmacokinetic-Pharmacodynamic Models .................................................... 151 5.4.3 Longitudinal Exposure-Tumor Growth Inhibition Models ....................................................... 152 5.5 Research Limitations ....................................................................................................................... 154 5.6 Future Directions ............................................................................................................................ 156 5.7 Concluding Remarks ........................................................................................................................ 160 References ................................................................................................................................................ 161 Appendices ................................................................................................................................................ 179 Appendix A: NONMEM Codes for “Retrospective Assessment of the Translational Pharmacokinetic-Pharmacodynamic Modeling Performance: A Case Study with Apitolisib, A Dual PI3K/mTOR inhibitor” .............................................................................................................................................................. 179 Appendix B: NONMEM Code for “Quantitative Assessment of Drug Efficacy and Emergence of Resistance in Patients with Metastatic Renal Cell Carcinoma Using a Longitudinal Exposure-Tumor Growth Inhibition Model: Apitolisib (dual PI3K/mTORC1/2 inhibitor) versus Everolimus (mTORC1 inhibitor)” .............................................................................................................................................. 185 Appendix C: NONMEM Codes for “Quantitative Characterization of the Effects of Fulvestrant Alone or in Combination with Taselisib (PI3Kinase Inhibitor) on Longitudinal Tumor Growth in Patients with Estrogen Receptor-positive, HER2-negative, PIK3CA-mutant, Advanced or Metastatic Breast Cancer” .............................................................................................................................................................. 188 xii List of Tables Table 1.1 Food and Drug Administration (FDA) approved PI3K Inhibitors……... 7 Table 2.1 Parameter estimates following fitting of PK-PD model describing pAkt modulation for xenograft mice (786-O)………………………………… 36 Table 2.2 Parameter estimates following fitting of PK-PD Model describing pAkt modulation for patients with advanced solid tumors (Phase 1 studies)… 37 Table 2.3 Integrated PK-PD-Efficacy model parameters estimate for xenografts (786-O)………………………………………………………………….. 46 Table 2.4 Integrated PK-PD-Efficacy model parameters estimate for patients with advanced solid tumors (Phase 1 studies)……………………………….. 46 Table 3.1 Everolimus population pharmacokinetic parameters…………………… 63 Table 3.2 Apitolisib population pharmacokinetic parameters…………………….. 63 Table 3.3 Parameter estimates of the final longitudinal exposure-tumor growth inhibition model for everolimus and apitolisib…………………………. 74 Table 4.1 Population pharmacokinetics parameters for taselisib…………………. 99 Table 4.2 Covariates investigated during model development……………………. 100 Table 4.3 Baseline continuous covariate statistics for covariates explored during development of the final model…………………………..…………… 101 Table 4.4 Baseline categorical covariate statistics for covariates that were explored during development of the final model …………………….. 102 Table 4.5 Baseline covariate statistics for external evaluation dataset………….. 107 Table 4.6 Parameter estimates of the base Fulvestrant TGI Model for patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone…………………………………….. 111 Table 4.7 Parameter estimates of the final covariate Fulvestrant TGI Model for patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone………………………… 112 Table 4.8 Parameter estimates of the base Combination Therapy TGI Model for patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone or in combination with 4 mg taselisib…………………………………………………………… 119 Table 4.9 Parameter estimates of the final covariate Combination Therapy TGI Model for patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone or in combination with 4 mg taselisib………………………………………. 120 Table 5.1 Key findings and impact of each specific study………………………. 150 xiii List of Figures Figure 1.1 The PI3K/AKT/mTOR pathway overview in cancer…………………. 4 Figure 2.1 Illustration of preclinical and clinical integrated PK-PD-Efficacy models structures………………………………………………………. 28 Figure 2.2 Observed concentrations versus individual and population predictions from the population pharmacokinetic model for apitolisib…………….. 32 Figure 2.3 Conditional weighted residuals versus population predictions and time from the population pharmacokinetic model for apitolisib…………….. 33 Figure 2.4 Mean observed and predicted %pAkt relative to baseline vs time……... 35 Figure 2.5 Observed versus preclinical PK-PD-Efficacy model predicted tumor volumes…………………………………………………………………. 39 Figure 2.6 Observed versus clinical PK-PD-Efficacy model predicted tumor size data……………………………………………………………………. 40 Figure 2.7 Conditional weighted residuals versus population predictions and time from the preclinical PK-PD-Efficacy model…………………………… 41 Figure 2.8 Conditional weighted residuals versus population predictions and time from the clinical PK-PD-Efficacy model……………………………… 42 Figure 2.9 Prediction corrected visual predictive check of tumor volume data based on the final preclinical PK-PD-Efficacy model………………….. 43 Figure 2.10 Prediction corrected visual predictive check of tumor size data based on the final clinical PK-PD-Efficacy model……………………………….. 44 Figure 2.11 Preclinical and clinical population integrated PK-PD-Efficacy models estimated relationship between tumor shrinkage rate constan vs %pAkt inhibition in xenograft (tumor tissue) and in a typical patient with advanced solid tumors (surrogate plasma)…………………………….. 47 Figure 3.1 Illustration of model structure for longitudinal exposure-tumor growth inhibition model……………………………………………………… 62 Figure 3.2 Longitudinal tumor size data. Individual time courses of tumor size data of patients with metastatic renal cell carcinoma treated with 40 mg apitolisib or 10 mg everolimus …………………………………………. 66 Figure 3.3 Longitudinal tumor size change from baseline data. Individual time courses of tumor size data change from baseline of patients with metastatic renal cell carcinoma treated with 40 mg apitolisib or 10 mg everolimus….…………………………………………………………. 67 Figure 3.4 Conditional weighted residuals versus time plots from the final longitudinal exposure-tumor growth inhibition model for patients treated with apitolisib or everolimus…………………………………… 68 Figure 3.5 Observed individual tumor size data versus predictions from the final longitudinal exposure-TGI model stratified by treatment with 40 mg apitolisib or 10 mg everolimus ………………………………………… 69 Figure 3.6 Observed individual baseline tumor size data versus predicted individual baseline tumor size from the final longitudinal exposure-TGI model stratified by treatment with 40 mg apitolisib or 10 mg everolimus ……………………………………………………………. 70 xiv Figure 3.7 Representative individual fits of tumor size from the final longitudinal exposure-TGI model for everolimus and apitolisib.………………….. 71 Figure 3.8 Prediction corrected visual predictive check of tumor size data versus time since first dose, for the final longitudinal exposure-tumor growth inhibition model, stratified by treatment……………………………… 72 Figure 3.9 Boxplots comparing of model-estimated Kg and Ks in patients with metastatic renal cell carcinoma treated with 40 mg apitolisib or 10 mg everolimus ……………………………………………………………. 75 Figure 3.10 Boxplots comparing half-life for loss of treatment effect over time in patients with metastatic renal cell carcinoma treated with 40 mg apitolisib or 10 mg everolimus ………………………………………... 77 Figure 3.11 Boxplots comparing observed baseline tumor size between everolimus or apitolisib treatment groups…………………………………………. 78 Figure 3.12 Relationships between individual on-treatment Kg and types of responders stratified by treatment group………………………………. 79 Figure 3.13 Simulations of predicted longitudinal tumor dynamics of a typical patient with metastatic renal cell carcinoma treated with 10 mg everolimus or 40 mg apitolisib…………………………………………. 81 Figure 4.1 Illustration of model structure for longitudinal tumor growth inhibition models………………………………………………………………….. 104 Figure 4.2 Diagram illustrating the process of model development……………….. 105 Figure 4.3 Observed longitudinal individual tumor size data. Individual time courses of tumor size data of patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone or in combination with 4 mg taselisib…………………………… 109 Figure 4.4 Observed longitudinal individual tumor size data change from baseline. Individual time courses of tumor size data of patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone or in combination with 4 mg taselisib……………….. 110 Figure 4.5 Fulvestrant TGI Model: observed tumor size data versus individual predictions from the tumor growth inhibition model………………….. 113 Figure 4.6 Fulvestrant TGI Model: individual weighted residuals versus time from the tumor growth inhibition model…………………………………….. 114 Figure 4.7 Fulvestrant TGI Model: representative individual patients fit…………. 115 Figure 4.8 Distribution of net tumor growth rate constant inter-individual variability vs covariates for the Fulvestrant TGI Model………………. 116 Figure 4.9 Fulvestrant TGI Model: relationships between individual fulvestrant tumor shrinkage rate constant and best overall response……………….. 117 Figure 4.10 Combination Therapy TGI Model: observed tumor size data versus individual predictions from the tumor growth inhibition model……….. 121 Figure 4.11 Combination Therapy TGI Model: individual weighted residuals versus time from the tumor growth inhibition model, stratified by treatment…. 122 Figure 4.12 Combination Therapy TGI Model: representative individual patients fit, stratified by treatment…………………………………………………... 123 xv Figure 4.13 Combination Therapy TGI Model: observed baseline tumor size data versus individual baseline tumor size predictions from the tumor growth inhibition model, stratified by treatment………………………. 124 Figure 4.14 Combination Therapy TGI Model: visual predictive check of tumor size data versus time, for the final model stratified by treatment………. 125 Figure 4.15 Distribution of net tumor growth rate constant inter-individual variability vs covariates for the Combination Therapy TGI Model……. 128 Figure 4.16 Relationships between β (taselisib) and best overall response…………. 129 Figure 4.17 Boxplots of observed individual baseline tumor size for patients treated with fulvestrant and fulvestrant+taselisib……………………………… 130 Figure 4.18 Correlation plot of inter-individual variability for the final Combination Therapy TGI Model…………………………………………………….. 132 Figure 4.19 Individual weighted residuals versus time since first dose, from the Interaction TGI Model………………………………………………….. 133 Figure 4.20 Interaction TGI Model: representative individual patients fits…………. 134 Figure 4.21 External evaluation of Combination Therapy TGI Model: observed tumor size data from external study versus individual predictions from the Combination Therapy TGI Model with covariates…………………. 135 Figure 4.22 External evaluation of Combination Therapy TGI Model: individual weighted residuals (Phase 1b/2 external data) versus time from the Combination Therapy TGI Model with covariates……………………... 136 Figure 4.23 External evaluation of Combination Therapy TGI Model: representative patients observed tumor size data versus individual predictions from the Combination Therapy TGI Model with covariates………………………………………………………………... 137 Figure 4.24 External evaluation of Combination Therapy TGI Model: visual predictive check of tumor size data from external study versus time for the Combination Therapy TGI Model with covariates…………………. 138 xvi Acknowledgements I would like to extend my deepest gratitude to my PhD advisor, Dr. Harvey Wong, for his unwavering support, guidance, and mentorship throughout this journey. His expertise, patience, and encouragement have been invaluable in shaping my research and academic growth. I am grateful for the countless hours spent reviewing drafts, providing insightful feedback, and challenging me to think critically. I am truly fortunate to have had the opportunity to work under his supervision, and I will always cherish the knowledge and skills I have gained. I am truly thankful for your support and mentorship. I am immensely grateful to Dr. Amita Joshi, Dr. Jin Jin, and Dr. Matthew Wright for their vital roles in supporting my pursuit of this degree. Special appreciation to Dr. Jin Jin and Dr. Matthew Wright for their ongoing interest in my development as members of my PhD Supervisory Committee, alongside Dr. Shyh-Dar Li. Your insightful feedback, encouragement, and unwavering commitment have been instrumental in shaping my research. I am truly grateful for the time and dedication you have invested in me, and I am honored to have had the opportunity to learn from each of you. Thank you for your mentorship and encouragement. I would also like to express my sincere gratitude to Dr. Thomas Chang for providing me with the opportunity to further my education through the UBC PhD program. I would like to express my appreciation to my esteemed colleagues, Dr. Tong Lu, Bruno Alicke, Dr. Pascal Chanu, Dr. Matts Kaagedal, and Dr. Kenta Yoshida, for their valuable insights and advice on analytical methodologies. Special thanks to my managers Dr. Rui Zhu and Dr. Nastya Kassir for their unwavering support in completing this work. Finally, my deepest gratitude to Dr. Joseph Ware and Dr. Angelica Quartino, I will forever be grateful to you for entrusting me with this opportunity. xvii Dedication To my daughter Lara and my Family 1 Chapter 1: Introduction 1.1 Background Cancer is a major public health problem worldwide and is the second leading cause of death in the United States (1). The landscape of oncology drug development is characterized by its complexity, owing to the diverse nature of cancer and its ability to adapt and resist treatments. Researchers and pharmaceutical companies continually endeavor to identify innovative compounds and therapeutic strategies that target specific molecular pathways, aiming to halt tumor growth, induce remission, or enhance the quality of life for cancer patients. Despite the promising advancements, the development of oncology drugs faces significant challenges, prominently reflected in high attrition rates during clinical trials (2-5). Attrition rates refer to the proportion of drug candidates that fail to progress through the various stages of clinical trials, culminating in a substantial number of compounds being discontinued before reaching approval for clinical use. The attrition rates in oncology drug development are influenced by numerous factors, including the intricate biology of cancer, the complexities associated with tumor heterogeneity (6), and evolving regulatory standards for demonstrating safety and efficacy (7). These factors contribute to the considerable expense and time required to bring a potential oncology drug from the initial discovery to market approval. By addressing these challenges, researchers aim to streamline the oncology drug development process, optimize trial designs, and enhance the likelihood of successful outcomes, ultimately fostering the creation of more effective therapies for cancer. 2 Despite the hurdles presented by high attrition rates, ongoing research and collaborations continue to pave the way for transformative breakthroughs for the treatment of this complex and multifaceted disease. 1.1.1 PI3K/AKT/mTOR Pathway Targeted therapy marks a paradigm shift in drug development, moving away from the traditional approach of “one size fits all” and the emphasis on nonspecific cytotoxicity (8). Instead, it focuses on identifying and disrupting specific molecular pathways involved in disease. This precision medicine approach tailors treatments to individual patients based on the unique molecular characteristics of their disease, promising more effective and less toxic therapies (9). The shift reflects a deeper understanding of the molecular basis of diseases, allowing for the development of drugs that selectively target the underlying causes at the molecular level (9). The PI3K/AKT/mTOR pathway stands as one of the critical signaling cascades within the field of cellular physiology. This intricate network of proteins regulates various cellular functions, including growth, proliferation, survival, and metabolism (10, 11). Its significance extends across multiple biological processes, with a pivotal role in both normal and pathological conditions, notably in oncology. The pathway's core components consist of phosphatidylinositol 3-kinase (PI3K), protein kinase B (AKT), and mammalian target of rapamycin (mTOR). The cascade is initiated by the activation of PI3K, which phosphorylates phosphatidylinositol lipids, leading to the production of second messengers that activate AKT (10). Activated AKT subsequently regulates mTOR, a key regulator of protein synthesis and cell growth (10). 3 In oncology, dysregulation or aberrant activation of the PI3K/AKT/mTOR pathway is frequently observed in various cancers (11). Figure 1.1 presents different components of PI3K/AKT/mTOR pathway gain or loss of function aberrations which lead to the deregulated activation of this pathway on various levels of signaling that is detected in many different types of cancers (10). Mutations or alterations in genes encoding proteins within this pathway can lead to uncontrolled cell proliferation, evasion of apoptosis, increased angiogenesis, and metabolic reprogramming which is hallmark features of cancer (11). The pathway's importance in oncology is manifold. Firstly, its dysregulation is associated with the initiation and progression of many cancers, making it an attractive target for therapeutic intervention. Additionally, its cross-talk with other signaling pathways and its role in conferring resistance to conventional cancer therapies further underscores its significance (11). 4 Figure 1.1 The PI3K/AKT/mTOR pathway overview in cancer. The PI3K/AKT/mTOR pathway represents pivotal molecular targets in anticancer therapy, characterized by prevalent sites of gain-of-function aberrations (shown in green) or loss-of-function aberrations (shown in red) (10). The deregulated activation of the PI3K/AKT/mTOR pathway on various levels of signaling is detected in many different types of cancers (10). This is an original figure adapted from Polivka J, et al. (10). 4EBP1, 4E-binding protein 1; AKT, protein kinase-B; AMPK, AMP-activated protein kinase; EIF4E, eukaryotic initiation factor 4E; ERK, extracellular-signal-regulated kinases; KRAS, Kirsten rat sarcoma viral oncogene homolog; LKB1, liver kinase B1; MAPK, mitogen-activated protein kinase; MEK, mitogen activated kinase kinase; mTOR, mammalian target of rapamycin; PDK1, phosphoinositide-dependent kinase 1; PI3K, phosphatidylinositol 3-kinase; PIP2, phosphatidylinositol 4,5-bisphosphate; PIP3, phosphatidylinositol 3,4,5-triphosphate; PTEN, phosphatase and tensin homolog; RHEB, Ras homolog enriched in brain; TSC1/2, tuberous sclerosis complex 1/2. 5 For instance, in clear cell renal cell carcinoma (ccRCC), aberrations within the PI3K/AKT/mTOR pathway, which is pivotal for cancer cell proliferation and survival, are observed in 28% of ccRCC cases (145-147). Moreover, mutations in the mammalian target of rapamycin (mTOR) gene are found in approximately 5-6% of ccRCC tumors (145-147). These genetic changes are particularly prevalent in highly vascularized regions of tumors, where nutrient and growth factor signals activate the mTOR (145-147). Notably, mutations affecting genes such as TSC1 and TSC2 are more frequently observed in patients who exhibit favorable responses to treatment compared to non-responders, suggesting a potential correlation with clinical effectiveness of mTOR inhibitors (145-147). 1.1.2 PI3K Function and Isoforms Phosphoinositidylinositol 3-kinase (PI3K) is an enzyme responsible for generating the second messenger phosphatidylinositol (3,4,5)-trisphosphate (PIP3) through phosphorylation of phosphatidylinositol 4,5-bisphosphate (PIP2), a prevalent lipid constituent of the plasma membrane (10). PIP3 recruits AKT to the plasma membrane, where it is activated through phosphorylation at threonine308 by the PDK1 kinase and at serine473 by the mTORC2 kinase complex (152). Activated AKT then phosphorylates several substrates, promoting cell growth, proliferation, survival and protein translation (10, 152). Activation of PI3K is typically triggered by stimulation of receptor tyrosine kinases (152). There are three identified classes of PI3Ks (I, II, and III), with mutations in class IA PI3K genes being prevalent in various cancer types (148). Class IA PI3Ks (comprising isoforms PI3Kα, β, and δ) are heterodimeric enzymes consisting of a regulatory subunit (p85) and one of three 6 catalytic subunits (p110α, p110β, or p110δ) (148), which are encoded by PIK3CA, PIK3CB, and PIK3CD, respectively. Class IB PI3K (PI3Kγ isoform) consists of a single catalytic subunit (p110γ) and a regulatory subunit (p101) (148), encoded by PIK3CG. These isoforms exhibit distinct tissue distributions and functional roles (148). Among the four class I catalytic isoforms, PIK3CA is one of the most commonly mutated genes in solid cancers. Particularly, the PIK3CA gene exhibits mutations in nearly 40% of human breast cancers (93, 94). Overall, members of the PI3K/AKT/mTOR pathway are often mutated and activated in cancer and play essential roles in cell survival, metastasis, metabolism, tumor environment, angiogenesis and inflammatory factor recruitment (152). 1.1.3 Approved PI3K Inhibitors Therapeutic strategies targeting the PI3K/AKT/mTOR pathway have garnered immense attention in oncology. Small molecule inhibitors and monoclonal antibodies designed to block various components of this pathway have been developed and are undergoing clinical trials. Inhibitors are subdivided into dual PI3K/mTOR inhibitors, pan-PI3K inhibitors and isoform-specific inhibitors (11). These targeted therapies aim to disrupt the aberrant signaling cascades in cancer cells, thereby inhibiting their growth and potentially enhancing the efficacy of existing cancer treatments. Despite significant resources invested in developing PI3K-targeted drugs, the number of approved inhibitors remains limited. Many trials evaluating these drugs have failed at various stages of clinical development (12) or even post-approval (13), making it necessary to improve the dose-finding and dose optimization approach to maximize both safety and efficacy when targeting this pathway. Table 1.1 provides an overview of limited approved PI3K inhibitors for 7 treating hematological malignancies (e.g. idelalisib and copanlisib) and breast cancer (alpelisib) (12,72). Table 1.1 Food and Drug Administration (FDA) approved PI3K Inhibitors (12,72). Drug PI3K Inhibitor Class Disease Indication Monotherapy or Combination Therapy Alpelisib PI3Kα PIK3CA-mutated, hormone receptor-positive (HR+), human epidermal growth factor receptor-2-negative (HER2−) advanced breast cancer Combination with fulvestrant (estrogen receptor down-regulator) Idelalisib PI3Kδ Chronic lymphocytic leukaemia (CLL), relapsed Combination with rituximab (anti-CD20 antibody) Follicular lymphoma (FL) after at least 2 prior systemic therapies Monotherapy Small lymphocytic lymphoma (SLL) after at least 2 prior systemic therapies Monotherapy Duvelisib Dual PI3K γ-δ Chronic lymphocytic leukemia (CLL) after at least two prior therapies; follicular lymphoma (FL) after at least two prior systemic therapies; small lymphocytic lymphoma (SLL) after at least 2 prior systemic therapies Monotherapy Copanlisib Pan-PI3K Relapsed follicular lymphoma after at least two prior systemic therapies Monotherapy Leniolisib PI3Kδ Activated PI3K delta syndrome (APDS) in patients 12 years of age and older Monotherapy Main factors limiting the success of PI3K inhibitors clinical trials are as follows: a) dose optimization: drug-related toxicity limits sustained target inhibition, the goal is to maximize efficacy while minimizing toxicity (12); b) overall patients’ survival: feedback upregulation of compensatory mechanisms when PI3K is blocked, the goal is to increase response rate and duration while minimizing adverse events with optimal patient selection and combination 8 therapy (14). Model-Informed Drug Development (MIDD) plays a crucial role in addressing these challenges. 1.2 Model-Informed Drug Development Model-Informed Drug Development (MIDD) is a paradigm-shifting approach revolutionizing the landscape of pharmaceutical research and drug development. This innovative methodology integrates quantitative modeling and simulation techniques with clinical trial data to optimize decision-making processes across various stages of drug development (15). MIDD harnesses computational models to predict drug behavior and efficacy, offering a more efficient, cost-effective, and scientifically robust framework for guiding key decisions in the development and regulatory approval of new therapeutic agents. By leveraging mathematical models, pharmacokinetic, pharmacodynamic, and tumor growth inhibition models, MIDD enables researchers to extrapolate insights, predict drug responses in diverse populations, optimize dosage regimens, and design trials. This approach minimizes the reliance on costly and time-consuming experimental trials by assessing the potential outcomes, thereby streamlining the drug development process and reducing the risk of late-stage failures. Moreover, MIDD facilitates improved understanding of the complex interactions between drugs, biological systems, and patients to make more informed decisions throughout the drug development lifecycle (15). The adoption of Model-Informed Drug Development represents a fundamental shift towards a more predictive and patient-centric approach in the pharmaceutical 9 industry, underlining its potential to drive innovation, optimize resources, and significantly improve the efficiency and success rates of bringing new medicines to market (15). 1.2.1 Pharmacokinetics and Pharmacodynamics Models Pharmacokinetics (PK) and Pharmacodynamics (PD) modeling and simulation are integral components of modern drug development and clinical pharmacology. These two disciplines play pivotal roles in understanding how a drug interacts within the body, from its absorption, distribution, metabolism, and excretion [PK], to its effects on the body and the relationship between drug concentration and response [PD]. PK focuses on the quantitative study of how the body affects a drug, encompassing the processes of absorption, distribution, metabolism, and excretion. Understanding PK involves analyzing how drugs move through the body, how quickly they are absorbed, how they are distributed to various tissues, how they are metabolized, and ultimately how they are eliminated (16). PK models are crucial in determining the optimal dosage regimen to achieve the desired drug concentration in the body for therapeutic effectiveness while minimizing adverse effects. On the other hand, PD deals with the relationship between drug concentration and its effects on the body. It involves studying the biochemical and physiological effects of drugs and how these effects are related to the drug concentration at the site of action. PD models help in comprehending the dose-response relationship, characterizing the onset and duration of drug action, and predicting the effects of dynamic drug concentrations on the body (17). 10 Modeling and simulation techniques are employed in PK and PD studies to predict drug behavior, optimize dosing regimens, and understand the potential outcomes of various scenarios without conducting extensive and costly experiments in humans (18). These techniques involve mathematical and computational models that integrate available data from preclinical and clinical studies, helping researchers and clinicians make informed decisions about drug development, dosage selection, and individualized therapy. Successful development of targeted drugs critically depends on pharmacodynamic biomarkers that aim to define the degree of target and pathway inhibition (19). Biomarkers are testable end-points indicative of a relevant biological aspect of cancer, discovered using molecular, cellular, and imaging methodologies focused on drug and disease mechanisms (20). PD biomarkers provide critical feedback about the interaction of novel therapies with their intended target and about the disease mechanism of action. There are two classes of biomarkers with promising predictive utilities in molecularly targeted drug development: I) phosphoproteins in biopsy samples that are markers of signaling pathways inhibition and are target sites for numerous novel oncology drugs; II) biomarkers of apoptosis in plasma that can quantify the extent of drug tumor cells killing (20, 21). There are many publications demonstrating that PK-PD modeling significantly enhances predictive power of biomarkers. For instance, activity of many drug combinations is highly dependent on the order of drugs administration; Orrell et al. used PD modeling of biomarker data to predict sequence-dependence of anti-neoplastic drug combination in xenograft tumor (22). Hansson, et al. using indirect response model described vascular endothelial growth factor 11 (VEGF), sVEGFR-2, sVEGFR-3, and soluble stem cell factor receptor data of patients with gastrointestinal stromal tumor taking sunitinib (23). Based on correlations between biomarker responses, a platform was developed to investigate relationships of model-predicted time courses of drug exposure, biomarkers, tumor SLD (sum of the longest diameters), adverse effects and survival. This platform combined with population PK-PD modeling of biomarkers used in sunitinib development to understand sunitinib mechanism of action, select relevant biomarkers for investigation, facilitate early evaluation of treatment efficacy and lastly predict long-term treatment outcomes (23, 24). Overall, the synergy between PK and PD modeling and simulation has revolutionized drug development and clinical practice by providing insights into drug behavior, enhancing therapeutic outcomes, and ensuring the safety and efficacy of pharmaceutical interventions (18). As technology advances and computational methods evolve, the integration of PK and PD modeling continues to be at the forefront of pharmaceutical research, offering innovative approaches to optimize drug therapies and improve patient care. 1.2.2 Translational Pharmacokinetics-Pharmacodynamics Xenografts Models Translational pharmacokinetic-pharmacodynamic xenograft modeling and simulation represents a pivotal bridge between preclinical research and clinical applications in the realm of drug development (25). This sophisticated approach integrates pharmacokinetics, which elucidates the drug's movement within the body, and pharmacodynamics, which assesses the drug's effects on the body, to create predictive mathematical models using preclinical data. In oncology, in vivo preclinical data used for translational models is most commonly anti-tumor data from a xenograft 12 mice studies. Xenograft mice are implanted with subcutaneous tumors of human origin. The utilization of xenograft mice provides a realistic platform to simulate and predict the anti-tumor activity of drugs in human systems. This method allows researchers to replicate human-like responses to medications, facilitating the assessment of drug efficacy, toxicity, and optimal dosing regimens prior to clinical trials (25). Leveraging mathematical and computational models, translational PK-PD xenograft modeling and simulation enables a deeper understanding of how drugs interact within the body and their impact on tumor growth or regression which ultimately enhance dose-finding and dose optimization studies. The high attrition rates in oncology drug development underscore the critical need for enhanced preclinical models to inform decision-making before initiating trials, mitigating significant financial losses and potential patient exposure to toxic effects. Prior publication examined 16 IGF-1R inhibitors across 183 clinical trials involving over 12,000 patients (5). Despite expenses exceeding $1.6 billion, none of the IGF-1R inhibitors gained approval for clinical use in oncology (5). Notably, over half of the analyzed in vivo preclinical data that were published revealed less than 50% inhibition of tumor growth by IGF-1R inhibitors (5). Capability of mechanistic quantitative models depends on strength of translational process between endpoints that connects target interaction to clinical response. Incorporating various levels of biomarkers has a significant value in terms of translational capabilities of biomarkers across different systems. Translational PK-PD xenografts models by utilizing integrated PD biomarkers could facilitate informed decision making on optimizing dosing regimen, and on whether to continue treatment, to stop treatment, or to switch to a different treatment (21). 13 Ultimately, by integrating data from preclinical studies (i.e. in-vitro and in-vivo), researchers can predict and optimize drug doses, explore various treatment scenarios, and enhance the likelihood of successful outcomes in clinical settings. Translational PK-PD xenograft modeling and simulation stands at the forefront of modern drug development, offering a robust platform to predict drug behavior, optimize therapeutic regimens, and ultimately improve patient outcomes. These models serve as invaluable tools in guiding decision-making processes for drug development, aiding in the selection of promising drug candidates and refining therapeutic strategies. 1.2.3 Clinical Exposure-Tumor Growth Inhibition Models In clinical oncology research and cancer treatment, the understanding of drug efficacy and its impact on tumor growth inhibition is of paramount importance to optimize patients’ outcomes. Clinical exposure-tumor growth inhibition modeling and simulation have emerged as indispensable tools in comprehending and predicting the response of anticancer drugs in patient populations. The longitudinal exposure-TGI model considers tumor growth dynamics and the impact of antitumor drugs (27-29), it defines tumor size as the sum of the longest diameters of target lesions based on RECIST criteria (30) in relation to both time and drug exposure (27). By integrating pharmacokinetics and pharmacodynamics data, these models aim to elucidate the complex relationship between drug exposure and tumor response. Different mathematical models have been developed and utilized clinically to describe tumor growth inhibition in patients. Here are examples of mathematical models used in oncology to describe tumor growth inhibition (31): The Gompertz model is one of the earliest and most 14 widely used model in tumor growth; it describes exponential growth that slows down over time, representing the natural growth curve of many tumors. The Exponential Growth Model, which assumes that the tumor grows at a constant rate without limitation. The Claret model which is a mathematical model that integrates pharmacokinetic and pharmacodynamic components; it incorporates drug effects and tumor growth inhibition by considering drug concentrations and their impact on tumor growth dynamics. Mechanism-based models focus on underlying biological mechanisms driving tumor growth and drug action; they use differential equations to represent complex interactions within the tumor microenvironment, including cell proliferation, death, and drug effects on specific targets. Each of these models has its advantages and limitations, and researchers select models based on their specific research objectives, available data, and the characteristics of the tumor being studied. In essence, clinical exposure-tumor growth inhibition modeling and simulation represent a powerful framework that integrates diverse data sources and computational methodologies to enhance our understanding of drug efficacy, optimize treatment strategies, and ultimately improve patient outcomes. These models play a pivotal role in drug development, they facilitate the translation of data into clinically relevant insights, guiding decision-making processes in the development and evaluation of novel anticancer therapies. 1.3 Research Aim and Specific Objectives Integrated modeling and simulation in pharmaceutical research and development not only enhances decision-making processes but also contributes to reducing the cost and time required for drug discovery and development. Additionally, it facilitates minimizing the risks associated 15 with clinical trials by providing insights into potential outcomes before experimental testing on humans. The overall aim of this thesis was to acquire a better understanding of the PI3K/AKT/mTOR pathway response to enhance future drug development by developing mechanistic PK-PD models to integrate and characterize dynamic relationship between exposure of targeted drugs, modulation of PD biomarkers/tumor triggered by inhibition of PI3K/AKT/mTOR pathway and estimation of longitudinal response including possible emergence of tumor resistance. These specific objectives are addressed in the following chapters listed below: Chapter 2: Retrospective Assessment of the Translational Pharmacokinetic-Pharmacodynamic Modeling Performance: A Case Study with Apitolisib, A Dual PI3K/mTOR inhibitor Chapter 3: Quantitative Assessment of Drug Efficacy and Emergence of Resistance in Patients with Metastatic Renal Cell Carcinoma Using a Longitudinal Exposure-Tumor Growth Inhibition Model: Apitolisib (dual PI3K/mTORC1/2 inhibitor) versus Everolimus (mTORC1 inhibitor) Chapter 4: Quantitative Characterization of the Effects of Fulvestrant Alone or in Combination with Taselisib (PI3Kinase Inhibitor) on Longitudinal Tumor Growth in Patients with Estrogen Receptor-positive, HER2-negative, PIK3CA-mutant, Advanced or Metastatic Breast Cancer 16 Chapter 2: Retrospective Assessment of the Translational Pharmacokinetic-Pharmacodynamic Modeling Performance: A Case Study with Apitolisib, A Dual PI3K/mTOR inhibitor Summary Despite significant progress in biomedical research, which led to a greater understanding of the molecular mechanisms of carcinogenesis and cancer growth, the rate of success in oncology drug development remains inferior to that of other therapeutic fields (25). Mechanistic models provide comprehensive understanding of drugs therapeutic effects that is crucial for designing effective clinical trials. This study was performed to acquire a better understanding of the PI3K-AKT-mTOR pathway modulation, and preclinical to clinical translational bridging for a specific compound, apitolisib (PI3K/mTOR inhibitor), by developing integrated mechanistic models. Integrated pharmacokinetics-pharmacodynamic-Efficacy models were developed for xenografts bearing human renal cell adenocarcinoma and patients with solid tumors (Phase 1 studies) to characterize relationships between exposure of apitolisib, modulation of pAkt biomarker triggered by inhibition of the PI3K-AKT-mTOR pathway and tumor response. Both clinical and preclinical integrated models show a steep sigmoid curve linking pAkt inhibition to tumor growth inhibition and quantified that minimum 35% to 45% pAkt modulation is needed for tumor shrinkage in patients based on platelet-rich plasma surrogate matrix and in xenografts based on tumor tissue matrix. Based on this relationship between targeted pAkt modulation and tumor shrinkage rate, it appeared that a constant pAkt inhibition of 61% and 65% would be necessary to achieve tumor stasis in xenografts and patients, respectably. These results help to evaluate the translatability of the preclinical analysis to the clinical target and provide 17 information that will enhance the value of future preclinical translational dose-finding and dose optimization studies to accelerate clinical drug development. 2.1 Introduction The PI3K-AKT-mTOR signaling pathway plays a critical role in cell growth, survival, and metabolism and is abnormally expressed in many types of cancers (10). Despite significant resources invested in developing PI3K-targeted drugs, the number of approved inhibitors remains limited. Many trials evaluating these drugs have failed at various stages of clinical development (12) or even post-approval (13), making it necessary to improve the dose-finding and dose optimization approach to maximize both safety and efficacy when targeting this pathway. Dose-finding trials for cytotoxic chemotherapy drugs used to treat cancer historically been designed to determine the maximum tolerated dose (MTD). In contrast, most modern oncology drugs are targeted therapies, such as targeted kinase inhibitors, which are designed to modulate specific targets with the resulting effect of suppressing molecular pathway(s) driving an oncologic disease (32). Hence, these targeted therapies are considered “safer” compared to commonly used cytotoxic drugs and can often achieve maximal therapeutic effects at doses well below the MTD (32). As a result, FDA created Project OPTIMUS (Optimizing Patient Treatment through Integrative Multi-omics USe) which is a research initiative aimed at developing new methods to use multi-omics data (such as genomics, proteomics, and metabolomics) to improve the selection and dosing of cancer therapies (7). The goal of the FDA project is to incorporate new biomarkers that can be used to predict how a patient will respond to a particular treatment, 18 and to move forward with a dose-finding and dose optimization paradigm across oncology that emphasizes selection of a dose or doses that maximizes not only the efficacy of a drug but the safety and tolerability as well (7). Quantitative integrated analyses that bridge preclinical research with clinical trials play a crucial role in regulatory decision-making, offering supportive evidence of efficacy when optimizing therapeutic outcomes. Integrated PK-PD-Efficacy models are mathematical models that integrate information from pharmacokinetics (PK), pharmacodynamic (PD) biomarker, and efficacy to predict the relationship between drug concentration, target modulation, and the therapeutic response (33, 34). The PK portion of these models describe how the body absorbs, distributes, and eliminates a drug to provide information on how the drug concentration changes over time in the body. The PD portion of these models provide information on how the drug concentration alter biological target modulation, such as the inhibition of a target protein. The efficacy portion of these models describe the relationship between the biological target modulation and the therapeutic outcome such as how the drug's effects on the target protein translate into treatment outcomes such as tumor shrinkage. Integrated PK-PD-Efficacy models are important tools in translational drug development to bridge preclinical to clinical studies, as they allow researchers to predict the efficacious dose, and to optimize dosing regimens. Despite the increased use of translational PK-PD modeling, there is little to no reported cases of a systematic examination of performance of translational PK-PD modeling using preclinical data on predicting patient response. In this study, we retrospectively employ an integrated PK-PD-Efficacy model approach to explore the exposure-response relationship of apitolisib, in both preclinical and initial clinical phases in 19 order to investigate relationships between drug exposure, biomarker modulation, and efficacy for apitolisib in xenograft mice and cancer patients in Phase 1 trials. Phosphorylated Akt (pAkt) is a key PD biomarker in the PI3K-AKT-mTOR pathway, which is frequently dysregulated and hyperactivated in cancer cells (11). Akt phosphorylates and activates downstream targets involved in cell survival, proliferation, and protein synthesis. For instance, it can activate the mammalian target of rapamycin (mTOR), a critical regulator of protein synthesis and cell growth (10). The detection and measurement of pAkt levels serve as a biomarker to assess the activation status of this pathway (19, 35). Apitolisib is a potent, selective dual inhibitor of PI3K and mTOR. Apitolisib has broad activity in xenograft efficacy tumor models (36), which is also demonstrated by collected pAkt protein. Clinical studies, reported previously by Dolly et al., have further established the PD evidence of apitolisib target modulation. Significant reductions in PI3K inhibition of ≥90% was observed in platelet-rich plasma PD markers including pAkt at doses ≥16 mg in patients (37). Dose optimization of targeted drugs can be informed by translational pharmacodynamic biomarkers that aim to define the degree of target and pathway modulation required for efficacy (19). The suitability of these PD biomarkers is typically assessed and characterized at preclinical stages of drug development providing an understanding of the relationship between drug concentrations and biomarker response as well as the biological relationship between modulation of the biomarker and downstream therapeutic effect. Often, in oncology, preclinical information regarding PD biomarker modulation are obtained from tumor tissue (site of action). Tumor tissue biomarkers provide a direct look at the extent and duration of target modulation. In contrast, in 20 the clinic, collection of plasma biomarkers is far more common and serves as a surrogate of target modulation in tumor. In this study, we aim to a) develop an integrated PK-PD-Efficacy model in xenograft mice to characterize both apitolisib’s ability to modulate pAkt in tumor tissue and to inhibit tumor growth; b) utilizing same modeling methodology to characterize apitolisib PK, surrogate PD (pAkt modulation/response) in plasma, and efficacy (tumor growth inhibition) in cancer patients in Phase 1 clinical trials; c) evaluate the translatability of the preclinical analysis in xenografts to the observations in cancer patients. These objectives provide information that will enhance the value of future clinical and preclinical translational dose-finding and dose optimization studies. 2.2 Methods 2.2.1 Xenograft Dataset Mean plasma concentration time profiles of apitolisib in nude mice after oral administration of 1, 5, and 10 mg/kg dose, comprised of plasma concentrations from samples collected at pre-dose and at 0.083, 0.25, 0.5, 1, 3, 6, 9, 24 hour post-dose (n=27 mice per dose group), was previously published (38), and was used to provide pharmacokinetics (PK) for xenograft mice in this analysis. The efficacy evaluation of apitolisib was conducted in female Beige Nude XID (bg.nu.xid Harlan) mice bearing subcutaneous 786-O human renal cell adenocarcinoma (RCC) xenografts. Mice were housed and maintained according to the animal use guidelines of Genentech, Inc, conforming to California State legal and ethical practices. Mice were inoculated subcutaneously in the right lateral thorax with tumor fragments from donor mice. The right flank used to gain 21 access to the subcutaneous space and deposit the tumor fragment. As tumors reach a volume in the range of 100-300 mm3, mice with similarly sized tumors separated into groups. The mean tumor volume (TV) across all groups was 181 mm3 at the initiation of dosing. Apitolisib was administered once a day (QD) orally (PO) in 200 µl MCT (0.5% methylcellulose, 0.2% Tween-80) for 17 days. The apitolisib doses administered were vehicle, 0.008, 0.026, 0.085, 0.256, 1, 2.5, 5, 7, 8.5, 10, and 11 mg/kg (n=6 per group). Tumors volume measurements were collected per mice at pre-dose and at 72, 96, 168, 240, 264, 336, and 408 hour from each treatment groups. Mice were euthanized if body weight loss was greater than 20% from their initial body weight or if the tumors exceeded 2000 mm3. Tumor volumes (TV) were determined using digital calipers (Fred V. Fowler Company, Inc.) using Equation 1. TV (mm3) = length ×width2 × 0.5 Equation 1 The apitolisib preclinical PK/PD study where the pAkt biomarker was collected was also conducted in female Beige Nude XID (bg.nu.xid Harlan) mice bearing subcutaneous 786-O human renal cell adenocarcinoma xenografts. To evaluate pAkt modulation in 786-O xenografts, tumor cells were implanted as described previously for the efficacy studies. Mice were divided into four dose groups and received a single oral dose of vehicle (MCT), 0.3, 3, or 10 mg/kg apitolisib in 200 µL of MCT. Tumors were collected at 0.5, 2, 6, 12, 18, and 24 hour post-dose from treatment groups (n = 3 per time-point), and at 2, 6, 12 hour from the vehicle group (n = 6 per time-point). Meso Scale Discovery (MSD) assay was used to quantify pAkt (Serine 473) levels in tumor tissues. %pAkt defined as %pAkt relative to control (i.e., baseline) was calculated using Equation 2. 22 %𝑝𝐴𝑘𝑡 =𝑝𝐴𝑘𝑡𝑝𝐴𝑘𝑡0× 100% Equation 2 where pAkt is the level of pAkt measured at a specific timepoint and pAkt0 is the pAkt at baseline where there is no drug present. By definition, the %pAkt at control baseline is 100% according to Equation 2. 2.2.2 Clinical Trials Dataset Two Phase 1 dose escalation studies using 3+3 design were conducted in patients with advanced solid tumors or non-Hodgkin’s lymphoma (37). Apitolisib was administered orally on Day 1, followed by 1 week of washout. It was then dosed daily (QD) for 28-days (1 cycle) or QD on a 3-weeks-on/1-week-off schedule, or once weekly (QW) for 28-days. Apitolisib doses that were administered are as follows: 30, 40, 50 mg QD, or 2, 4, 8, 16, 32, 40, 50, 70 mg QD on a 3-weeks-on/1-week-off or 6, 12, 25, 50, 100, 150, 200 mg QW. Trials were approved by the institutional review board or independent ethics committee. All patients provided written informed consent. PK sampling was done in the first cycle on day 1 (pre-dose, 0.5, 1, 2, 3, 4, 8 hours post-dose), on days 2 (24 hour post-dose) and 3 (48 hour post-dose), on day 8 (pre-dose and 2 hours post-dose), on day 15 (pre-dose dose and 0.5, 1, 2, 3, 4, and 8 hours post-dose), and on days 22 and 29 (pre-dose and 2 hours post-dose); and on the first day (pre-dose) of each cycle thereafter. Blood samples for surrogate PD marker (pAkt) to evaluate platelet-rich plasma (PRP) were collected pre-dose, 1, 3, 8, and 24 hours post-dose on day 1. Apitolisib plasma concentrations was quantified using a LC-MS/MS assay with a lower limit of quantification (LLOQ) of 0.5 ng/mL (Tandem Labs, Inc., Salt Lake City, UT). Changes in pAkt in PRP in subset of patients (n=37) 23 were measured using the Meso Scale Discovery (MSD) assay, and the percent change in pAkt relative to baseline was calculated (Equation 2). Tumor lesions were measured using computed tomography or magnetic resonance imaging at baseline and at regular intervals afterward (after the first and second cycle and every two cycles subsequently). Longitudinal tumor size data, defined as the sum of the longest diameters of target lesions at each visit according to RECIST 1.0 (39) or in the case of malignant pleural mesothelioma patients modified RECIST (40), were used for the estimation of tumor growth inhibition. Patients with at least baseline and one post-baseline tumor size measurements were defined as evaluable (n=117), and data from patients who only had baseline tumor assessments were excluded from the analysis. 2.2.3 Pharmacokinetic Models 2.2.3.1 Mouse Pharmacokinetic Model The pharmacokinetics of apitolisib appeared to be linear over the range of doses tested. A one-compartment model with first-order oral absorption was simultaneously fit to the mean plasma concentration-time data from mice following single PO administrations of 1, 5 and 10 mg/kg. The parameter estimates of the absorption rate constant (ka), the apparent oral clearance (CL/F), and the apparent volume of distribution (V/F) were used to simulate the apitolisib plasma concentrations for xenograft biomarker and tumor growth inhibition analysis. 24 2.2.3.2 Patient Population Pharmacokinetic Model A nonlinear mixed effects models (two-compartment model with oral absorption) was used to fit the concentration–time data of apitolisib from patients given oral doses of apitolisib. Apparent clearance (CL/F) after oral dosing, apparent volume of distribution parameters for the central (V1/F) and peripheral (V2/F) compartments, apparent and inter-compartmental clearance (CLd/F), and absorption rate (ka) were estimated. Inter-individual variability (IIV) in PK parameters were modeled as exponential random-effect models in order to constrain the individual parameter values positively, which were thus assumed to follow a log-normal distribution. The residual error model was a proportional error model. 2.2.4 Pharmacokinetic-Pharmacodynamic (PK-PD) Models Describing pAkt Modulation In xenograft analysis the relationship between pAkt in tumor tissue and apitolisib plasma concentrations was evaluated using an indirect response model which describes the inhibition of pAkt formation rate by apitolisib (Equation 3). The selection of this model was based on our understanding of apitolisib’s biological mechanism of action. Also, this is a common model structure used to characterize biomarkers in this particular pathway (41). 𝑑(%𝑝𝐴𝑘𝑡)𝑑𝑡= 𝑘𝑖𝑛 (1 −𝐼𝑚𝑎𝑥 × 𝐶𝑝𝛾1𝐼𝐶50𝛾1 + 𝐶𝑝𝛾1 ) − 𝑘𝑜𝑢𝑡 × %𝑝𝐴𝑘𝑡 Equation 3 where γ1 = sigmoidicity factor, Imax = maximum inhibition of %pAkt, kin = rate of biomarker production, kout = first-order rate constant describing biomarker loss, IC50 = apitolisib concentration producing 50% of Imax , t = time, and Cp = apitolisib plasma concentration. At baseline, %pAkt is equal to 100% in the absence of apitolisib. Plasma concentrations of apitolisib 25 were simulated using the mouse PK model described in previous section. To construct the preclinical indirect response model, a naïve average pooled PD analysis was conducted. First, %pAkt inhibition relative to baseline was estimated for each individual tumor tissue sample collected from xenograft mice (n = 3 mice per time-point). Next, values were averaged per time-point for each dose level. In earlier iterations of preclinical indirect response model, kin and kout, were both estimated allowing pAkt rebound to be captured by the model fit. However, since apitolisib drug was administered daily in the xenograft efficacy study (which data was used to construct preclinical Integrated PK-PD-Efficacy Model), in the later versions of model the estimation of kout was fixed to kout=kin/%pAkt (0), where %pAkt (0) is the baseline %pAkt at time zero = 100%. Based on observed pAkt data, maximum inhibition of %pAkt (Imax) was fixed to 1 to allow for 100% inhibition of the biomarker. Similarly, the sigmoidicity parameter (γ1) was fixed to 1 as estimates of earlier iterations of the model resulted in estimates that were approximately 1 and fixing the parameter to 1 improved model stability. The residual error model was a proportional error model. The clinical indirect response model utilized the same model structure as the preclinical model described above except that a population PK-PD analysis utilizing individual data was performed with the clinical data. Patients’ individual PK parameters estimated by population PK model was used to predict apitolisib plasma concentrations and changes in pAkt in PRP (platelet-rich plasma) expressed as a % of control (i.e., baseline) was simultaneously assessed for different dose levels using Equation 3. Inter-individual variability (IIV) was modeled as exponential random-effect models in order to constrain the individual parameter values positively, which were thus assumed to follow a log-normal distribution. Based on observed data, maximum inhibition of %pAkt (Imax) was fixed to 1 to allow for 100% inhibition of the biomarker. 26 Estimated sigmoidicity parameter (γ1) in earlier iterations of the model was ~0.9; therefore; it was fix to 1 in the final model to improve model stability. The residual error model was a proportional error model. 2.2.5 Integrated PK-PD-Efficacy Models Mechanistic models were developed to integrate and characterize the relationship between plasma concentrations of apitolisib, modulation of pAkt biomarkers triggered by inhibition of PI3K-AKT-mTOR pathway and tumor response in xenografts and in patients. These integrated models (Figure 2.1) assume that the decrease in pAkt (i.e., inhibition of phosphorylation of Akt) is representative of the inhibition of the PI3K-AKT-mTOR pathway which is assumed to be the primary driver of tumor growth. The changes in %pAkt were predicted for each dose using the PK-PD model (Equation 3) parameter estimates. Next, the %pAkt were related to the tumor metrics using Equations 4 and 5. 𝑑(𝑇𝑢𝑚𝑜𝑟)𝑑𝑡= 𝐾𝑔 × 𝑇𝑢𝑚𝑜𝑟 − 𝐾𝑠 × 𝑇𝑢𝑚𝑜𝑟 Equation 4 where Tumor= tumor volume for xenografts or tumor size for patients, Kg = net tumor growth rate constant, and Ks= tumor shrinkage rate constant. Tumor at time 0 was set as the baseline tumor observations prior to the application of apitolisib. 𝐾𝑠 = 𝐾𝑚𝑎𝑥 × 𝐼γ2𝐾𝐼50𝛾2 + 𝐼γ2 𝑤ℎ𝑒𝑟𝑒 𝐼 = 100 − %𝑝𝐴𝑘𝑡 Equation 5 where Ks= tumor shrinkage rate constant, I = % inhibition of Akt phosphorylation, Kmax = maximum value of Ks, KI50 = I where Ks is 50% of Kmax and γ2 = sigmoidicity factor of the sigmoid Kmax equation. 27 In the xenograft mice integrated PK-PD-Efficacy model, apitolisib plasma concentrations, %pAkt and the corresponding I in tumor tissue were predicted based on the parameters determined by the mouse PK and mouse PK-PD models (Equation 3). Tumor volumes from all dose groups (ranging from 0.008 to 11 mg/kg) were fitted simultaneously to obtain parameter estimates describing the PD-efficacy relationship from the integrated PK-PD-Efficacy model. In the integrated PK-PD-Efficacy model used to describe clinical data of patients with cancer, individual patients PK parameters and individual patients dosing records was used to predict the apitolisib plasma concentrations; therefore, any dosing reduction or dosing interruption for specific patients was captured. For pAkt, only a subset of patients had pAkt data collected. In those patients with pAkt data, individual PK parameters and individual IC50 estimates along with the PK-PD model described by Equation 3 were used to predict %pAkt and the corresponding I in the integrated model. For patients where pAkt data was not collected, individual PK parameters and a typical estimated IC50 was used for this purpose. Tumor size data from all patient dose groups (ranging from 2 to 200 mg) were fitted simultaneously in order to estimate parameters describing the PD-efficacy relationship from the integrated PK-PD-Efficacy model developed using patient data. In both integrated models, inter-individual variability (IIV) of parameters were modeled as exponential random-effect models in order to constrain the individual parameter values positively, which were thus assumed to follow a log-normal distribution. In the clinical integrated model, IIV values for KI50, and γ2 (sigmoidicity factor) were fixed to a small value 28 (0.0225) to enhance the numerical estimation capability of the NONMEM model. The residual error model was a proportional error model. Figure 2.1 Illustration of preclinical and clinical integrated PK-PD-Efficacy models structures. The application of integrated-PK-PD-Efficacy models allows for a quantitative understanding of the biological relation between target modulation and disease efficacy that is not possible with a PK-PD model alone. ka = first-order absorption rate constant, CL = apparent oral clearance, CLd = apparent inter-compartmental clearance, F = bioavailability, V1 = apparent central volume of distribution, V2 = apparent peripheral volume of distribution, Cp = plasma compartment, Ct = tissue compartment, Imax = maximum inhibition of %pAkt, kin = rate of biomarker production, kout = first-order rate constant describing biomarker loss, IC50 = apitolisib concentration producing 50% of Imax, Kg= net tumor growth rate constant, Kmax= maximum value of Ks (tumor shrinkage rate constant), KI50= I where Ks is 50% of Kmax, I = % inhibition of Akt phosphorylation, γ2= sigmoidicity factor 29 2.2.6 Models Evaluation Model evaluation was based on the inspection of graphical diagnostics, such as goodness-of-fit plots, changes in the objective function value (OFV) provided by NONMEM, relative standard errors (RSE) and plausibility of the parameters estimate. If more than one inter-individual variability (IIV) term was estimated, correlations between IIV terms were evaluated. 2.2.7 Models Assumptions and Limitations One of the limitations of translational modeling is the assumption of similarities in tumor response between xenograft mice implanted with cancer cell lines of human origin and patients. Subcutaneous tumors implanted in xenograft mice may not reflect the heterogeneity of tumors observed in patients with metastatic tumors. As this analysis is based on preclinical study that was conducted in xenografts with renal cancer carcinoma (786-O cell lines), relationships between apitolisib concentrations and pAkt inhibition, and pAkt modulation and tumor growth inhibition may differ when compared to patients with different cancer types enrolled in the Phase 1 studies. Another assumption of the translational modeling is the presumption of similar drug distribution in the subcutaneous tumor environment of xenograft models and human tumors (42, 43). In this analysis, we assumed that drug distribution is similar, despite reported differences in tumor vasculature and transport in xenograft versus human tumors (44). For molecular targeted cancer therapies, mechanism-based biomarkers (i.e., indicative of a relevant biological aspect of cancer) can serve as true intermediate or surrogate end points during 30 the drug development process (20). Biomarkers indicative of disease mechanisms became targets for therapy or can served as tools for design of preclinical studies and as predictive factors for treatment response in the clinic (20) such as pAkt. In this analysis, we assumed that modulation of disease mechanism-based biomarker (pAkt) triggered by inhibition of the PI3K-AKT-mTOR pathway and is reflective of inhibition of the entire pathway which is directly responsible for tumor response/tumor growth inhibition. 2.2.8 Software Models were developed using NONMEM version 7.4 (ICON Development Solutions, Ellicott City, MD, USA), with the first-order conditional estimation (FOCE) and the INTERACTION option (45). Data management and further processing of NONMEM output were performed using R version 4.2.3 (46). 2.3 Results 2.3.1 Pharmacokinetic Models 2.3.1.1 Mouse Pharmacokinetic Model The final PK model that well characterized the mouse concentration-time data was a linear one-compartment model with first-order absorption and oral clearance (data not shown). The estimated parameters (RSE%) were 0.387 (9.5%) L/hr/kg for apparent oral clearance (CL/F), 1.13 (17.3%) L/kg for apparent volume of distribution after oral dosing (V/F), and 1.1 (36.4%) hr-1 for absorption rate constant (ka). 31 2.3.1.2 Patient Population Pharmacokinetic Model A linear two-compartment PK model with first-order absorption and elimination best described the apitolisib plasma concentration–time data in patients (n= 146; 1835 PK observations). Population typical values (RSE%) were 21.3 (4.28%) L/hr for apparent oral clearance (CL/F), 210.6 (3.51%) L for apparent volume of the central compartment (V1/F), 639.1 (15.1%) L for apparent volume of distribution of the peripheral compartment (V2/F), 5.93 (8.53%) L/hr for apparent inter-compartmental clearance (CLd/F), and 3.35 (16.8%) hr-1 for absorption rate constant (ka). Also, based on observed data a delay was detected in apitolisib absorption which was captured in the PK model by lagged time estimate of 0.465 (0.43%) hr. Estimates of IIV (RSE%) [shrinkage%] were 0.17 (17.6%) [13.7%] for CL/F, 0.0639 (23.2%) [23.2%] for V1/F, 0.208 (33.5%) [44.2%] for CLd/F, 0.881 (44.8%) [40.5%] for V2/F and 2.09 (16.4%) [13.2%] for ka. The goodness-of-fit plots from model fitting showed that the predictions from the final model were generally consistent with the observed data (Figure 2.2 and Figure 2.3). 32 Figure 2.2 Observed concentrations versus individual and population predictions from the population pharmacokinetic model for apitolisib. Observed apitolisib concentrations versus model predicted A) individual concentration and B) population concentration, on natural logarithmic scales. Individual data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Line of identity (black) was included as reference for observed vs model predicted. AB33 A B Figure 2.3 Conditional weighted residuals versus population predictions and time from the population pharmacokinetic model for apitolisib. Conditional weighted residuals (CWRES) versus A) population predicted apitolisib concentration, and B) time since first dose. Individual data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Black dashed line included as reference for goodness of fit. For enhance visualizations, 2 time-points at day 112 and day 196 were removed from the CWRES vs time plot. 34 Assuming reference body weight of 70 kg, body weight normalized PK parameters were 0.304 L/hr/kg for apparent oral clearance (CL/F), 3.01 L/kg for apparent volume of the central compartment (V1/F), 9.13 L/kg for apparent volume of distribution of the peripheral compartment (V2/F), and 0.085 L/hr/kg for apparent inter-compartmental clearance (CLd/F). As expected, a faster elimination rate constant (CL/V) is observed in xenografts (0.3 hr-1) compared to patients (0.1 hr-1). 2.3.2 PK-PD Models Describing pAkt Modulation Observed mean %pAkt versus time data for xenograft mice and for patients, and PK-PD models fitted lines (average individual predictions for patients) are presented in Figure 2.4. The levels of pAkt were measured in tumors after a single oral administration of apitolisib at 0.3, 3, and 10 mg/kg in 786-O tumor-bearing mice (Figure 2.4-A). A dose dependent decrease in pAkt was observed at the three doses. The suppression of the pAkt was pronounced at 30 min post-dose and sustained for 6-12 hour at the 3 and 10 mg/kg doses, respectively. In contrast, the pAkt reduction was very weak and recovered 1-2 hours post-dose at the 0.3 mg/kg dose level. In general, higher apitolisib doses resulted in greater and more sustained suppression of the pAkt in tumor tissue of xenografts. In patients, pAkt levels were measured in platelet rich plasma over a large range of doses (2 to 70 mg) (Figure 2.4-B). A dose-dependent decrease in pAkt in plasma was observed with increasing doses of apitolisib. Peak suppression of the platelet pAkt was 90% observed at doses ≥12 mg. 35 Figure 2.4 Mean observed and predicted %pAkt relative to baseline vs time. A) Tumor tissue mean %pAkt relative to baseline from 786-O xenografts following oral administration of 0.3, 3, and 10 mg/kg apitolisib. B) Surrogate plasma mean %pAkt relative to baseline from patients with advanced solid tumors (Phase 1 studies) following oral administration of 2 to 70 mg apitolisib, stratified by dose. Observed mean %pAkt relative to baseline data presented with dots and model predicted presented with solid line. 36 In general, the PK-PD models were able to capture the %pAkt inhibition (Figure 2.4). Estimates of PD parameters from fitting the %pAkt data to the PK-PD models described by Equation 3 are shown in Table 2.1 for xenografts, and Table 2.2 for patients. Model estimates of kin and kout were comparable when comparing xenograft mice to patients suggestive of biomarker production and elimination are comparable between human and xenograft mice with human origin tumor. In contrast, model estimated IC50 differed being 43-fold higher when the estimate was obtained from %pAkt measurements from xenograft tumor tissue (403 µg/L) compared to %pAkt measurement from surrogate plasma for a typical patient (9.32 µg/L). The unbound fraction of apitolisib was similar between mice [fraction unbound=29.4%] and human [fraction unbound=38.8%] suggesting similar free concentrations of apitolisib in plasma and tumor upon equilibration which does not appear to provide an explanation to the differences in IC50. Overall, the PK-PD models described by Equation 3 could adequately describe the relationship between apitolisib plasma concentrations and pAkt reductions in tumor from xenograft mice and platelet rich plasma in patients. Table 2.1 Parameter estimates following fitting of PK-PD model describing pAkt modulation for xenograft mice (786-O) Parameter Unit Estimate RSE% IC50 μg/L 403 14.7 kin %/hr 88698 0.8 kout* 1/hr 886.98 - Imax - 1 (fix) - γ1 - 1 (fix) - Proportional Error - 0.353 5.6 γ1 = sigmoidicity factor, Imax = maximum inhibition of %pAkt, kin = rate of biomarker production, kout = first-order rate constant describing biomarker loss, IC50 = apitolisib concentration producing 50% of Imax , t = time, and Cp = apitolisib plasma concentration *kout=kin/%pAkt(0), where %pAkt(0) is the baseline %pAkt at time zero = 100% 37 Table 2.2 Parameter estimates following fitting of PK-PD Model describing pAkt modulation for patients with advanced solid tumors (Phase 1 studies) Parameter Unit Estimate RSE% Shrinkage% IC50 μg/L 9.32 12.7 - kin %/hr 88699 3.8 - kout* 1/hr 886.99 - - Imax - 1 (fix) - - γ1** - 1 (fix) - - Proportional Error - 0.672 9.5 - IIV IC50 variance 0.296 44.3 15.5 γ1 = sigmoidicity factor, Imax = maximum inhibition of %pAkt, kin = rate of biomarker production, kout = first-order rate constant describing biomarker loss, IC50 = apitolisib concentration producing 50% of Imax, t = time, and Cp = apitolisib plasma concentration. * kout=kin/ %pAkt(0), where %pAkt(0) is the baseline %pAkt at time zero = 100% **Sigmoidicity parameter estimate was 0.868-0.937 therefore it was fix to 1 in the final model 2.3.3 Integrated PK-PD-Efficacy Models The relationship between inhibition of the PI3K pathway and efficacy was investigated using a PK-PD-Efficacy model that describes the relations between apitolisib plasma concentrations, pAkt modulation, and tumor growth inhibition. The models’ structures used to fit the preclinical and clinical data are presented in Figure 2.1. Model codes are provided in Appendix A. Two integrated models were independently developed for xenografts (n=64; 381 tumor volume observations) and patients (n=117; 417 tumor size observations). Individual baseline tumor data were used for model development (Equation 4). Median baseline tumor observations were 173.5 mm3 and 130.0 mm for xenograft mice and Phase 1 patient population, respectively. The described integrated PK-PD-Efficacy models were used to fit tumor data collected from individual xenograft mice and patients. The goodness-of-fit (GOF) plots support the use of both integrated models to fit preclinical and clinical data. Models GOF plots indicated a good model fit as shown in plots of individual observed versus predicted tumor data presented in Figure 2.5 38 and Figure 2.6. Additionally, GOF plots of conditional weighted residuals versus time and population predicted tumor data also indicated a good model fit as shown in Figure 2.7 and Figure 2.8 for preclinical and clinical model, respectably. Visual predictive check of the final models shows that the models relatively well captured the central tendency, extreme values as well as the variability in the observed preclinical and clinical tumor data (Figure 2.9 and Figure 2.10). 39 Figure 2.5 Observed versus preclinical PK-PD-Efficacy model predicted tumor volumes. Xenografts observed versus model predicted A) individual tumor volumes and B) population tumor volumes. Individual data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Line of identity (black) was included as reference for observed vs model predicted. AB40 Figure 2.6 Observed versus clinical PK-PD-Efficacy model predicted tumor size data. Patients observed versus model predicted A) individual tumor size and B) population tumor size. Individual data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Line of identity (black) was included as reference for observed vs model predicted. AB41 A B Figure 2.7 Conditional weighted residuals versus population predictions and time from the preclinical PK-PD-Efficacy model. Conditional weighted residuals versus A) population predicted tumor volumes, and B) time since first dose. Individual xenograft data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Black dashed line included as reference for goodness of fit. 42 A B Figure 2.8 Conditional weighted residuals versus population predictions and time from the clinical PK-PD-Efficacy model. Conditional weighted residuals versus A) population predicted tumor size, and B) time since first dose. Individual data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Black dashed line included as reference for goodness of fit. 43 Figure 2.9 Prediction corrected visual predictive check (pcVPC) of tumor volume data based on the final preclinical PK-PD-Efficacy model. Tumor volume data are displayed versus time since first dose, on linear scale. The solid and dashed black lines represent the median, 5th and 95th percentiles of the observations; the shaded gray and blue areas represent the 95% confidence interval of the median, 5th and 95th percentiles predicted by the model. The observed data are indicated by circles. 44 Figure 2.10 Prediction corrected visual predictive check (pcVPC) of tumor size data based on the final clinical PK-PD-Efficacy model. Tumor size data are displayed versus time since first dose, on linear scale. The solid and dashed black lines represent the median, 10th and 90th percentiles of the observations; the shaded gray and blue areas represent the 95% confidence interval of the median, 10th and 90th percentiles predicted by the model. The observed data are indicated by circles. 45 The estimated PD parameters are presented in Table 2.3 (xenografts) and Table 2.4 (patients). The net growth rate constant was 98.7 fold higher in xenograft mice subcutaneous tumors compared to tumors in patients, which is consistent with prior publication of growth rate detection comparing diameter and volume in measuring tumor size (47). Specific to the relationship between target modulation and anti-tumor efficacy, Kmax was more than 200-fold lower in patients when compared to xenograft mice. In contrast, KI50 and sigmoidicity factors were similar in xenografts and patients suggesting that the shape but not magnitude of the relationship between %pAkt and Ks was similar (Figure 2.11-A). When Ks is normalized as a % of Kmax, this similarity in the relationship between target modulation and anti-tumor effect can be more clearly seen (Figure 2.11-B). In both xenograft mice and humans, Kmax>Kg suggesting that apitolisib given at high enough concentrations can cause tumor regressions. Based on the relationship between %pAkt inhibition and the tumor shrinkage rate constant (Ks) (Figure 2.11-A), a similar constant pAkt inhibition of 61% and 65% would be necessary to achieve tumor stasis (where Ks=Kg) in 786-O xenografts and patients, respectably. 46 Table 2.3 Integrated PK-PD-Efficacy model parameters estimate for xenografts (786-O) Parameter Unit Estimate RSE% Variability% Shrinkage% Kg 1/hr 0.0057 3.9 - - Kmax 1/hr 0.0194 43.2 - - KI50 %pAKT Inhibition 67.2 12.6 - - γ2 - 9.4 208.5 - - Proportional error - 0.248 5.1 - - IIV Kg variance 0.0276 29.6 16.6 22.6 IIV Kmax variance 0.0529 54.6 23.0 45.8 IIV= inter-individual variability, Kg= net tumor growth rate constant, Kmax= maximum value of Ks (tumor shrinkage rate constant), KI50= I where Ks is 50% of Kmax, RSE= relative standard error, γ2= sigmoidicity factor of the sigmoid Kmax equation Table 2.4 Integrated PK-PD-Efficacy model parameters estimate for patients with advanced solid tumors (Phase 1 studies) Parameter Unit Estimate RSE% Variability% Shrinkage% Kg 1/week 0.0097 20.7 - - Kmax 1/week 0.0142 43.9 - - KI50 %pAKT Inhibition 58.0 34.3 - - γ2 - 6.52 101.4 - - Proportional error - 0.141 2.3 - - IIV Kg variance 0.668 34.9 81.7 37.9 IIV Kmax variance 0.377 44.6 61.4 55.8 IIV KI50 variance 0.0225 (fix) - - - IIV γ2 variance 0.0225 (fix) - - - IIV= inter-individual variability, Kg= net tumor growth rate constant, Kmax= maximum value of Ks (tumor shrinkage rate constant), KI50= I where Ks is 50% of Kmax, RSE= relative standard error, γ2= sigmoidicity factor 47 Figure 2.11 Preclinical and clinical population integrated PK-PD-Efficacy models estimated relationship between tumor shrinkage rate constant (Ks) vs %pAkt inhibition in xenograft (tumor tissue) and in a typical patient with advanced solid tumors (surrogate plasma). A) Steep sigmoid curve describes relationship between tumor shrinkage rate constant vs %pAkt inhibition in xenografts (tumor tissue site, red line) and typical patient (surrogate plasma site, blue line). B) Tumor shrinkage rate constant normalized to Kmax (maximum value of Ks) vs %pAkt inhibition in xenografts (tumor tissue site, red line) and typical patient (surrogate plasma site, blue line). 48 2.4 Discussion The PI3K-AKT-mTOR signaling pathway is essential for numerous fundamental cellular functions such as cell differentiation, growth, proliferation, mobility, and metabolism (10, 19). Somatic alterations and genetic amplifications causing activation of this pathway are frequently found in cancer, as a result, there has been a significant effort to develop therapeutics that target critical members of the pathway (19). Successful development of these drugs requires pharmacodynamic biomarkers that aim to define the degree and duration of target and pathway inhibition (19); such as pAkt (phosphorylated Akt) which is a protein biomarker that is often used as a marker of cellular signaling through the PI3K-AKT-mTOR pathway. Drugs that target this pathway, such as apitolisib, lead to the inhibition of pAkt phosphorylation and the induction of apoptosis in cancer cells (36). In this study, preclinical and clinical apitolisib concentration-response relationships were explored to investigate the utility of pAkt biomarker in assessing extend of PI3K-AKT-mTOR pathway inhibition in terms of tumor growth inhibition. More importantly, we present a case study of a formal assessment on the real-world translatability of preclinical translational PK-PD analyses to clinical response in patients using common endpoints that are collected at preclinical and early clinical stages of drug development. Formal assessment on the translatability of preclinical PK-PD is lacking in the literature. Levels of the biomarker, pAkt, can be measured in both tumor tissue and plasma. However, measurement of pAkt in the tumor tissue is typically considered more relevant to therapy and serves to better inform cancer prognosis. Development for targeted therapeutics for cancer at preclinical research stage is conducted on the xenograft models to determine drug efficacy and identify active doses based on assessment of the drug’s in vivo concentration and target 49 engagement at the site of action. At this stage the extent and duration of target modulation typically is quantified by measuring tumor tissue biomarkers. However, once drug moves into clinical stage, often target modulation and response is assessed by surrogate plasma biomarkers, which are less invasive. PD biomarkers provide invaluable insights into the interaction of novel therapies with their intended targets; however, use of these biomarkers requires a deep understanding of their relationship to drug concentrations and clinical outcomes. Over the past few decades, there has been a significant rise in preclinical understanding of drug concentrations and biomarker response as evident by numerous publications (48-50). This development is driven by advancements in technologies and methodologies for measuring drug levels and biomarkers in various biological matrices. One of the key factors driving the interest in preclinical understanding of drug concentrations and biomarker response is the need to improve the efficacy and safety of drugs in clinical development and design more effective dosing regimens which minimize the risk of adverse events. Based on our knowledge, this is the first report to quantitatively examine the relationship between target modulation and efficacy in humans for a PI3K compound using a translational biomarker (pAkt). Additionally, this is the first attempt to quantitatively assess similarities and differences between biomarker response observed in preclinical and clinical phases in order to assess the translatability of preclinical PD and efficacy data within the PI3K-AKT-mTOR pathway. In this study, we focused on a translational PD biomarker in the pathway, pAkt and developed an integrated sequential PK-PD-Efficacy model to facilitate the interpretation of efficacy studies conducted preclinically to early-phase clinical development for a specific PI3K/mTOR inhibitor compound (apitolisib). These integrated 50 models can be used to predict the optimal dosing regimen for a drug, considering not only the PK properties of the drug, but also the relationship between drug concentrations, pAkt levels, and tumor growth inhibition. The model used to characterize the relationship between apitolisib and pAkt levels is an indirect response model. Indirect response models are used when the response measured is the product of an indirect mechanism, such as the inhibition or stimulation of the formation (kin) or loss (kout) of the mediator controlling the physiological effect (51, 52). Hence, in the present study, the levels of pAkt in tumor tissue (preclinically) and plasma (clinically) that were monitored after upstream inhibition of PI3K by apitolisib were characterized using indirect response models to quantify the inhibition of the production of pAkt in tumor tissue or surrogate plasma. The quantified kin estimates were comparable between xenograft mice and humans suggesting comparable rates of production and loss (kout is derived from kin) for pAkt (Table 2.1 and Table 2.2) in surrogate plasma from patients vs tumor from xenograft mice. Notably, the estimated IC50 was ~ 40-fold lower in a typical patient being 9.32 µg/L compared to 403 µg/L in xenografts when the PD biomarker was assessed in surrogate plasma rather than from tumor tissue. The higher pAkt IC50 estimates in xenograft study could be partially due to the RCC tumor type (786-O cell line) being less responsive to apitolisib treatment compared to other tumor types such as MCF-7 in in vitro studies conducted using cancer cell lines (36, 53). In patients that plasma pAkt biomarker was collected individual IC50 range from 4.03 to 26.1 µg/L; notably within this group individual IC50 estimate for a patient with metastatic renal cell carcinoma was 19.12 µg/L which was on the higher end. 51 The higher potency observed in patient surrogate plasma may be attributed to differences in assay conditions that likely favor greater inhibition in the plasma, or differences in drug concentrations between normal and tumor tissues due to variances in tissue architecture and hemodynamics may also contribute to this phenomenon (54). These differences underline the complexity of accurately defining the pharmacokinetic-pharmacodynamic relationship of molecularly targeted drugs based on observed data alone, as well as the important issues of extrapolation of preclinical models to predict effects in patients and differences in analytical sensitivity/methodology between platelet-rich plasma and tumor biopsies (54). Model informed drug development can identify and characterize these differences and their correlation to treatment effect, therefore disease mechanism-based biomarkers that are indicative of a relevant biological aspect of cancer can serve as additional surrogate of anti-tumor activity during the drug development process and bridge preclinical studies efficacy to clinical response. The relationship between pAkt modulation and its impact on tumor growth was investigated preclinically and clinically by developing integrated PK-PD-Efficacy models which assume that tumor growth inhibition has dependence on the PI3K-AKT-mTOR signaling pathway (Figure 2.1). Apitolisib is dual PI3K/mTOR inhibitor which targets two crucial points in the same pathway that could lead to higher efficacy compared to a PI3K inhibitor alone by possibly overcoming mTOR negative feedback due to inhibition of pathway (55). In our current integrated models used for both the preclinical and clinical analyses, pAkt inhibition serves as surrogate for both PI3K and mTORC1 inhibition by apitolisib; hence the models utilized have some limitations. Specifically, the role/contribution of mTORC2 inhibition to tumor growth inhibition is not accounted for separately and is “lumped” with PI3Kinase inhibition by the 52 models used. Further, preclinical study was conducted in xenografts with renal cancer carcinoma (786-O cell lines) and relationships between pAkt modulation and tumor inhibition may differ when compared to patients with different cancer types enrolled in the Phase 1 studies utilized in this analysis. Individual longitudinal tumor profiles were adequately described by both preclinical and clinical integrated PK-PD-Efficacy models. Numerical and graphical model-diagnostics were used to evaluate different components of the integrated PK-PD-Efficacy models which verified adequacy of the underlying structural models to capture observed preclinical and clinical data. A steep sigmoid curve describing the relationship between inhibition of Akt phosphorylation and tumor growth inhibition, represented by the rate constant Ks was observed in xenograft mice and patients despite differences in species and matrices where pAkt inhibition was evaluated. In both species, a threshold of approximately 35% to 45% pAkt inhibition is required prior to rapid increases in tumor growth inhibition with increasing pAkt modulation (Figure 2.11). The commonality of curve shape has implications in clinical trial design as pharmacodynamic endpoints can be appropriately selected in clinical trials based on similarity in observed pharmacodynamic thresholds required prior to onset of an anti-tumor effect. Similar steep relationship (sigmoidicity factor ~9) was estimated for target modulation (Gli mRNA inhibition) and vismodegib efficacy (i.e., the rate constant describing the measure of antitumor effect) in the preclinical models of hedgehog pathway, and approximately minimum 50% Gli mRNA inhibition was needed for tumor growth inhibition (56). Finally, of note, the net growth rate constant was considerably lower in patients compared to xenograft mice. This is consistent with 53 previous publications of tumor growth rate constant in humans versus preclinical xenografts models (56, 57). Previous study delves into the translational relevance of preclinical murine subcutaneous tumor models in predicting clinical response (58). Through a retrospective pharmacokinetic-pharmacodynamic analysis of eight agents, including both molecularly targeted and cytotoxic ones, with known clinical response data, the research sheds light on the correlation between simulated tumor growth inhibition in xenografts/allografts using human exposures and actual clinical response (58). Significant correlation was found between TGI driven by human pharmacokinetics and clinical response, contrasting with TGI observed at maximum tolerated doses in mice (58). Agents inducing over 60% TGI in preclinical models, at clinically relevant exposures, exhibited a higher likelihood of eliciting clinical response (58). These findings establish a framework for effectively utilizing murine subcutaneous tumor models for selecting promising agents for clinical advancement (58). In summary, the use of translational pharmacokinetics (PK)-pharmacodynamic (PD) modeling of preclinical efficacy data to identify clinically active doses in patients is increasing common. However, enhancing the predictivity of the tools employed to assess the effectiveness of a drug candidate is the main challenge of translational PK-PD analyses (59). There is limited to no retrospective analysis to evaluate the performance of translational PK-PD modeling of preclinical data. In this thesis, the analysis aids in the understanding of the value of preclinical translational dose-finding and dose optimization studies in the context of “clinical drug development”. Phase 1 and 2 clinical trials are designed based on dose finding and efficacy 54 experiments (proof of mechanism of action) that are conducted at preclinical stages of drug development, where the extent and duration of target modulation is quantified by measuring xenografts tumor tissue biomarkers. Typically, in Phase 1 studies, surrogate plasma biomarkers are collected for patient convenience, since these biomarkers are less invasive to obtain and can be easily collected through a blood test. In this thesis, our objective was to perform a retrospective assessment and compare quantitative similarities and differences between the type of data that is typically collected in Phase 1 studies (surrogate plasma biomarker) versus data collected from preclinical xenografts studies (tumor tissue biomarker). With advancement in model informed drug development, these differences and their correlation to treatment effect can be better identified and characterized. 2.5 Conclusions Modeling can play a critical role in bridging the gap between xenograft and human studies, and in facilitating the development of more effective cancer treatments. Complexity of accurately defining treatment exposure-response relationship based on different matrices of origin (tumor tissue vs surrogate plasma) due to analytical sensitivity and methodology is challenging specifically at lower drug exposures. The preclinical and clinical developed integrated PK-PD-Efficacy models bring together the information from PK, PD, and efficacy studies to provide a more complete understanding of the relationship between drug dose, drug concentration, and therapeutic response. Primary objective of our analysis was to examine a real-world translational analysis and assess both insights gained and shortcomings of the analysis. The overall goal of this analysis was to better characterize preclinical to clinical translation, with the aim of improving predictivity and use of translational biomarkers such as pAkt which reflect the 55 biological response of a drug. These PD biomarkers can be used to monitor the efficacy of the treatment and facilitate informed decision making on dose finding and dosing regimen optimization to better inform future clinical trials design and interpretation based on preclinical studies. 56 Chapter 3: Quantitative Assessment of Drug Efficacy and Emergence of Resistance in Patients with Metastatic Renal Cell Carcinoma Using a Longitudinal Exposure-Tumor Growth Inhibition Model: Apitolisib (dual PI3K/mTORC1/2 inhibitor) versus Everolimus (mTORC1 inhibitor) Summary Cancer remains a significant global health challenge, and despite remarkable advancements in therapeutic strategies, poor tolerability of drugs (causing dose reduction/interruptions) and/or the emergence of drug resistance are major obstacles to successful treatment outcomes. Metastatic renal cell carcinoma (mRCC) accounts for 2% of global cancer diagnoses and deaths. Despite the initial success of targeted therapies in mRCC, challenges remain to overcome drug resistance that limits the long-term efficacy of these treatments. Our analysis aim was to develop a semi-mechanistic longitudinal exposure-tumor growth inhibition (TGI) model for patients with mRCC to characterize and compare everolimus (mTORC1) and apitolisib’s (dual PI3K/mTORC1/2) ability to inhibit tumor growth, and quantitate each drug’s efficacy decay caused by emergence of tumor resistance over time. TGI metrics were adequately predicted for each drug. Model estimated on-treatment tumor growth rate constant was 1.7-fold higher for apitolisib compared to everolimus. Estimated half-life for loss of treatment effect over time for everolimus was 16.1 weeks compared to 7.72 weeks for apitolisib suggesting a faster rate of tumor re-growth for apitolisib patients likely due to the emergence of resistance. Goodness-of-fit plots including visual predictive check indicated a good model fit and model was able to capture individual tumor size-time profiles. Based on our knowledge, this is the first clinical report to quantitatively assess everolimus (mTORC1) and apitolisib (PI3K/mTORC1/2) efficacy decay in patients with 57 mRCC. These results highlight the difference in overall efficacy of two drugs due to the quantified efficacy decay caused by emergence of resistance, and emphasizes the importance of model informed drug development for targeted cancer therapy. 3.1 Introduction The development of targeted therapies has revolutionized the treatment landscape for various types of cancer, including metastatic renal cell carcinoma (mRCC) which is a highly aggressive form of kidney cancer that has traditionally been challenging to treat due to its resistance to conventional chemotherapy and radiation therapy. Among the promising therapeutic approaches, the inhibition of the mammalian target of rapamycin (mTOR) pathway has emerged as a significant strategy in mRCC drug development. mTOR inhibitors, such as temsirolimus and everolimus, have shown promising results in the treatment of mRCC. These agents function by specifically targeting and inhibiting the activity of mTOR, thereby disrupting the signaling cascades involved in tumor growth and angiogenesis. Clinical trials evaluating the efficacy of mTOR inhibitors as monotherapy or in combination with other agents have demonstrated improved progression-free survival (PFS) and overall survival (OS) rates in patients with mRCC, leading to their approval by regulatory authorities for the treatment of advanced kidney cancer. Despite the clinical success of mTOR inhibitors, challenges remain in optimizing their therapeutic potential. Resistance to mTOR inhibitors and the development of adverse events are areas of current research. Ongoing research efforts are focused on the development of novel targeted therapy drugs, combination treatment strategies, and innovative approaches to overcome drug resistance, with the ultimate goal to: improve patient outcomes, prolong survival, and transform mRCC into a manageable chronic condition. 58 FDA approved everolimus (mTOR inhibitor), for renal cell carcinoma, directly inhibits mTOR complex 1 (mTORC1) which is integral to the phosphatidylinositol-3-kinase (PI3K)/AKT/ mTOR signaling pathway. Abnormal functioning of the mTOR pathway may contribute to the pathogenesis of renal cell carcinoma; by inhibiting mTORC1-mediated signaling, everolimus arrests cell cycle progression, and diminishes angiogenesis in cancer cells (60, 61). Phase 3 clinical study (RECORD-1) demonstrated that everolimus stabilizes tumor progression in patients with mRCC. Everolimus selectively inhibits mTORC1 and does not interfere with mTOR complex 2 (mTORC2), which is responsible for activating AKT (62). However, analysis of samples from patients with advanced solid tumors and neuroendocrine tumors has demonstrated that everolimus treatment results in increased AKT activation through the silencing of an S6 kinase-dependent negative feedback-induced loop, particularly in patients with clinical responses (62-64). It has been hypothesis that activation of AKT by way of insulin like growth factor 1, or insulin-like growth factor 1 receptor and mTORC2 signaling activation due to the inhibition of S6 kinase (S6K) negative feedback, are mechanisms of everolimus resistance (62, 65, 66). Consequently, targeting the PI3K/mTOR pathway via PI3K, mTORC1, and mTORC2 inhibition may potentially suppress treatment resistance and enhance patient outcomes compared with inhibition of mTORC1 alone (62). These findings have spurred the development of dual PI3K/mTOR inhibitors such as dactolisib (BEZ235), SAR245409 (XL765), BGT226, and apitolisib (GDC-0980), which subsequently have been assessed in various solid tumors (67-71). Notably, apitolisib is a small molecule pan-PI3K and mTOR (mTORC1/2) inhibitor that potently blocks PI3K/mTOR pathway signaling in cancer cell lines and has demonstrated significant antitumor activity in xenograft mice (36, 70). Treatment of cancer cell lines with apitolisib resulted in G1 cell-cycle arrest, and in contrast to mTOR inhibitors apitolisib triggered apoptosis 59 in certain cancer cells, such as those with direct pathway activation via PI3K and PTEN (36). However, clinical trials demonstrated that the modest efficacy and poor tolerability of dual pan-PI3K and mTOR inhibitors including apitolisib may impose limitations on their clinical development. Targeted oncology drug development is challenging due to diverse nature of cancer (tumors heterogeneity) and possible emergence of tumor resistance in patients. Traditionally, the goal of Phase 1 and 2 studies were to assess drug tolerability and safety (Phase 1) and over-all efficacy in specific population (Phase 2). There are typically limited data collected at these stages of drug development with high variability. Quantitative integrated analyses represent an important tool that provide additional insights on drug response and maximizes the amount of information that can be attained from Phase 1 and 2 clinical trials. Traditional methods for evaluating drug efficacy typically rely on single time-point measurements or focus solely on response rates, often failing to capture the dynamic nature of the disease and drug’s anti-tumor effect over time. In contrast, longitudinal exposure-tumor growth inhibition models integrate both drug exposure data and tumor growth measurements obtained at multiple time points during treatment. By accounting for the complex interplay between drug concentrations and tumor growth dynamics, these models offer a comprehensive understanding of drug response kinetics and can provide valuable quantitative insights into the development of resistance mechanisms. The aim of the current study was to develop an integrated longitudinal exposure-tumor growth inhibition model for patients with mRCC to 60 characterize and compare apitolisib versus everolimus’ ability to inhibit tumor growth and quantitate the extent of drug efficacy decay caused by emergence of tumor resistance over time. 3.2 Methods 3.2.1 Clinical Trial ROVER study (NCT01442090) was conducted in accordance with Good Clinical Practice guidelines and the Declaration of Helsinki. Prior to enrollment, written informed consent was acquired from all patients, in alignment with the approved protocols from the ethics committees at each study site. All clinical trial information can be accessed through the following website. https://clinicaltrials.gov/. 3.2.2 Study Design and Data Tumor size data from Phase 2, multicenter, international, open-label, randomized trial designed to evaluate apitolisib versus everolimus in patients with metastatic renal cell carcinoma (mRCC) was used in the model development (70). Eligible patients included those 18 years of age or older, with metastatic clear-cell RCC and progression of disease after exposure to at least one vascular endothelial growth factor (VEGF) pathway-targeted therapy, exposure to mTOR inhibitors was an exclusion criterion (70). Patients were required to have measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 (30). Patient demographic and baseline characteristics was previously published (70). Patients were randomized 1:1 to receive one of the following treatment: 40 mg apitolisib orally daily or 10 mg everolimus orally daily. Dose interruptions of up to 28 days and reductions (5 mg for everolimus; 20 mg or 30 mg for apitolisib) were permitted (70). 61 Computed tomography (CT) or magnetic resonance imaging (MRI) scan was used to measure tumor lesions at baseline and at regular intervals afterward (approximately every 8 weeks until disease progression (based on RECIST v1.1) or patient withdrawal from the study). Longitudinal tumor size data, defined as the sum of the longest diameters of target lesions at each visit according to RECIST v1.1 (30), were used for the estimation of TGI metrics. Patients with at least baseline and one post-baseline tumor size measurements were defined as evaluable, and data from patients who only had baseline tumor assessments were excluded from the analysis. 3.2.3 Population Longitudinal Exposure-Tumor Growth Inhibition Model 3.2.3.1 Population Pharmacokinetic Models Everolimus population pharmacokinetic (PK) parameters used in the analysis were previously published in the FDA’s clinical pharmacology and biopharmaceutics review (72). Population PK parameters used for apitolisib was previously determined using two Phase 1 clinical trials (37) with intensive PK samples collected for doses ranged from 2 to 200 mg (data not shown). Two-compartment models with first-order absorption and first-order clearance were used to predict the concentration–time data of patients given oral doses of apitolisib or everolimus. Apparent clearance (CL/F) after oral dosing, apparent volume of distribution parameters for the central (V1/F) and peripheral (V2/F) compartments, apparent inter-compartmental clearance (CLd/F), and absorption rate constant (Ka) were used to parameterize the PK models. Apitolisib PK model included a lagged time for absorption. The pharmacokinetic model used to describe everolimus and apitolisib is shown in Figure 3.1 and the associated pharmacokinetic parameters for everolimus and apitolisib are presented in Table 3.1 and Table 3.2, respectively. Individual 62 patients dosing records were used to predict the everolimus or apitolisib plasma concentrations; therefore, any dosing modification or dosing interruption for individual patients were captured. Figure 3.1 Illustration of model structure for longitudinal exposure-tumor growth inhibition model. Ka= first-order absorption rate constant, CL/F= apparent oral clearance, CLd/F= apparent inter-compartmental clearance, F= bioavailability, V1/F= apparent central volume of distribution, V2/F= apparent peripheral volume of distribution, Cp= plasma compartment, Ct= tissue compartment, Kg= net tumor growth rate constant, Ks= tumor shrinkage rate constant, tlag= absorption lag time 63 Table 3.1 Everolimus population pharmacokinetic parameters Parameters (unit) Estimate (%RSE) V1/F (L) 172 (8.2) V2/F (L) 495 (7.6) CL/F (L/hr) 14.8 (3) CLd/F (L/hr) 48 (7.5) Ka (hr-1) 6.07 CL/F = apparent clearance after oral dosing, V1/F = apparent volume of distribution for the central compartment, V2/F = apparent volume of distribution for the peripheral compartment, CLd/F = apparent inter-compartmental clearance, Ka = absorption rate constant Table 3.2 Apitolisib population pharmacokinetic parameters Parameters (unit) Estimate (%RSE) V1/F (L) 210.61(3.51) V2/F (L) 639.06 (15.1) CL/F (L/hr) 21.33 (4.28) CLd/F (L/hr) 5.93 (8.53) Ka (hr-1) 3.35 (16.8) Absorption Lag (hr) 0.465 (0.43) CL/F = apparent clearance after oral dosing, V1/F = apparent volume of distribution for the central compartment, V2/F = apparent volume of distribution for the peripheral compartment, CLd/F = apparent inter-compartmental clearance, Ka = absorption rate constant 64 3.2.3.2 Tumor Growth Inhibition Model A sequential PK-TGI modeling approach was used in this analysis. PK samples were not collected for everolimus, hence population predictions of concentration instead of individual predictions was utilized in the sequential PK-TGI modeling approach for both drugs based on actual dosing records of patients. The population PK models describe above were used to predict apitolisib or everolimus concentrations over time which were used to drive the anti-tumor effect of each drug. The structure of the TGI model is described using Equation 1. Model structure is presented in Figure 3.1. Model code is provided in Appendix B. 𝑑(𝑇𝑆)𝑑𝑡 = 𝐾𝑔 × 𝑇𝑆 (𝑡) − 𝐾𝑠 × 𝑇𝑆 (𝑡) × 𝐶𝑝 (𝑡) × 𝐸𝑋𝑃(−𝜆 × 𝑡) Equation 1 where TS is the tumor size defined as the sum of longest diameters of target lesions based on investigator assessment, t is time, Kg and Ks are the estimated on-treatment tumor growth and tumor shrinkage rate constants, respectively, Cp is the longitudinal predicted apitolisib or everolimus concentration by the population PK models. The λ is an exponential decay constant describing the loss of treatment effect over time (apitolisib or everolimus), and is equal to Ln(2) / T50λ, where T50λ, an estimated parameter, is the time in weeks to achieve 50% of the loss of treatment effect over time. An additional parameter, TS0 defined as the TS at the time of the first assessment in the absence of drug was estimated and called baseline TS. Data from the entire clinical trial which included both apitolisib and everolimus treated patients were fit together. The model fit provided estimates of pharmcodynamic parameters (i.e. Kg, Ks, and T50λ) for each drug with the exception of TS0 and residual error which were shared parameters between both treatment groups. A log-normal distribution was assumed for inter-individual 65 variability. Additionally, model-based simulations, using parameter estimates for the “typical” patient, were performed in order to illustrate the impact of Kg, Ks and treatment effect decay over time (λ) due to appearance of drug resistance for apitolisib or everolimus treatment in a typical patient with mRCC. 3.2.3.3 Model Evaluation Model evaluation was based on the inspection of graphical diagnostics, including goodness-of-fit plots and prediction-corrected visual predictive checks (pcVPCs) (73, 74) as well as changes in the objective function value (OFV) provided by NONMEM, relative standard errors (RSE) and plausibility of the parameter estimate. 3.2.4 Software The modeling analyses were performed using Nonlinear mixed effect models (NONMEM, version 7.4), with the first-order conditional estimation algorithm with interaction (75). Data management and further processing of NONMEM output were performed using R version 4.2.3 (46). 3.3 Results 3.3.1 Population Longitudinal Exposure-Tumor Growth Inhibition Model 3.3.1.1 Data The exposure-tumor growth inhibition model analysis dataset included a total of 180 tumor size observations from 38 mRCC patients treated with everolimus; and 152 tumor size observations from 41 mRCC patients treated with apitolisib. As described in the methods, the modeling 66 approach was sequential with individual everolimus or apitolisib pharmacokinetics predicted using PK parameters shown in Table 3.1 and Table 3.2, and individualized dosing records when fitting the longitudinal tumor data. As individual dosing records were utilized any dosing modification or dosing interruption for individual patients were captured. Figure 3.2 shows individual time courses of tumor size data, and Figure 3.3 shows individual longitudinal tumor size change from baseline in mRCC patients treated with everolimus or apitolisib. The exposure-TGI model was found to adequately characterize the tumor inhibition over time, accounting for time-varying exposures due to poor drug tolerability (i.e. dose reductions or dose interruptions). Figure 3.2 Longitudinal tumor size data. Individual time courses of tumor size data of patients with metastatic renal cell carcinoma treated with 40 mg apitolisib (left panel) or 10 mg everolimus (right panel). Start of treatment indicated with dashed vertical line (red). 67 Figure 3.3 Longitudinal tumor size change from baseline data. Individual time courses of tumor size data change from baseline of patients with metastatic renal cell carcinoma treated with 40 mg apitolisib (left panel) or 10 mg everolimus (right panel). 3.3.1.2 Model Evaluation Goodness-of-fit plots of the final model indicated a good model fit as shown in plots of conditional weighted residuals versus time for everolimus and apitolisib treated patients (Figure 3.4), and plots of individual observed versus predicted tumor size (Figure 3.5) and baseline tumor size (Figure 3.6). Representative individual patient fits are shown in Figure 3.7 to illustrate that the model was able to capture a variety of individual tumor size-time profiles. Finally, a visual predictive check of the final model (Figure 3.8) shows that the model captured the central tendency, extreme values as well as the variability in the observed tumor size data. 68 Figure 3.4 Conditional weighted residuals versus time plots from the final longitudinal exposure-tumor growth inhibition model for patients treated with apitolisib or everolimus. Patients with metastatic renal cell carcinoma treated with 40 mg apitolisib or 10 mg everolimus. Individual data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Black dashed lines (-2, 0, 2) included as reference for goodness of fit. 69 Figure 3.5 Observed individual tumor size data versus predictions from the final longitudinal exposure-TGI model stratified by treatment with 40 mg apitolisib or 10 mg everolimus. Individual data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Line of identity (black) was included as reference for observed vs model predicted data. 70 Figure 3.6 Observed individual baseline tumor size data versus predicted individual baseline tumor size from the final longitudinal exposure-TGI model stratified by treatment with 40 mg apitolisib or 10 mg everolimus. Individual data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Line of identity (black) was included as reference for observed vs model predicted data. 71 Figure 3.7 Representative individual fits of tumor size from the final longitudinal exposure-TGI model for everolimus and apitolisib. Individual data points are indicated by black circles. Black line in each plot indicates the individual predictions from the model. 72 Figure 3.8 Prediction corrected visual predictive check of tumor size data versus time since first dose, for the final longitudinal exposure-tumor growth inhibition model, stratified by treatment. Tumor size are displayed versus time since first dose. The solid red and upper and lower blue lines represent the median, 10th and 90th percentiles of the observations, respectively; the shaded red and blue areas represent the 95% confidence interval of the median, 10th and 90th percentiles predicted by the model. The observed data are indicated by open circles. 73 3.3.1.3 Tumor Growth Inhibition Metrics Parameter estimates from the final longitudinal exposure-tumor growth inhibition model are presented in Table 3.3. Distinct Kg, Ks and T50λ parameters as well as their inter-individual variabilities were estimated for everolimus and apitolisib. Comparisons between everolimus and apitolisib individual tumor growth and tumor shrinkage rates is presented as boxplots in Figure 3.9. As interindividual variability estimates of parameters are high, our comparisons of typical parameter estimates for the two compounds represent general trends. Patients treated with everolimus had lower on-treatment tumor growth rate constant versus patients treated with apitolisib with Kg being 1.7-fold higher for apitolisib. In contrast, the shrinkage rate constants that are reflective of drug potency were similar. 74 Table 3.3 Parameter estimates of the final longitudinal exposure-tumor growth inhibition model for everolimus and apitolisib Parameter Unit Estimate **90% CI **RSE (%) Shrinkage (%) TS0 mm 69.2 61.6 - 79.6 8.0 - Kg (everolimus) week-1 0.00277 0.00115 - 0.00510 44.3 - Ks (everolimus) mg-1.L.week-1 0.337 0.132 - 0.588 41.8 - T50λ (everolimus) week 16.1 7.06 - 38.9 61.3 - *λ (everolimus) week-1 0.043 - - - Kg (apitolisib) week-1 0.00475 0.00233 - 0.00816 36.5 - Ks (apitolisib) mg-1.L.week-1 0.233 0.081 - 0.365 37.0 - T50λ (apitolisib) week 7.72 2.10 - 23.7 87.5 - *λ (apitolisib) week-1 0.090 - - - Variance of additive residual variability - 76.9 67.6 - 82.1 5.7 - IIV TS0 variance 0.442 0.325 - 0.566 16.6 4.6 IIV Kg (everolimus) variance 1.25 0.553 - 2.43 46.3 45.4 IIV Ks (everolimus) variance 1.14 0.403 - 2.19 48.3 39.1 IIV T50λ (everolimus) variance 1.2 (fix) - - - IIV Kg (apitolisib) variance 1.13 0.465 - 2.13 45.0 40.7 IIV Ks (apitolisib) variance 0.84 0.35 - 1.83 54.5 41.1 IIV T50λ (apitolisib) variance 5.66 2.43 - 14.0 63.9 57.4 *λ = Ln(2) / T50λ **Obtained from Sampling Importance Resampling. CI= confidence interval, IIV= inter-individual variability, Kg= net tumor growth rate constant, Ks= tumor shrinkage rate constant, T50λ = time to achieve 50% of the loss of treatment effect over time, λ = constant accounting for loss of treatment effect over time, TS0=baseline tumor size. FIX indicates that the parameter was estimated, then fixed in order to improve model stability. 75 A B Figure 3.9 Boxplots comparing of model-estimated Kg and Ks in patients with metastatic renal cell carcinoma treated with 40 mg apitolisib or 10 mg everolimus. Dots indicate individual model-estimated A) Kg or B) Ks on log-scale, ends of boxes indicate 25th and 75th percentiles (i.e., interquartile range), horizontal lines indicate medians, and ends of whiskers indicate 1.5 times the interquartile range. Kg= net tumor growth rate constant, Ks= tumor shrinkage rate constant 76 Figure 3.10 presents boxplots comparing half-life for loss of treatment effect over time for everolimus compared to apitolisib. The model estimated time to achieve 50% of the loss of treatment effect over time (i.e. half-life, T50λ) was longer for everolimus (16.1 weeks) compared to apitolisib (7.72 week) by 2-fold suggesting a longer duration of time before the emergence of resistance for the everolimus treated group. For everolimus T50λ inter-individual variability (IIV) was initially estimated and was later fixed in the final model to improve model stability. For apitolisib T50λ IIV, shrinkage impact should be considered when drawing conclusions (76). Based on the estimated T50λ, the predicted exponential decay constant describing loss of treatment effect (λ) over time was 0.043 and 0.090 week-1 for everolimus and apitolisib, respectably. Baseline tumor size (TS0) was a shared parameter in the model between two treatment groups since observed tumor size at baseline was similar. The median observed baseline tumor size was 65.5 mm and 79.0 mm for everolimus and apitolisib, respectively. Figure 3.11 presents boxplots comparing baseline tumor size between patients treated with apitolisib versus everolimus which illustrate that both treatment groups had similar tumor size at baseline. Furthermore, target tumor response was assessed by investigators according to RECIST v1.1. Figure 3.12 presents boxplots of on-treatment LnKg (natural log of Kg) versus target tumor response for everolimus and apitolisib. In both everolimus and apitolisib treatment cohorts, responders (complete and partial response) and patients with stable disease had smaller on-treatment Kg compared to non-responder group (progressive disease). 77 Figure 3.10 Boxplots comparing half-life for loss of treatment effect over time (T50λ) in patients with metastatic renal cell carcinoma treated with 40 mg apitolisib or 10 mg everolimus. Dots indicate individual model-estimated T50λ, ends of boxes indicate 25th and 75th percentiles (i.e., interquartile range), horizontal lines indicate medians, and ends of whiskers indicate 1.5 times the interquartile range. An outlier with T50λ =147.3 months was removed to enhance plot visualization (this patient was one of partial responders with lowest estimated Kg in apitolisib treatment group). 78 Figure 3.11 Boxplots comparing observed baseline tumor size between everolimus or apitolisib treatment groups. Dots indicate individual observed baseline tumor sizes, ends of boxes indicate 25th and 75th percentiles (i.e., interquartile range), solid horizontal lines indicate medians, and ends of whiskers indicate 1.5 times the interquartile range. The observed median baseline tumor size is 76 mm across both treatment cohorts. 79 A B Figure 3.12 Relationships between individual on-treatment Kg and types of responders stratified by treatment group, apitolisib (A) and everolimus (B). Patients’ measurable disease (target response) assessed by investigators at the end of the study based on Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 presented. CR= complete response, PD= progressive disease, PR= partial response, SD= stable disease, LnKg = natural log of Kg 80 3.3.1.4 Model-Based Simulation Simulations showing predicted tumor growth inhibition profiles generated using typical population parameter estimates stratified by treatment are shown in Figure 3.13. Figure 3.13-A shows simulations of the predicted changes in tumor size over time with treatment while Figure 3.13-B shows predicted tumor size change from baseline. As can be seen in Figure 3.13, the initial tumor growth inhibition was similar when comparing the two treatment groups with both treatments resulting in decreases in tumor size. However, while tumors in typical patients treated with everolimus present a sustained treatment response for 7.5 months, tumors in typical patients treated with apitolisib show less sustained response and re-growth after 4 months of treatment. It is noteworthy that Figure 3.13 illustrates the difference between treatment effects in a typical patient assuming perfect treatment compliance. In reality, treatment was interrupted, reduced and/or discontinued more frequently for apitolisib (dual pan-PI3K and mTORC1/2 inhibitor) compared to everolimus (mTORC1 inhibitor) due to adverse events, suggesting that the difference in durability of the tumor response in the real world would be larger. 81 A B Figure 3.13 Simulations of predicted longitudinal tumor dynamics of a typical patient with metastatic renal cell carcinoma treated with 10 mg everolimus or 40 mg apitolisib. A) model predicted tumor size over time, B) model predicted tumor size change from baseline over time. 82 3.4 Discussion Cancer remains a significant global health challenge, and despite remarkable advancements in therapeutic strategies, the emergence of drug resistance poses a major obstacle to successful treatment outcomes. Evaluating the efficacy of anticancer drugs over time is critical for optimizing treatment regimens and predicting patient responses. Longitudinal exposure-tumor growth inhibition (TGI) models have emerged as a valuable tool in this endeavor, providing a quantitative framework to assess drug efficacy in cancer patients. The fundamental principle underlying longitudinal exposure-TGI models is the integration of pharmacokinetic data with tumor growth inhibition dynamics. By quantifying drug concentrations in plasma, alongside tumor size measurements over time, these models enable the estimation of critical parameters such as the rate of tumor growth and drug efficacy in the form of tumor shrinkage. More recently, longitudinal exposure-TGI models have been used to quantitatively characterize the effects of drug resistance. Claret, et al. reported a longitudinal TGI model quantifying the emergence of drug resistance using tumor size data collected from colorectal cancer patients (29). In this model the daily dose was used as a metric for exposure to drive drug effect and resistance (29). The longitudinal exposure-TGI model was used for prediction of the results of a Phase 3 clinical trial comparing overall survival (OS) following treatment with either fluorouracil or capecitabine in colorectal cancer patients using tumor dynamics data from a capecitabine Phase 2 trial and historical fluorouracil Phase 3 data (29). As drug exposures were not available, the daily dose was used as a metric for exposure to drive drug effect and resistance (29). Overall, the integration of longitudinal exposure-TGI models in the evaluation of drug efficacy decay represents a promising approach for improving drug 83 development (i.e. PFS or OS) by providing a more comprehensive understanding of the complex dynamics of drug response kinetics, tolerability and resistance development. These models have the potential to improve individual patient outcomes by guiding treatment decision-making, and facilitating the development of novel therapeutic strategies. In the current study, an integrated sequential longitudinal exposure-tumor growth inhibition model was developed based on longitudinal tumor size data of patients with mRCC enrolled in ROVER clinical trial. The ROVER trial, a randomized Phase 2 clinical study, aimed to directly compare the efficacy of simultaneously targeting multiple nodes within the PI3K/mTOR signaling pathway (apitolisib) with the isolated inhibition of mTORC1 (everolimus) (70). Prior preclinical investigations had indicated that dual inhibitors of PI3K/mTOR exhibited superior activity compared to rapalogs that exclusively targeted mTORC1 (77). However, in contradiction to the hypothesis, the results of the ROVER study demonstrated that the PI3K/mTORC1/mTORC2 inhibitor, apitolisib, significantly underperformed in comparison to the mTORC1 inhibitor, everolimus (70). Our longitudinal exposure-TGI model was able to adequately quantify the anti-tumor activity of both apitolisib and everolimus, and assessed the extent of each drug treatment efficacy decay caused by appearance of tumor resistance over time for both agents. Our analysis provided valuable insights into the tumor response patterns and highlight the heterogeneity in treatment outcomes of each drug identifying the more rapid emergence of drug resistance as a factor which limited the therapeutic efficacy of apitolisib. Currently, no dual PI3K/mTOR inhibitor has received FDA approval and other PI3K/mTOR inhibitor compounds such as dactolisib were also withdrawn from further development in RCC. 84 As previously published by Powles et al., different hypotheses can be considered to explain the efficacy difference between apitolisib and everolimus. Firstly, it's plausible that mTORC1 assumes a pivotal role in the mRCC PI3K/AKT/mTOR pathway, supported by the effectiveness of both temsirolimus and everolimus (70). Consequently, attempting to inhibit the upstream PI3K and mTORC2 signaling may result in excessive toxicity without substantial efficacy (70). Secondly, resistance to mTORC1 inhibition might be attributed to the activation of parallel signaling pathways, hence horizontal inhibition could potentially succeed where vertical inhibition ineffective (70). Preclinical data even suggests that PI3K/mTOR inhibition could trigger compensatory activation of HER family receptors and the MAP kinase pathway (70, 78) . Therefore, combination of mTOR inhibitor with inhibitors of VEGF, EGFR, or MEK may achieve greater clinical efficacy by overcoming this bypass mechanism, although likely with increased toxicity as demonstrated in prior clinical trials (70, 79, 80). These hypothesis by Powles et al. could account for the lower efficacy of apitolisib compared to everolimus, particularly given that apitolisib, similar to other dual PI3K/mTOR inhibitors under development for solid tumors, exhibited poor tolerability, leading to frequent dose interruptions and reductions (70, 81). The current study quantifying the disparity in efficacy between the two drugs offer valuable insights into the potential limitations of PI3K/mTOR dual inhibition strategies in a clinical context for mRCC treatment. To characterize the exposure profiles of everolimus and apitolisib, two-compartment disposition models with first-order absorption and first-order clearance were employed, and pharmacokinetic (PK) parameters obtained from population pharmacokinetic studies were used. The concentration-time profiles of the drugs were predicted using individual patients’ dosing records, 85 ensuring that any dosing modifications and/or interruptions were captured. A key objective of this study was to compare the on-treatment tumor growth and shrinkage rates between everolimus and apitolisib and assess each drug loss of efficacy over time due to emergence of tumor resistance. Overall, apitolisib exhibited 1.7-fold higher on-treatment tumor growth rate (Kg) compared to everolimus. However, the initial tumor growth inhibition response (Ks) appeared to be relatively similar between the drugs. The main difference when comparing apitolisib and everolimus was the durability of response and tumor re-growth rate. Apitolisib had a 2-fold higher rate of loss of treatment effect (λ) compared to everolimus (λ = 0.090 week-1 and 0.043 week-1 for apitolisib and everolimus, respectably), which correspond to half-life for loss of treatment effect over time of 7.72 weeks for apitolisib compared to 16.1 weeks for everolimus. The combination of pharmacodynamic parameter described this leads to shorter durability of treatment effect and faster re-growth of the tumor for apitolisib compared to everolimus. The boxplots in Figure 4 provides additional insights by illustrating the time required to reach half of the λ effect for each drug, with everolimus showing a longer half-life for loss of treatment effect (16.1 weeks) compared to apitolisib (7.72 weeks). TGI metrics has been shown to be a significant predictor of progression-free survival (PFS) or overall survival (OS), and faster tumor growth rate often correlates with a higher likelihood of disease progression and shorter PFS or OS (82, 83). As presented in Figure 3.12, responders (complete and partial response) and patients with stable disease had lower on-treatment Kg compared to non-responder group (progressive disease) in both everolimus and apitolisib treatment cohorts. Furthermore, based on ROVER clinical trial results, the objective response rate (ORR) was 7.1% for apitolisib and 11.6% for everolimus. Therefore, ORR was 1.6-fold 86 higher for everolimus compared to apitolisib. This is in accordance with model estimated on-treatment tumor growth rate constant which was 1.7-fold higher for apitolisib compared to everolimus. Furthermore, model estimated half-life (T50λ) for efficacy decay was 2-fold longer for everolimus (16.1 weeks) compared to apitolisib (7.72 week) suggesting a longer duration of time before the emergence of resistance for the everolimus treated group. The results of current analysis (i.e. Kg and T50λ) are also consistent with progression-free survival outcomes from the ROVER clinical trial which reported median PFS of 6.1 months for patients treated with everolimus versus 3.7 months for apitolisib treated patients (1.65-fold difference) (70). Also, hazard ratio estimated by Cox proportional hazards regression was 2.12 for PFS and 1.77 for overall survival for apitolisib compared to everolimus in ROVER trial.(70) In an everolimus Phase 3 trial for metastatic renal cell carcinoma, the median PFS was 5.5 months for treated patients versus 1.9 months placebo patients (60); this study ended early due to the statistically significant efficacy results favoring everolimus treatment (72). Additionally, in everolimus Phase 2 clinical trial in patients with predominantly clear-cell RCC, the median PFS was 11.2 months, and the median OS was 22.1 months; stable disease ≥3 months occurred in 73%, and stable disease lasting ≥6 months in 57% of patients (61). These clinical outcomes are consistent with the exposure-TGI model predicted typical tumor growth inhibition profiles for everolimus vs apitolisib illustrated in Figure 3.13. As presented in simulations of a typical patient with metastatic renal cell carcinoma (Figure 3.13), treatment efficacy decay due to emergence of tumor resistance occurs earlier and tumor re-growth is at a faster rate with apitolisib (dual pan-PI3K and mTORC1/2 inhibitor) compared to everolimus (mTORC1 inhibitor). Class I PI3Ks regulate a broad range of essential 87 functions including cellular metabolism and immune system functions (84). The more rapid emergence of tumor resistance is characteristic of what has been observed for PI3K inhibitors in the clinic due to development of signaling feedback loops which neutralizes PI3K inhibition (12, 14, 85). Therefore, with addition of pan-PI3K inhibition, there will be faster development of tumor resistance with apitolisib (dual pan-PI3K and mTORC1/2 inhibitor) compared to everolimus (mTORC1 inhibitor). These results (i.e. apitolisib efficacy decay) also further support the development of isoform-specific PI3K inhibitors, particularly in combination with other targeted agents, in treating patients with PI3K pathway dependent tumors. Based on our knowledge, this is the first report to quantitatively assess everolimus efficacy decay in patients with metastatic renal cell carcinoma using longitudinal exposure-tumor growth inhibition model. A pharmacodynamic model of tumor response has been developed previously that utilizes the everolimus dosing history and the tumor time course of each patient from the RECORD-1 trial to link everolimus dose to tumor size (86) and confirming that administering a daily 10 mg dose of everolimus is more effective in reducing tumor growth in mRCC patients compared to a daily 5 mg dose. However, the sustainability of response was not assessed with that model. By incorporating time-varying drug exposures (rather than dose), quantifying tumor growth and shrinkage rates, and estimating loss of efficacy constant (λ) that accounts for a decrease in Ks over time (due to appearance of tumor resistance) our model provided a comprehensive understanding of the temporal dynamics of treatment response. Additionally, based on our knowledge this is also the first clinical report to quantitatively assess TGI metrics for a dual PI3K/mTOR inhibitor in patients with metastatic renal cell carcinoma using longitudinal exposure-tumor growth inhibition model. The quantified differences between 88 everolimus (mTORC1 inhibitor) vs apitolisib (PI3K/mTORC1/mTORC2) efficacy decay, highlight the distinct characteristics of these two drugs in terms of their long-term efficacy in patients with mRCC. The current longitudinal exposure-tumor growth inhibition model developed has limitations due to limited number of patients used in analysis, which is reflected in the variability (RSE) of the model parameter estimates. Phase 1-2 oncology clinical trials face a critical limitation in their ability to assess the efficacy of new compounds due to the small cohorts of patients enrolled. However, by leveraging model-informed drug development (MIDD), general trends within the dataset can be assessed to provide meaningful insights from the available data and enable a deeper understanding of drug behavior and efficacy across broader patient populations. This approach not only compensates for the inherent constraints of limited patient cohorts in early-phase trials but also facilitates informed decision-making processes in drug development, ultimately advancing the development and optimization of novel oncology targeted therapeutics. 3.5 Conclusions The longitudinal exposure-tumor growth inhibition model developed provided a quantitative framework for evaluating the time-varying treatment effects, allowing for a comprehensive assessment and comparison of everolimus and apitolisib efficacy over time. The observed differences in on-treatment TGI metrics such as loss of treatment effect over time between the two drugs contributed to superior efficacy of everolimus compared to apitolisib. This finding emphasizes the importance of longitudinal exposure-tumor growth inhibition models and model informed drug development for targeted cancer therapy. Future studies should explore potential 89 mechanistic factors contributing to the divergent treatment outcomes observed in this study, such as patient genetic variations characteristics underlying tumor biology, to facilitate the development of personalized therapeutic approaches, optimize dosing regimens, and explore novel therapeutic combination strategies. 90 Chapter 4: Quantitative Characterization of the Effects of Fulvestrant Alone or in Combination with Taselisib (PI3Kinase Inhibitor) on Longitudinal Tumor Growth in Patients with Estrogen Receptor-positive, HER2-negative, PIK3CA-mutant, Advanced or Metastatic Breast Cancer Summary Breast cancer is the most common occurring cancer in women worldwide. Among cases of breast cancer, estrogen receptor-positive (ER+), PIK3CA-mutant, HER2- advanced breast cancer stands as a particularly complex clinical indication where approximately 40% of ER+/HER2- breast carcinomas present mutations in the PIK3CA gene. A significant hurdle in treating ER+ breast cancer lies in surmounting the challenges of endocrine resistance. In the clinical setting, a multifaceted approach is essential for this indication, one that not only explores the effectiveness of individual treatments but also delves into the potential gains in therapeutic outcome from combination therapies. In the current study, longitudinal tumor growth inhibition (TGI) models were developed to characterize tumor response over time in postmenopausal women with ER+/HER2- advanced or metastatic breast cancer undergoing treatment with fulvestrant alone or in combination with the PI3K inhibitor, taselisib. Impact of clinically relevant covariates on TGI metrics was assessed to identify patient subsets most likely to benefit from treatment with fulvestrant monotherapy or combination with taselisib. Tumor growth rate constant (Kg) was found to increase with increasing baseline tumor size and in the absence of baseline endocrine sensitivity. Further, Kg decreased in the absence of baseline liver metastases both in fulvestrant monotherapy and combination therapy with taselisib. Overall, additive/potentially synergistic 91 anti-tumor effects were observed in patients treated with the taselisib-fulvestrant combination. These results have important implications for understanding the therapeutic impact of combination treatment approaches and individualized responses to these treatments. Finally, this study emphasizes the importance of model informed drug development for targeted cancer therapy. 4.1 Introduction Breast cancer remains a formidable adversary in the field of oncology, with various subtypes presenting unique challenges for clinicians and researchers. Among these, estrogen receptor-positive (ER+), human epidermal growth factor receptor 2 negative (HER2-), phosphatidylinositol-4,5-bisphosphate 3-kinase catalytic subunit alpha (PIK3CA)-mutant advanced breast cancer stands as a particularly intricate clinical indication. Approximately 40% of ER+/HER2-breast carcinomas present mutations in the PIK3CA gene (93, 94). In the clinical setting, a multifaceted approach is essential for this indication, one that not only explores the effectiveness of individual treatments but also delves into the potential gains in therapeutic outcome that can be achieved through combination therapies. Endocrine therapy stands as the primary approach for managing ER+ breast cancer. Fulvestrant represents the first selective estrogen receptor (ER) down-regulator available in clinical oncology (87). Since fulvestrant is a pure antiestrogen with no agonistic effects leading to degradation of ER alpha, it shows efficacy in tamoxifen-resistant breast cancer models (87). In the Phase 3 study (FALCON), fulvestrant significantly prolonged progression-free survival (PFS) when compared to anastrozole in endocrine treatment-naïve patients with hormone receptor-positive, 92 HER2- advanced breast cancer (87). Nevertheless, a significant hurdle in treating ER+ breast cancer still lies in surmounting the challenges of endocrine resistance to prolong therapeutic efficacy (88). Fulvestrant serves as an ideal backbone for combination therapies because of to its distinctive mechanism of action and pharmacokinetic attributes (87). Preclinical investigations have revealed synergistic effects when combining fulvestrant with drugs that target signaling pathways associated with the emergence of endocrine resistance, such as the cyclin D/cyclin-dependent kinase 4-6/retinoblastoma pathway and the phosphatidylinositol-3-kinase (PI3K)/AKT/mammalian target of rapamycin (mTOR), contributing to overcoming or delaying endocrine resistance (87). PI3Ks are a group of kinases whose function are necessary for normal cell growth and proliferation (89). The PI3K/AKT signaling pathway assumes a pivotal role in numerous cellular processes governing growth, viability, mobility, and metabolism (90). Notably, somatic mutations affecting various constituents of the PI3K/AKT pathway manifest in a substantial proportion of approximately 70% of breast cancer cases. These mutations encompass alterations and amplifications in the catalytic (p110) subunits of PI3K, alongside mutations in key PI3K modulators like phosphatase and tensin homolog (PTEN), AKT, and mTOR (91, 92). Particularly, the PIK3CA gene exhibits mutations in nearly 40% of human breast cancers (93, 94). Majority of these aberrations clustered within the kinase (H1047R) and helical domains (E542K and E545K) of p110α, thereby triggering hyper-activation of PI3K (93, 94). Taselisib (GDC-0032) is a potent selective inhibitor of Class I PI3K α, δ and γ isoforms, with 30-fold less potent biochemical inhibition of the β isoform and increased potency in tumor cells 93 bearing mutant PI3K over wild-type PI3K cells (95-97). Nonclinical studies demonstrate that taselisib inhibits proliferation and induces apoptosis of PI3Kα-mutant breast cell lines, inhibits tumor growth in human breast xenograft models harboring PI3K mutations, and reduces downstream PI3K-pathway biomarkers, including pAKT, pPRAS40, and pS6. Results of in vitro combination studies indicated positive combination effects between taselisib and endocrine therapies. In the PIK3CA-mutant breast cancer cell line, taselisib alone caused growth inhibition. Effects on tumor growth were also observed in combination with letrozole and fulvestrant. However, in clinical setting numerous challenges persist in identifying the patient subsets most likely to benefit from this combination targeted therapy. Model-informed drug development (MIDD) plays a crucial role in modern pharmaceutical research, helping to optimize drug development processes and make informed decisions about potential therapies. Longitudinal tumor growth inhibition (TGI) models allow the assessment of tumor growth metrics and the anti-tumor efficacy of drugs in a quantitative and predictive manner. By leveraging these models, valuable insights on how drugs impact tumor growth can be gained for the selection of effective combination treatment regimens. MIDD not only streamlines the drug development process but also enhances our understanding of how drugs and drug combinations work in specific patient populations. The integration of MIDD represents a fundamental shift towards a more predictive and patient-centric approach in the pharmaceutical industry, underlining its potential to drive innovation, optimize resources, and significantly improve the efficiency and success rates of bringing new medicines to market (15). 94 In oncology, there is high attrition rate in Phase 3 trial which underscores the need for more quantitative approaches to improve the success rate of drugs (27). Longitudinal exposure-TGI models have been used to quantitatively characterize drugs’ efficacy. A recent study highlights the difference in overall efficacy of two targeted drugs due to the quantified treatment decay caused by emergence of tumor resistance (149). This emphasizes the importance of MIDD to support early clinical drug development for targeted cancer therapy. Furthermore, integration of MIDD can facilitate novel combination strategies to improve the success rate of developing targeted oncology compounds. The aim of the current study is to develop longitudinal tumor growth inhibition models in patients with ER+/HER2- breast cancer to characterize the efficacy of fulvestrant alone versus in combination with taselisib to inhibit tumor growth; to quantitate the extent of fulvestrant efficacy decay (caused by emergence of tumor resistance over time) alone versus in combination with taselisib; to assess the impact of potential clinically relevant covariates on TGI metrics; and to evaluate the extent of the interactions between fulvestrant and taselisib on anti-tumor efficacy. These analyses will help to advance development of fulvestrant-based treatment combinations with targeted PI3K inhibitors in patients with ER+/HER2- breast cancer. 4.2 Methods 4.2.1 Clinical Trial The SANDPIPER study (NCT02340221) was conducted in accordance with Good Clinical Practice guidelines and the Declaration of Helsinki. Prior to enrollment, written informed consent was acquired from all patients, in alignment with the approved protocols from the ethics 95 committees at each study site. All clinical trial information can be accessed through the following website. https://clinicaltrials.gov/. 4.2.2 Study Design and Data The SANDPIPER study, a pivotal Phase 3 clinical trial was a randomized, double-blind, placebo-controlled design, conducted across multiple international centers. Patients were administered 500 mg of fulvestrant intramuscularly, with initial dosing on days 1 and 15 of the first cycle, followed by day 1 in each subsequent 28-day cycle. This was combined with either a 4 mg oral daily dose of taselisib tablets or a placebo until disease progression or the emergence of unacceptable toxicity. Adjustments in taselisib or placebo dosages were permissible in response to treatment-related adverse effects, whereas fulvestrant dose interruptions (but not reductions) were allowed. Eligible participants, recruited from 155 centers spanning 28 countries, were postmenopausal females diagnosed with histologically or cytologically confirmed invasive, ER+ metastatic breast cancer or locally advanced inoperable breast cancer (98). According to treatment guidelines, patients were also candidates for endocrine therapy alone. Exclusion criteria encompassed prior exposure to fulvestrant, PI3K inhibitors, mammalian target of rapamycin inhibitors, or AKT (protein kinase B) inhibitors. Patient demographic and baseline characteristics has been previously published (98). Computed tomography (CT) or magnetic resonance imaging (MRI) scans were used to measure tumor lesions at baseline (within 28 days before cycle 1, day 1) and at regular intervals afterward (approximately every 8 weeks). Longitudinal tumor size data, defined as the sum of the longest diameters of target lesions at each visit according to RECIST 1.1 (30), were used for the 96 estimation of TGI metrics. Patients with at least baseline and one post-treatment tumor size measurements were defined as evaluable. Data from patients who only had baseline tumor assessments were excluded from the analysis. 4.2.3 Longitudinal Tumor Growth Inhibition Models 4.2.3.1 Base Fulvestrant and Fulvestrant+Taselisib Model Development Data from patients treated with fulvestrant alone was used in the development of Fulvestrant TGI Model. Data from patients treated with fulvestrant and taselisib was added later to develop Combination Therapy TGI Model. Graphical illustration of the structural model is provided in Figure 4.1. The process of model development is illustrated in Figure 4.2. The code for the models are provided in Appendix C. 4.2.3.2 Tumor Growth Dynamics For structural model development, several semi-mechanistic longitudinal tumor growth inhibition models with different tumor growth characteristics explored, such as exponential net growth, Gompertz growth model with maximum tumor burden (TSmx), and exponential drug induced tumor shrinkage for taselisib independent of net growth (31). Based on the objective function value (-2∙log-likelihood) and graphical diagnostics, a Gompertz growth model with maximum tumor burden was used in the model structure. TSmx was estimated initially and was fixed later to 1000 mm. 97 4.2.3.3 Fulvestrant TGI Model In the structural model, as discussed in the prior section, tumor growth was characterized by a Gompertz function. As fulvestrant pharmacokinetic data were not available, the anti-tumor rate associated specifically with the clinical efficacy of fulvestrant was utilized (Ks (fulvestrant)). Decay of efficacy caused by emergence of tumor resistance over time was introduced into the model as published previous by Claret et al., to describe the individual patients’ tumor size changes over time (29). The structure of the longitudinal TGI model for fulvestrant monotherapy is described using Equation 1. 𝑑(𝑇𝑆)𝑑𝑡 = [𝐾𝑔 × 𝐿𝑛 𝑇𝑆𝑚𝑥𝑇𝑆 (𝑡) × 𝑇𝑆 (𝑡)] − [𝐾𝑠 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡)(𝑡) × 𝑇𝑆 (𝑡)] 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 1 𝐾𝑠 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡) (𝑡) = 𝐾𝑠 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡),0 × 𝐸𝑋𝑃(−𝜆 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡) × 𝑡) where TS is the tumor size defined as the sum of longest diameters of target lesions based on investigator assessment, t is time, Kg is the estimated tumor growth rate constant, TSmx is maximum tumor size, Ks (fulvestrant) is the estimated tumor shrinkage rate constant for fulvestrant. Ks (fulvestrant),0 is the estimated value of Ks (fulvestrant) at time 0 corresponding to treatment initiation. λ (fulvestrant) is exponential decay constant to account for the loss of treatment effect over time for fulvestrant due to effect of dosing interruptions and/or development of tumor resistance. Additionally, tumor size at the start of treatment and in the absence of drug was estimated (TS0). 4.2.3.4 Combination Therapy TGI Model Fulvestrant monotherapy structural model (Equation 1) was modified to include the taselisib anti-tumor effect in order to characterize the additional data from patients treated with fulvestrant combined with taselisib. A sequential pharmacokinetic (PK)-TGI modeling approach incorporating individualized dosing records was used for describing taselisib to better estimate 98 the loss of treatment effect over time as there were many dose reductions and dose interruptions observed for taselisib. Taselisib pharmacokinetics data were obtained from previous taselisib studies where intensive pharmacokinetic sampling was performed over a dose range from 2 to 16 mg (data not shown). A two-compartment model was used to describe the pharmacokinetics of taselisib in a “typical” patient (Table 4.1). This taselisib pharmacokinetic model was used to predict taselisib systemic concentrations which served as the driver of taselisib effect in the longitudinal TGI model. A modification was made to the model such that taselisib tumor shrinkage rate was proportional to tumor growth rate in order to provide the best model fit to the tumor data as well as improve model stability. For subjects that only received fulvestrant, the taselisib model was not dosed when the model is fit to the tumor size data from those patients. The structure of the longitudinal TGI model is described using Equation 2. 𝑑(𝑇𝑆)𝑑𝑡 = [𝐾𝑔 × 𝐿𝑛 𝑇𝑆𝑚𝑥𝑇𝑆 (𝑡) × 𝑇𝑆 (𝑡)] − [𝐾𝑠 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡)(𝑡) × 𝑇𝑆 (𝑡)] − [𝐾𝑠 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏)(𝑡) × 𝐶 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏) (𝑡) × 𝑇𝑆 (𝑡)] 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 2 𝐾𝑠 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡) (𝑡) = 𝐾𝑠 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡),0 × 𝐸𝑋𝑃(−𝜆 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡) × 𝑡) 𝐾𝑠 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏)(𝑡) = 𝐾𝑠 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏),0 × 𝐸𝑋𝑃(−𝜆 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏) × 𝑡) 𝐾𝑠 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏),0 = 𝐾𝑔 × 𝛽 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏) where Ks (taselisib) is the estimated tumor shrinkage rate for taselisib. C (taselisib) is the longitudinal taselisib concentration predicted by the population PK model. Ks (taselisib),0 is the estimated value of Ks (taselisib) at time 0 corresponding to treatment initiation, and λ (taselisib) is exponential decay constant to account for the loss of treatment effect over time for taselisib. β (taselisib) is a constant relating Ks (taselisib),0 to Kg, and is representative of the sensitivity of the tumor response to taselisib. Tumor size at the start of treatment and in the absence of drug was also estimated (TS0). 99 Table 4.1 Population pharmacokinetics parameters for taselisib. A two-compartment model with first-order absorption, and first-order clearance was used to describe the pharmacokinetics of taselisib. Parameters (unit) Estimate (%RSE) Central volume (L) 165 (4.70) Peripheral volume (L) 35.2 (27.8) Clearance (L/hr) 3.02 (3.50) Inter-compartmental clearance (L/hr) 1.57 (46.8) First-order absorption rate constant (hr-1) 1.48 (12.0) Absorption Lag (hr) 0.416 (2.40) RSE = Relative Standard Error 4.2.3.5 Covariate Analysis The covariate Fulvestrant TGI Model and covariate Combination Therapy TGI Model were developed based on mechanistic and exploratory covariates listed on Table 4.2. Baseline continuous and categorical covariate statistics for the covariate model development are provided in Table 4.3 and Table 4.4, respectively. The mechanistic covariate in Table 4.2, the PIK3CA-mutation status on β(taselisib), was included in the base Combination Therapy TGI Model with no statistical evaluation performed since taselisib has greater in vitro efficacy against mutant PI3Kα isoforms and cells that express these mutations than those with wild-type PI3Kα (98). The exploratory covariates were evaluated using a stepwise covariate model building procedure (SCM) in two subsequent phases (99). The exploratory covariates were evaluated and retained in the model based on statistical significance (p<0.05 forward and p<0.01 backward) and if the parameter estimates were biologically reasonable. For estimation of covariate coefficients, the baseline/screening value of the covariates were used. Continuous covariates (e.g., baseline tumor size, age and body weight) were implemented as power model, and categorical covariates (e.g., liver metastases status and endocrine sensitivity status) were evaluated as a fractional change in 100 parameter value, in relation to the most common category, except for PIK3CA-mutation status which was implemented as categorical power model. Table 4.2 Covariates investigated during model development Covariate type Parameter Covariate a Mechanistic b β(taselisib) PIK3CAST Exploratory c, d Kg, Ks (fulvestrant), λ (fulvestrant), β(taselisib), λ (taselisib) SLDBL, AGE, BWT, BMI, ROWORLD, REGION, PRST, IXRSENDO, LOBULAR, DUCTAL, PRIORTAM, PIK3CAST, METLINE, BONEANY, BONE, LUNG, LIVER, PRIORCHM, PRIORADJ, PRIORNEO Kg= net tumor growth rate constant, Ks= tumor shrinkage rate constant, β = constant relating Ks (taselisib),0 to Kg, and is representative of the sensitivity of the tumor response to taselisib, λ = constant accounting for loss of treatment effect over time, PIK3CAST= phosphatidylinositol-4,5-bisphosphate 3-kinase catalytic subunit alpha (PIK3CA) mutation, SLDBL=observed baseline tumor size, BWT= body weight, BMI= Body mass index, PRST= progesterone receptor , IXRSENDO= Endocrine sensitivity, LOBULAR= lobular carcinoma, DUCTAL= Ductal carcinoma, BONEANY= Bone-only disease, BONE= Bone metastasis, LIVER= Baseline liver metastases, LUNG= Baseline lung disease, PRIORCHM= Prior chemotherapy, PRIORADJ=Prior adjuvant therapy, PRIORNEO= Prior neo-adjuvant therapy, PRIORTAM= Prior tamoxifen, ROWORLD= Rest of the world (Reference: Western Europe/USA/Canada/Australia and Asia Regions) a The baseline/screening value of the covariate was used b Power function: Categorical Mechanistic Covariate IF(COV.EQ.1) PARCOV = 1 ; Most common IF(COV.EQ.0) PARCOV = θ c Linear function: Categorical covariates (COV) IF(COV.EQ.1) PARCOV = 1 ; Most common IF(COV.EQ.0) PARCOV = (1 + θ) d Power function with normalized covariate: Continuous covariates IF(COV.EQ.1) PARCOV = 1 ; Most common IF(COV.EQ.0) PARCOV = θ PARCOV= ((COV/median)θ) 101 Table 4.3 Baseline continuous covariate statistics for covariates explored during development of the final model (Phase 3 analysis dataset). Continuous Variates Metric Fulvestrant Alone Fulvestrant + Taselisib Total Age (years) Median 61 61 61 Mean 61 60 60 SD 10 10 10 N 150 287 437 Body Weight (kg) Median 68 65 65 Mean 70 67 68 SD 15 15 15 N 150 287 437 BMI (kg/m2) Median 27 26 26 Mean 27 27 27 SD 5 6 5 N 150 287 437 Baseline Tumor Size (mm) Median 35 42 39 Mean 46 50 49 SD 37 36 37 N 150 287 437 N: number of patients (for continuous, with non-missing covariate value), SD: standard deviation, BMI= Body mass index 102 Table 4.4 Baseline categorical covariate statistics for covariates that were explored during development of the final model (Phase 3 analysis dataset). Categorical Covariates Categories Fulvestrant Alone N Fulvestrant + Taselisib N Total N PIK3CAST Mutation not detected 30 57 87 Mutation detected 120 230 350 PRST No 34 65 99 Yes 116 222 338 IXRSENDO Not Sensitive 37 79 116 Sensitive 113 208 321 LOBULAR No 119 241 360 Yes 31 46 77 DUCTAL No 36 61 97 Yes 114 226 340 BONEANY No 52 85 137 Yes 98 202 300 BONE No 143 271 414 Yes 7 16 23 LIVER No 75 135 210 Yes 75 152 227 LUNG No 83 149 232 Yes 67 138 205 PRIORCHM No 33 74 107 Yes 117 213 330 PRIORADJ No 76 152 228 Yes 74 135 209 PRIORNEO No 127 236 363 Yes 23 51 74 PRIORTAM No 72 155 227 Yes 78 132 210 ROWORLD No 95 194 289 Yes 55 93 148 N= number of patients, PIK3CAST= phosphatidylinositol-4,5-bisphosphate 3-kinase catalytic subunit alpha mutation , PRST= progesterone receptor , IXRSENDO= Endocrine sensitivity, LOBULAR= lobular carcinoma, DUCTAL= Ductal carcinoma, BONEANY= Bone-only disease, BONE= Bone metastasis, LIVER= Baseline liver metastases, LUNG= Baseline lung disease, PRIORCHM= Prior chemotherapy, PRIORADJ=Prior adjuvant therapy, PRIORNEO= Prior neo-adjuvant therapy, PRIORTAM= Prior tamoxifen, ROWORLD= Rest of the world (Reference: Western Europe/USA/Canada/Australia and Asia Regions) 103 4.2.3.6 Interaction TGI Model Interaction TGI Model was developed based on final Combination Therapy TGI Model (Equation 2) with fixed covariates to evaluate fulvestrant and taselisib interaction effect using Equation 3 which incorporates an additional parameter quantifying the interaction between fulvestrant and taselisib. 𝑑(𝑇𝑆)𝑑𝑡 = [𝐾𝑔 × 𝐿𝑛𝑇𝑆𝑚𝑥𝑇𝑆 (𝑡) × 𝑇𝑆 (𝑡)] − [(𝐾𝑠 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡)(𝑡)+ [𝐾𝑠 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏)(𝑡) × 𝐶 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏)(𝑡)]) × 𝑇𝑆(𝑡)]× 𝐼𝑁𝑇 Equation 3 where INT is the typical interaction between fulvestrant and taselisib, assuming INT=>1 is indicative of additive/potentially synergistic effect and INT<1 is a less than additive effect. Data from Phase 1 taselisib monotherapy (3-16 mg) in patients with locally advanced or metastatic hormone receptor-positive breast cancer (108) [clinicaltrials.gov: NCT01296555] was modeled separately (data not shown). The structurally similar longitudinal exposure-TGI model developed with this Phase 1 data estimated β (taselisib) for taselisib monotherapy. Subsequently, this taselisib monotherapy estimate was used to provide the initial value and upper boundary for estimation of the β (taselisib) in the Interaction TGI Model. Code for the Interaction TGI Model is provided in Appendix C. 104 Figure 4.1 Illustration of model structure for longitudinal tumor growth inhibition models. ka= taselisib first-order absorption rate constant, CL/F= taselisib apparent oral clearance, CLd/F= taselisib apparent inter-compartmental clearance, F= taselisib bioavailability, V1/F= taselisib apparent central volume of distribution, V2/F= taselisib apparent peripheral volume of distribution, Cp= taselisib plasma compartment, Ct= taselisib tissue compartment, Cp (taselisib)= taselisib plasma concentration, tlag= taselisib absorption lag time, Kg= net tumor growth rate constant, Ks= tumor shrinkage rate constant 105 Figure 4.2 Diagram illustrating the process of model development. Model differential equations and data used in the development of the various models are presented. Kg= net tumor growth rate constant, Ks = tumor shrinkage rate constant, C = plasma concentration, β = constant relating Ks (taselisib),0 to Kg, and is representative of the sensitivity of the tumor response to taselisib, TSmx= maximum tumor size, t = time, TS=tumor size, INT = typical interaction between fulvestrant and taselisib, Ln= natural logarithm Fulvestrant TGI Model 𝑑(𝑇𝑆)𝑑𝑡 = [𝐾𝑔 × 𝐿𝑛 𝑇𝑆𝑚𝑥𝑇𝑆 (𝑡) × 𝑇𝑆 (𝑡)] − [𝐾𝑠 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡)(𝑡) × 𝑇𝑆 (𝑡)] 𝐾𝑠 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡)(𝑡) = 𝐾𝑠 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡),0 × 𝐸𝑋𝑃(−𝜆 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡) × 𝑡) Data: Fulvestrant Monotherapy Treatment Cohort Combination Therapy TGI Model 𝑑(𝑇𝑆)𝑑𝑡 = [𝐾𝑔 × 𝐿𝑛 𝑇𝑆𝑚𝑥𝑇𝑆 (𝑡) × 𝑇𝑆 (𝑡)] − [𝐾𝑠 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡)(𝑡) × 𝑇𝑆 (𝑡)] − [𝐾𝑠 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏)(𝑡) × 𝐶 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏) (𝑡) × 𝑇𝑆 (𝑡)] 𝐾𝑠 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡)(𝑡) = 𝐾𝑠 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡),0 × 𝐸𝑋𝑃(−𝜆 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡) × 𝑡) 𝐾𝑠 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏)(𝑡) = 𝐾𝑠 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏),0 × 𝐸𝑋𝑃(−𝜆 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏) × 𝑡) 𝐾𝑠 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏),0 = 𝐾𝑔 × 𝛽(𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏) Data: Fulvestrant Monotherapy and Fulvestrant+Taselisib Combination therapy Treatment Cohort Interaction TGI Model 𝑑(𝑇𝑆)𝑑𝑡 = [𝐾𝑔 × 𝐿𝑛𝑇𝑆𝑚𝑥𝑇𝑆 (𝑡) × 𝑇𝑆 (𝑡)] − [(𝐾𝑠 (𝑓𝑢𝑙𝑣𝑒𝑠𝑡𝑟𝑎𝑛𝑡)(𝑡)+ [𝐾𝑠 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏)(𝑡) × 𝐶 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏)(𝑡)]) × 𝑇𝑆(𝑡)] × 𝐼𝑁𝑇 Data: Fulvestrant Monotherapy and Fulvestrant+Taselisib Combination therapy Treatment Cohorts 106 4.2.3.7 Models Internal Evaluation Models’ evaluation was based on the inspection of graphical diagnostics, including goodness-of-fit plots and visual predictive checks (VPC) as well as changes in the objective function value (OFV) provided by NONMEM, relative standard errors (RSE) and plausibility of the parameter estimate. 4.2.3.8 Models External Evaluation The final Combination Therapy TGI Model with covariates was externally evaluated with data from a Phase 1b/2 study of taselisib in combination with fulvestrant in patients with same tumor type (i.e. HER2-, hormone receptor-positive (HR+) advanced or metastatic breast cancer, n=23 patients) [clinicaltrials.gov: NCT01296555]. Study design and patients’ demographics were previously published (150,151). Patients were administered 500 mg of fulvestrant intramuscularly combined with 6 or 9 mg oral daily dose of taselisib. Baseline covariate statistics for external evaluation dataset is presented in Table 4.5. Final Combination Therapy TGI Model with covariates was evaluated using visual predictive check (VPC). The VPC was performed with 1000 simulations of the external evaluation dataset. 107 Table 4.5. Baseline covariate statistics for external evaluation dataset (Phase 1b/2 dataset). a) Continuous covariates Continuous Variates Metric Fulvestrant + Taselisib Age (years) Median 62 Mean 60 SD 12 N 23 Body Weight (kg) Median 69 Mean 71 SD 16 N 23 Baseline Tumor Size (mm) Median 52 Mean 56 SD 29 N 23 N: number of patients (for continuous, with non-missing covariate value), SD: standard deviation b) Categorical covariates Categorical Covariates Categories Fulvestrant + Taselisib N PIK3CAST Mutation not detected 8 Mutation detected 15 ERST No 4 Yes 19 PRST No 3 Yes 19 Missing 1 IXRSENDO Not Sensitive 4 Sensitive 19 LIVER No 11 Yes 12 HER2- No 2 Yes 20 Missing 1 N= number of patients, HER2-= human epidermal growth factor receptor 2 negative, PIK3CAST= phosphatidylinositol-4,5-bisphosphate 3-kinase catalytic subunit alpha mutation, ERST= estrogen receptor, PRST= progesterone receptor , IXRSENDO= Endocrine sensitivity, LIVER= Baseline liver metastases 108 4.2.4 Software The modeling analyses were performed using Nonlinear mixed effect models (NONMEM, version 7.4), with the first-order conditional estimation algorithm with interaction (100). Data management and further processing of NONMEM output were performed using R version 4.2.3 (101). 4.3 Results 4.3.1 Data Fulvestrant TGI Model was developed using a total of 704 tumor size observations from 150 postmenopausal women with ER+/HER2- advanced or metastatic breast cancer treated with fulvestrant monotherapy. Combination Therapy TGI Model included an additional 1441 tumor size observations from 287 postmenopausal women with ER+/HER2- advanced or metastatic breast cancer treated with fulvestrant in combination with taselisib (i.e. total of 2145 tumor size observations from 437 patients). Individual longitudinal time courses of tumor size data and tumor change from baseline are presented in Figure 4.3 and Figure 4.4. 109 Figure 4.3 Observed longitudinal individual tumor size data. Individual time courses of tumor size data of patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone (n=150) or in combination with 4 mg taselisib (n=287). Start of treatment indicated with dashed vertical line (red). 110 Figure 4.4 Observed longitudinal individual tumor size data change from baseline. Individual time courses of tumor size data of patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone (n=150) or in combination with 4 mg taselisib (n=287). 4.3.2 Longitudinal Tumor Growth Inhibition Models 4.3.2.1 Fulvestrant TGI Model Parameter estimates from the base and final covariate Fulvestrant TGI Model are presented in Table 4.6 and Table 4.7, respectably. Kg, Ks (fulvestrant) and λ (fulvestrant) parameters as well as their inter-individual variabilities were estimated for fulvestrant monotherapy. The base and final covariate TGI model for fulvestrant were found to adequately characterize tumor inhibition over time, accounting for fulvestrant efficacy decay. Models goodness-of-fit (GOF) plots indicated a good model fit as shown in plots of individual observed versus predicted tumor size presented in 111 Figure 4.5. Additionally, GOF plots of individual weighted residuals versus time also indicated a good model fit as shown in Figure 4.6 for base and covariate Fulvestrant TGI Model. Models were able to capture variety of tumor size-time profiles for patients treated with fulvestrant alone as demonstrated by representative individual fits shown in Figure 4.7. The anti-tumor effect of 500 mg fulvestrant expressed as Ks (fulvestrant) was greater than tumor growth rate constant (Kg) such that the predicted ratio of fulvestrant tumor shrinkage to tumor growth rate constant (i.e., Ks (fulvestrant)/Kg) was 2.53 and 2.88 for the fulvestrant base and covariate model, respectively. Both models predicted comparable baseline tumor size (TS0 = 36 mm). Table 4.6 Parameter estimates of the base Fulvestrant TGI Model for patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone Parameter Unit Estimate **90% CI **RSE (%) Shrinkage (%) TS0 mm 35.5 31.4, 39.0 6.59 - Kg week-1 0.0015 0.0008, 0.0022 28.1 - Ks (fulvestrant) week-1 0.0038 0.0021, 0.0060 29.9 - λ (fulvestrant) week-1 0.0064 0.0014, 0.0154 69.5 - Variance of additive residual variability - 23.2 22.2, 24.2 2.60 - IIV TS0 variance a 0.571 0.48, 0.716 12.8 4.0 IIV Kg variance a 1.90 1.18, 3.05 32.1 36.0 IIV Ks (fulvestrant) variance a 1.82 1.00, 2.67 26.4 41.1 IIV λ (fulvestrant) variance a 3.37 1.36, 9.17 73.3 78.9 **Obtained from Sampling Importance Resampling. CI= confidence interval, IIV= inter-individual variability, RSE=relative standard error, Kg= net tumor growth rate constant, Ks= tumor shrinkage rate constant, λ = constant accounting for loss of treatment effect over time, TS0=baseline tumor size a Coefficient of variation (CV) estimated for inter-individual variabilities: IIVTS0 = 0.756, IIVKg =1.378, IIVKs (fulvestrant) =1.349, IIVλ (fulvestrant) =1.836 112 Table 4.7 Parameter estimates of the final covariate Fulvestrant TGI Model for patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone Parameter Unit Estimate **90% CI **RSE (%) Shrinkage (%) TS0 mm 35.8 32.0, 39.3 6.31 - Kg week-1 0.00166 0.0009, 0.0026 32.0 - Ks (fulvestrant) week-1 0.00478 0.0028, 0.0072 28.1 - λ (fulvestrant) week-1 0.00667 0.0019, 0.0152 63.9 - SLDBL on Kg - 1.14 0.747, 1.66 25.2 - Liver (absence of metastases) on Kg a Relative change -0.408 c -0.577, -0.111 44.5 - IXRSENDO (absence of Endocrine sensitivity) on Kg a Relative change 0.536 c 0.077, 1.20 82.3 - Variance of additive residual variability - 22.9 22.0, 23.7 2.28 - IIV TS0 variance b 0.549 0.453, 0.700 13.6 4.10 IIV Kg variance b 0.989 0.630, 1.59 30.3 43.2 IIV Ks (fulvestrant) variance b 1.57 0.948, 2.38 26.3 39.8 IIV λ (fulvestrant) variance b 2.73 0.920, 7.20 69.9 78.4 **Obtained from Sampling Importance Resampling. CI= confidence interval, IIV= inter-individual variability, CV=coefficient of variation, RSE=relative standard error, Kg= net tumor growth rate constant, Ks= tumor shrinkage rate constant, λ = constant accounting for loss of treatment effect over time, TS0=baseline tumor size, SLDBL= observed baseline tumor size, LIVER= baseline liver metastases: Yes=Reference, IXRSENDO= endocrine sensitivity: Yes=Reference a Relative change versus presence of baseline liver metastases, and endocrine sensitivity status, respectably. b Coefficient of variation (CV) estimated for inter-individual variabilities: IIVTS0 = 0.741, IIVKg =0.994, IIVKs (fulvestrant) =1.253, IIVλ (fulvestrant) =1.652 c For categorical covariates 80% CI reported. 113 A) Base Model B) Covariate Model Figure 4.5 Fulvestrant TGI Model: observed tumor size data versus individual predictions from the tumor growth inhibition model. Observed versus model predicted individual tumor size data of patients with ER+/HER2- advanced or metastatic breast cancer (n=150) treated with 500 mg intramuscular fulvestrant alone for base model (A) and covariate model (B). Individual data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Line of identity (black) was included as reference for observed vs model predicted. 114 A) Base Model B) Covariate Model Figure 4.6 Fulvestrant TGI Model: individual weighted residuals versus time from the tumor growth inhibition model. Patients with ER+/HER2- advanced or metastatic breast cancer (n=150) treated with 500 mg intramuscular fulvestrant alone for base model (A) and covariate model (B). Individual data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Black dashed lines included as reference. 115 Figure 4.7 Fulvestrant TGI Model: representative individual patients fit (n=12). Individual data points are indicated by black circles. Black line is the individual predictions from the model. The covariate analysis (SCM) identified the following covariate effects: tumor growth rate constant (Kg) was dependent on baseline tumor size (SLDBL), baseline liver metastases (LIVER) and baseline endocrine sensitivity status (IXRSENDO). The exponent for the effect of baseline tumor size on Kg (1.14) suggests a higher growth rate for larger baseline tumor size. Tumor growth rate constant was 40.8% lower in the absence of baseline liver metastases and increased 53.6% in the absence of baseline endocrine sensitivity status (relative change compared to reference). The distribution of inter-individual variability (IIV) for Kg versus these covariates from the base and final fulvestrant covariate model is presented in Figure 4.8, demonstrating that the impact of identified covariates on Kg is accounted for in the final covariate model. 116 Figure 4.8 Distribution of net tumor growth rate constant (Kg) inter-individual variability vs covariates for the Fulvestrant TGI Model. Distribution of inter-individual variability (IIV) for Kg versus baseline tumor size (SLDBL), baseline liver metastases and endocrine sensitivity from the base and covariate Fulvestrant TGI Model. Pearson method was used to assess the correlation between IIV Kg and baseline tumor size. Baseline liver metastases: 0= absence of liver metastases, 1= presence of liver metastases. Baseline endocrine sensitivity: 0= absence of endocrine sensitivity, 1= presence of endocrine sensitivity. *** indicates a high level of statistical significance Base Model Covariate Model 117 Furthermore, best overall response was assessed by investigators according to RECIST 1.1. Figure 4.9 presents boxplots of fulvestrant tumor shrinkage rate constant versus best overall response. Responders (partial response) and patients with stable disease had higher tumor shrinkage rate constant compared to non-responder group (progressive disease). Figure 4.9 Fulvestrant TGI Model: relationships between individual fulvestrant tumor shrinkage rate constant and best overall response. Fulvestrant tumor shrinkage rate constant (Ks (fulvestrant)) versus individual patients’ best overall response assessed by investigators at the end of the study based on Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 presented. The y-axis is on natural log scale. PD= progressive disease, PR= partial response, SD= stable disease 118 4.3.2.2 Combination Therapy TGI Model Parameter estimates from the base and final covariate Combination Therapy TGI Model are presented in Table 4.8 and Table 4.9, respectively. Baseline tumor size (TS0), tumor growth rate constant (Kg), fulvestrant tumor shrinkage rate constant (Ks (fulvestrant)), sensitivity of the tumor response to taselisib (β (taselisib)), and drug efficacy decay rate constants for fulvestrant and taselisib (λ (fulvestrant) and λ (taselisib)) as well as their inter-individual variabilities were estimated. Models adequately characterize the tumor inhibition over time, accounting for each drug efficacy decay and time-varying taselisib exposures. Goodness-of-fit plots indicated a good model fit for base and covariate models as shown in plots of individual observed versus predicted tumor size (Figure 4.10), individual weighted residuals versus time (Figure 4.11) and representative individual fits (Figure 4.12). Model estimated parameter for baseline tumor size (TS0, in the absence of drugs) correlated well with observed individual data as presented in the Figure 4.13. Visual predictive check of the final model stratified by treatment (fulvestrant monotherapy vs combination therapy with taselisib) shows that the model captured the central tendency, extreme values as well as the variability in the observed tumor size data (Figure 4.14). 119 Table 4.8 Parameter estimates of the base Combination Therapy TGI Model for patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone or in combination with 4 mg taselisib Parameter Unit Estimate **90% CI **RSE (%) Shrinkage (%) TS0 mm 37.9 36.0, 40.2 3.47 - Kg week-1 0.0028 0.0021, 0.0034 14.0 - Ks (fulvestrant) week-1 0.0070 0.0054,0.0089 17.3 - λ (fulvestrant) week-1 0.0028 0.0011, 0.0066 60.7 - β (taselisib) mg-1.L 158 121, 210 17.1 - λ (taselisib) week-1 0.117 0.0912, 0.1592 17.6 - PIK3CA(no mutation) on β (taselisib) - 0.659 0.430, 0.966 26.5 Variance of additive residual variability - 21.7 21.1, 22.3 1.83 - IIV TS0 variance a 0.533 0.481, 0.600 6.98 4.30 IIV Kg variance a 1.06 0.772, 1.40 18.4 30.6 IIV Ks (fulvestrant) variance a 1.02 0.744, 1.36 18.8 42.7 IIV λ (fulvestrant) variance a 4.21 2.07, 8.79 50.3 83.1 IIV β(taselisib) variance a 0.75 0.403, 1.08 27.3 46.9 IIV λ (taselisib) variance a 0.347 0.090, 0.776 58.9 64.7 **Obtained from Sampling Importance Resampling. CI= confidence interval, IIV= inter-individual variability, RSE=relative standard error, Kg= net tumor growth rate constant, Ks= tumor shrinkage rate constant, λ = constant accounting for loss of treatment effect over time, TS0=baseline tumor size, β (taselisib)= constant relating Ks (taselisib),0 to Kg, and is representative of the sensitivity of the tumor response to taselisib a Coefficient of variation (CV) estimated for inter-individual variabilities: IIVTS0 = 0.730, IIVKg =1.030, IIVKs (fulvestrant) =1.010, IIVλ (fulvestrant) =2.052 , IIVβ(taselisib) = 0.866 , IIVλ (taselisib)=0.589 120 Table 4.9 Parameter estimates of the final covariate Combination Therapy TGI Model for patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone or in combination with 4 mg taselisib Parameter Unit Estimate **90% CI **RSE (%) Shrinkage (%) TS0 mm 38.1 35.6, 40.3 3.64 - Kg week-1 0.00321 0.0024, 0.0039 13.5 - Ks (fulvestrant) week-1 0.00764 0.0059, 0.0093 13.8 - λ (fulvestrant) week-1 0.00453 0.0019, 0.0077 39.5 - β (taselisib) mg-1.L 160 142, 176 6.50 - λ (taselisib) week-1 0.131 0.104, 0.165 14.5 - PIK3CA(no mutation) on β(taselisib) - 0.661 0.399, 0.937 24.6 - SLDBL on Kg - 0.624 0.454, 0.832 18.5 - Liver(absence of metastases) on Kg a Relative change -0.548 -0.650, -0.446 11.0 - IXRSENDO(absence of Endocrine sensitivity) on Kg a Relative change 0.386 0.062, 0.731 52.9 - PRST(absence of progesterone Receptor) on β(taselisib) a Relative change -0.382 -0.574, -0.139 34.7 - Variance of additive residual variability - 22.0 21.5, 22.5 1.42 - IIV TS0 variance b 0.527 0.463, 0.604 8.22 4.0 IIV Kg variance b 0.784 0.590, 1.01 16.2 37.2 IIV Ks (fulvestrant) variance b 1.08 0.825, 1.35 15.3 38.8 IIV λ (fulvestrant) variance b 2.58 1.22, 4.97 44.4 81.2 IIV β(taselisib) variance b 0.42 0.186, 0.678 35.8 60.1 IIV λ (taselisib) variance b 0.455 0.199, 0.823 41.8 63.5 **Obtained from Sampling Importance Resampling. CI= confidence interval, IIV= inter-individual variability, RSE=relative standard error, Kg= net tumor growth rate constant, Ks= tumor shrinkage rate constant, λ = constant accounting for loss of treatment effect over time, TS0=baseline tumor size, β (taselisib) = constant relating Ks (taselisib),0 to Kg, and is representative of the sensitivity of the tumor response to taselisib, SLDBL= observed baseline tumor size, LIVER= baseline liver metastases: Yes=Reference, IXRSENDO= endocrine sensitivity: Yes=Reference, PRST= progesterone receptor: Yes=Reference a Relative change versus baseline liver metastases, endocrine sensitivity and progesterone receptor expression status, respectably. b Coefficient of variation (CV) estimated for inter-individual variabilities: IIVTS0 = 0.726, IIVKg =0.885, IIVKs (fulvestrant) =1.039, IIVλ (fulvestrant) =1.606, IIVβ(taselisib) = 0.648, IIVλ(taselisib)=0.675 121 A) Base Model B) Covariate Model Figure 4.10 Combination Therapy TGI Model: observed tumor size data versus individual predictions from the tumor growth inhibition model. Observed versus model predicted individual tumor size data of patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone (left panels, n=150) or in combination with 4 mg taselisib (right panels, n=287) for base model (A) and covariate model (B). Individual data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Line of identity (black) was included as reference for observed vs model predicted. 122 A) Base Model B) Covariate Model Figure 4.11 Combination Therapy TGI Model: individual weighted residuals versus time from the tumor growth inhibition model, stratified by treatment. Patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone (left panels, n=150) or in combination with 4 mg taselisib (right panels, n=287) for base model (A) and covariate model (B). Individual data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Black dashed lines included as reference. 123 A) Fulvestrant alone B) Fulvestrant combination with taselisib Figure 4.12 Combination Therapy TGI Model: representative individual patients fit (n=12 per treatment group), stratified by treatment. Patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone (A) or in combination with 4 mg taselisib (B). Individual data points are indicated by black circles. Black line is the individual predictions from the model. 124 Figure 4.13 Combination Therapy TGI Model: observed baseline tumor size data versus individual baseline tumor size predictions (TS0) from the tumor growth inhibition model, stratified by treatment. Observed versus model predicted individual baseline tumor size data of patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone (left panel, n=150) or in combination with 4 mg taselisib (right panel, n=287). Individual data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Line of identity (black) was included as reference for observed vs model predicted tumor size. 125 Figure 4.14 Combination Therapy TGI Model: visual predictive check of tumor size data versus time, for the final model stratified by treatment. The black solid line and upper and lower black dash lines represent the median, 5th and 95th percentiles of the observations, respectively; the shaded blue and red areas represent the 95% confidence interval of the median, 5th and 95th percentiles predicted by the model. The observed data are indicated by circles. 126 The estimated initial anti-tumor effect (Ks,0) prior to tumor tolerance development was 0.0076 week-1 and 0.0283 week-1 for fulvestrant and taselisib, respectably. To compare initial anti-tumor effect of taselisib and fulvestrant (i.e. prior to development of tumor resistance), 𝐾𝑠 (𝑡𝑎𝑠𝑒𝑙𝑖𝑠𝑖𝑏),0 was estimated based on average steady-state taselisib concentration (Cave,ss = 0.0552 mg/L). The initial anti-tumor effect of fulvestrant was 3.71-fold lower compared to taselisib for the fulvestrant-taselisib treatment cohort. Final model estimated drug efficacy decay over time was 0.0045 week-1 and 0.131 week-1 for fulvestrant and taselisib, respectively (Table 4.9). In the combination cohort, taselisib efficacy decay was estimated to occur at a more rapid rate compared to fulvestrant. In patients given both fulvestrant and taselisib, the taselisib exposure was more variable when compared to that of fulvestrant due to a high rate of dose reductions (36.5%) and dose interruptions with taselisib administration. The sequential PK-TGI modeling approach integrated time-varying taselisib exposures based on patients’ actual dosing records and account for tolerability and safety events observed (i.e. individual patients dosing modification or dosing interruptions were captured). Hence, the λ (taselisib) parameter estimate captures possible development of tumor resistance over time. For fulvestrant, pharmacokinetic data were not available. Fulvestrant dose reduction was not allowed and fulvestrant dose interruptions observed due to serious adverse events was very low in patients (less than 5% in the fulvestrant cohort). This exposure reduction was accounted for in the model by λ (fulvestrant) parameter estimate in addition to possible emergence of tumor resistance. Based on a significant change in the model objective function value (-2∙log-likelihood) of -27.48, the estimated IIV for λ (fulvestrant) was added to the base model, however shrinkage impact should be considered when drawing conclusions (76). 127 The impact of baseline covariates on the tumor dynamics were evaluated (SCM) and significant covariates were determined. Consistent with Fulvestrant TGI Model (i.e. fulvestrant monotherapy), in the Combination Therapy TGI covariate model tumor growth rate constant (Kg) was dependent on baseline tumor size (SLDBL), liver metastases (LIVER) and endocrine sensitivity status (IXRSENDO). The exponent for the effect of baseline tumor size on Kg was 0.624. Kg decreased 54.8% in the absence of baseline liver metastases and increased 38.6% in the absence of baseline endocrine sensitivity status. Distribution of inter-individual variability for Kg versus these covariates from the base and final Combination Therapy TGI Model is presented in Figure 4.15, demonstrating that the impact of identified covariates on Kg is accounted for in the final covariate model. Additionally, β (taselisib) decreased 33.9% in the absence of PIK3CA-mutation, and was lower by 38.2% in the absence of progesterone expression status at baseline (PRST). 128 Base Model Covariate Model Figure 4.15 Distribution of net tumor growth rate constant (Kg) inter-individual variability vs covariates for the Combination Therapy TGI Model. Distribution of inter-individual variability (IIV) for Kg versus baseline tumor size (SLDBL), baseline liver metastases and endocrine sensitivity from the base and covariate Combination Therapy TGI Model. Pearson method was used to assess the correlation between IIV Kg and baseline tumor size. Baseline liver metastases: 0= absence of liver metastases, 1= presence of liver metastases. Baseline endocrine sensitivity: 0= absence of endocrine sensitivity, 1= presence of endocrine sensitivity. *** indicates a high level of statistical significance 129 Figure 4.16 presents boxplots of individual β (taselisib) versus best overall response. Responders (complete and partial response) and patients with stable disease had higher sensitivity to taselisib and consequently more tumor shrinkage compared to non-responder group (progressive disease). Figure 4.16 Relationships between β (taselisib) and best overall response. Patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant in combination with 4 mg taselisib. Individual patients’ best overall response assessed by investigators at the end of the study based on Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 presented. The y-axis is on natural log scale. β (taselisib) = representative of the sensitivity of the tumor response to taselisib, CR = complete response, PD = progressive disease, PR = partial response, SD = stable disease 130 Figure 4.17 presents boxplots comparing baseline tumor size observed in fulvestrant monotherapy compared to fulvestrant combination therapy with taselisib. Approximately similar baseline tumor sizes were observed across both treatment groups. However, comparing the exponent for the effect of baseline tumor size on Kg in Fulvestrant TGI Model (1.14) with Combination Therapy TGI Model (0.624), the impact changed by approximately 2-fold; which indicates slower tumor growth in patients with larger baseline tumor size in taselisib-fulvestrant combination cohort. Figure 4.17 Boxplots of observed individual baseline tumor size for patients treated with fulvestrant (n=150) and fulvestrant+taselisib (n=287). Individual observed baseline tumor size data of patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant alone or in combination with 4 mg taselisib. Dash line is the median baseline tumor size (39 mm) across both treatment cohorts. 131 Correlation of the inter-individual variability (IIV) values from the final covariate Combination Therapy TGI model is presented in Figure 4.18. For assessment of the IIV correlation between taselisib and fulvestrant TGI metrics, Kendall method was used and data from fulvestrant monotherapy cohort was removed. There was positive correlation (0.45) between inter-individual variabilities of β(taselisib) and fulvestrant tumor shrinkage rate constant. Alternatively, negative correlation (-0.48) was observed for the inter-individual variabilities of fulvestrant tumor shrinkage rate constant and taselisib loss of treatment effect over time. These correlation relations between fulvestrant and taselisib individualized responses variabilities (i.e. TGI metrics IIVs), supports the positive anti-tumor interactions for combination of these two drugs and provides insights into positive and potential additive anti-tumor combination effect. 132 Figure 4.18 Correlation plot of inter-individual variability for the final Combination Therapy TGI Model. Matrix plot of the correlation of the parameters inter-individual variability (IIV) values from the final covariate Combination Therapy TGI Model for fulvestrant in combination with taselisib. Kendall method was used to assess correlation. Fulvestrant monotherapy treatment cohort data was excluded. *** indicates a high level of statistical significance 4.3.2.3 Interaction TGI Model The Interaction TGI Model was developed based on fulvestrant monotherapy and combination therapy with taselisib data from Phase 3 SANDPIPER study (i.e. 2145 tumor size observations from 437 patients) using final Combination Therapy TGI Model with fixed covariates. This model quantified the extent of the interaction (INT) between fulvestrant and taselisib efficacy (Equation 3). Model code for the Interaction TGI Model is provided in Appendix C. The Interaction TGI Model estimated typical interaction parameter [INT] (RSE%) was 2.01 (16.4%), 133 with 95% confidence interval of 1.365 to 2.655 suggesting additivity/ potential synergism of the combination. Goodness-of-fit plots indicated a good model fit as shown in individual weighted residuals versus time (Figure 4.19) and representative individual fits (Figure 4.20). Figure 4.19 Individual weighted residuals versus time since first dose, from the Interaction TGI Model. Patients with ER+/HER2- advanced or metastatic breast cancer treated with 500 mg intramuscular fulvestrant in combination with 4 mg taselisib. Individual data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Black dashed lines (-2, 0, 2) included as reference for goodness of fit. 134 Figure 4.20 Interaction TGI Model: representative individual patients fits (n=12). Individual data points are indicated by black circles. Black line is the individual predictions from the model. 4.3.2.4 Model External Evaluation Phase 1b/2 clinical trial data (fulvestrant treatment in combination with taselisib in patients with HR+/HER2- advanced or metastatic breast cancer) was utilized for external evaluation of the final Combination Therapy TGI Model with covariates. Goodness of fit plots indicated that the model reliably predicted the external observed data (with MAXEVAL=0), as shown in plots of individual observed tumor size from external study versus predicted tumor size (Figure 4.21), individual weighted residuals versus time (Figure 4.22) and representative patients’ time courses of tumor size data predicted by the model (Figure 4.23). 135 Figure 4.21 External evaluation of Combination Therapy TGI Model: observed tumor size data from external study (Phase 1b/2) versus individual predictions from the Combination Therapy TGI Model with covariates (MAXEVAL=0). Observed versus model predicted individual tumor size data from patients with HR+/HER2- advanced breast cancer treated with 500 mg intramuscular fulvestrant in combination with 6-9 mg oral taselisib. Individual data points are indicated by black open circles. Loess trend line (red) was used as a fitting diagnostic. Line of identity (black) was included as reference for external observed data vs model predicted tumor size. 136 Figure 4.22 External evaluation of Combination Therapy TGI Model: individual weighted residuals (Phase 1b/2 external data) versus time from the Combination Therapy TGI Model with covariates (MAXEVAL=0). Patients with HR+/HER2- advanced breast cancer treated with 500 mg intramuscular fulvestrant in combination with 6-9 mg oral taselisib. Individual data points are indicated by black open circles. Loess trend line (red) was used as fitting diagnostics. Black dashed lines included as reference. 137 Figure 4.23 External evaluation of Combination Therapy TGI Model: representative patients observed tumor size data (n=12, Phase 1b/2 external data) versus individual predictions from the Combination Therapy TGI Model with covariates (MAXEVAL=0). Patients with HR+/HER2- advanced breast cancer treated with 500 mg intramuscular fulvestrant or in combination with 6-9 mg oral taselisib. Individual data points are indicated by black circles. Black line is the individual predictions from the model (MAXEVAL=0). 138 Figure 4.24 presents the external evaluation visual predictive check (VPC) of Combination Therapy TGI Model with covariates (n=1000 simulations). The external observed tumor size data from Phase 1b/2 study was adequately described by the model (median as well as 90% prediction interval). Figure 4.24 External evaluation of Combination Therapy TGI Model: visual predictive check of tumor size data from external study (Phase 1b/2) versus time for the Combination Therapy TGI Model with covariates. The observed external tumor size data are displayed versus time. The solid red and upper and lower blue lines represent the median, 5th and 95th percentiles of the observations, respectively; the shaded red and blue areas represent the 95% confidence interval of the median, 5th and 95th percentiles predicted by the model. The observed data are indicated by open circles. 139 4.4 Discussion Tumors in breast cancer commonly exhibit characteristics of estrogen receptor positive (ER+) and human epidermal growth factor receptor negative (HER2-), suggesting potential responsiveness to endocrine therapy. Despite substantial advancements in endocrine therapy over recent decades, the persistent emergence of endocrine resistance continues to pose a significant challenge in the management of this tumor subtype (102). This has led to development of spectrum of novel targeted therapies with the potential to circumvent or preempt endocrine resistance; nonetheless, numerous challenges persist in identifying the patient subsets most likely to benefit from these new targeted agents (102). Fulvestrant is the first selective estrogen receptor down-regulator (SERD) that exhibits evident efficacy as a monotherapy, however, its potential role in treating ER+ breast cancer is increasingly considered in the context of combination therapy (103). PI3K/AKT/mTOR pathway is one of main target for combination endocrine therapy since activation of this pathway demonstrated a major role in instigating resistance to endocrine treatment (104). This resistance mechanism can be attributed to either mutations in or up-regulation of the PIK3CA gene (103). PIK3CA mutations (i.e. gene encoding the p110α catalytic subunit of PI3K) are prevalent in luminal breast cancer and frequently induce constitutive activity of the enzyme (105). Preclinical investigations have demonstrated synergistic effects and delayed onset of endocrine resistance when combining fulvestrant with PI3K inhibitors (106, 107). However, the application of pan-PI3K inhibitors, while displaying efficacy, has been hindered by their associated toxicity profile (87). The inactivation of various PI3K isoforms can lead to 140 diverse side effects, including hyperglycemia, rash, elevated liver enzymes, and mood disorders, thereby limiting the tolerability of these agents. Consequently, ongoing research efforts are exploring combinations of fulvestrant with more selective inhibitors targeting the α-catalytic subunit of PI3K, which have exhibited activity against PIK3CA-mutant tumors, exemplified by the approved agent alpelisib (108, 109). The Phase 3 SANDPIPER study investigated the efficacy of potent, selective PI3K inhibitor taselisib (a beta-sparing PI3K inhibitor active on mutant PIK3CA) when combined with fulvestrant in locally advanced or metastatic breast cancer patients with ER+/ HER2- tumors mostly harboring PIK3CA mutations. The results showed a significant improvement in median progression-free survival in the taselisib-fulvestrant cohort (7.4 months) compared to the fulvestrant monotherapy cohort (5.4 months) (98). However, increased rate of serious adverse events (grade ≥3) were observed in combination cohort, primarily gastro-intestinal issues and hyperglycemia, attributed to the partial inhibition of delta and gamma PI3K isoforms by taselisib (110). As a result, taselisib required more frequent dose reductions (36.5%) compared to fulvestrant (2.3%) (110). Ultimately, although SANDPIPER trial attained its primary endpoint (stratified hazard ratio of 0.70 (95% CI: 0.56-0.89) for taselisib plus fulvestrant treatment group versus fulvestrant monotherapy cohort), taselisib safety profile deemed clinically impractical. Based on our knowledge, this is the first report to quantitatively assess tumor growth inhibition based on tumor size data of fulvestrant alone and in combination with a PI3K inhibitor in patients with ER+/HER2- tumors. The tumor growth inhibition models developed based on tumor size data from the SANDPIPER study adequately characterized tumor response over time 141 in postmenopausal women with ER+/HER2- advanced or metastatic breast cancer undergoing treatment with 500 mg intramuscular fulvestrant alone or in combination with 4 mg taselisib. The structural TGI models developed, integrated a Gompertz growth model characterized by a proliferation rate that is restricted by a maximum tumor burden. This structural tumor growth model for breast cancer is supported by cellular kinetics studies which consistently revealed that, typically, tumor expansion undergoes a period of restriction following an initial exponential phase of growth (111, 112). Previous publication on a TGI model developed for patients with metastatic breast cancer undergoing treatment with capecitabine and/or docetaxel also included a Gompertz growth (113). To account for taselisib tolerability and safety events observed, the Combination Therapy TGI Model and Interaction TGI Model structurally integrated time-varying taselisib exposures based on patients’ actual dosing records. Additionally, loss of treatment effect over time was estimated for taselisib due to possible emergence of tumor resistance. For fulvestrant, the PK data was not available. Hence, the estimated fulvestrant efficacy decay over time was due to possible development of tumor resistance, in addition to effect of dosing interruptions. However, fulvestrant incidents of dose interruptions observed due to serious adverse events was lower in patients (serious adverse events, fulvestrant: 8.9% vs taselisib: 32.0%) and fulvestrant dose reduction was not allowed. Therefore, models estimated fulvestrant efficacy decay over time is most likely due to the emergence of tumor resistance. Furthermore, the fulvestrant efficacy decay estimate from the base Combination Therapy TGI Model (0.0028 week-1) was 2-fold less that the estimate from the base Fulvestrant TGI Model (0.0064 week-1) consistent with a reduction in 142 fulvestrant resistance when combined with a PI3K inhibitor. This is in agreement with prior preclinical studies that demonstrated synergistic effects when combining fulvestrant with PI3K inhibitors (106). Moreover, clinically it has been reported that most patients with ER+ metastatic breast cancer treated with endocrine therapy will develop endocrine resistance, and activation of several signaling pathways such as PI3K have been described as the drivers of resistance to endocrine treatment (114-116). Covariate analysis was conducted to quantitate the impact of patient baseline characteristics on TGI metrics. Baseline tumor size, baseline endocrine sensitivity (not sensitive compare to reference: sensitive endocrine status) and baseline liver metastases (absence of liver metastases compare to reference: liver metastases status) were identified as statistically significant covariates of Kg. In both cohorts (i.e. fulvestrant monotherapy and combination therapy with taselisib), Kg increased with increasing baseline tumor size, indicating that larger baseline tumor size are more difficult to treat. This is in accordance with a recent consensus review published, that signified primary tumor size as a prognostic factor associated with both short and long term prognosis in HR+/HER2- breast cancer patients (117). Previous studies also demonstrated in patients with breast cancer that have extensive nodal status (with or more than nine positive lymph nodes), tumor size is a prognostic factor independent of other factors, such as estrogen receptor, progesterone receptor, HER2, and disease severity (118). Furthermore, in both treatment groups, Kg increased in the absence of baseline endocrine sensitivity; and decreased in the absence of baseline liver metastases. The influence of these covariates on Kg is consistent with previous observations in patients with breast cancer. Presence of liver metastases is predictive of poor outcome in metastatic breast cancer and high risk of disease progression (119). 143 In alignment with our covariate analysis results, previous studies also found a significant association between liver metastasis with poor tumor response (120), progression-free survival and overall survival (OS) (102, 117, 119, 121-123). Additionally, a prior study that investigated baselines characteristics that affect the survival benefit derived from palbociclib-fulvestrant combination in patients with HR+/HER2- breast cancer (PALOMA-3 trial), similarly identified endocrine sensitivity as prognostic factor (124). In the Combination Therapy TGI Model, the absence of baseline progesterone receptor expression was identified as statistically significant covariate of taselisib tumor shrinkage rate (reduced taselisib shrinkage rate) in patients treated with fulvestrant combined with taselisib. Independent expression level of progesterone receptor is an observed prognostic factor in HR+/HER2- breast cancer (125-128). Progesterone receptor expression levels have been reported to be positively associated with OS (117, 129). The absence or low (<20%) expression of progesterone receptor, even in the presence of estrogen receptor expression, represents a negative prognostic factor, potentially indicative of uncertain endocrine sensitivity (117). Several studies have suggested that progesterone receptor carries independent prognostic information in addition to estrogen receptor, particularly in premenopausal breast cancer patients (117, 130, 131). In the current study, the Combination Therapy TGI Model developed has a limitation wherein the potential synergistic impact of the combination of taselisib and fulvestrant on tumor growth inhibition was not individually assessed for each drug in the combination treatment group; instead, it was consolidated with anti-tumor effect of PI3Kinase inhibition (reflected in 144 β (taselisib)). To better quantitate the combination effect of two drugs, the Interaction TGI Model was developed, which estimated the interaction between fulvestrant and taselisib. The typical interaction estimated parameter was 2.01 (95% confidence interval (CI): 1.365 to 2.655) which is suggestive of at least an additive if not a potential synergistic effect. Exploratory analysis of TGI metrics (Figure 4.18) revealed positive correlation (0.45) between β (taselisib) and fulvestrant tumor shrinkage rate constant inter-individual variabilities (i.e. indicative of patients’ individualized response), which is consistent with the additive/potential synergistic anti-tumor effect of these two drugs in ER+/HER2- breast cancer population. Prior preclinical studies also support this hypothesis. Studies reported that combination of alpelisib (PI3Kα inhibitor) with fulvestrant had synergistic antitumor activity as compared with either agent alone in PIK3CA-mutated, ER+ xenograft models (106, 132). Furthermore, in a preclinical study which investigated the effects of PI3Kα inhibition on the ER signaling pathway, the inhibition of the PI3K pathway triggered the activation of the ER-dependent transcription, which subsequently limited the efficacy of PI3K inhibition (106); study reported that fulvestrant markedly sensitized ER+ tumors to PI3Kα inhibition, resulting in major tumor regressions in vivo (106). Investigators proposed that combined PI3K and ER inhibition is a rational approach to target these tumors (106). Overall, the population-based tumor growth inhibition models developed effectively captured the complex aspects inherent to combination therapy, allowing for the quantification of critical TGI metrics related to the assessment of inter-individual variability among patients. This approach could be a powerful tool to select the most advantageous combination therapies with fulvestrant or to design more efficient and safer clinical trials by optimizing the drug regimen and dose 145 modifications for PI3K inhibitor treatment. The external evaluation based on data from Phase 1b/2 clinical trial provided further validation of the models. The final Combination Therapy TGI Model with covariates adequately described the external data, supporting the utility of model-informed drug development for early/interim evaluation of treatments efficacy. 4.5 Conclusion The final Fulvestrant TGI Model and Combination Therapy TGI Model adequately characterized tumor response over time in postmenopausal women with ER+/HER2- advanced or metastatic breast cancer undergoing treatment with fulvestrant alone or in combination with taselisib. TGI models allow to predict drugs’ efficacy decay rates in individual patients. Covariate relationships identified using TGI models are clinically relevant to guide therapeutic decisions: Kg increased with increasing baseline tumor size and in the absence of baseline endocrine sensitivity; and Kg decreased in the absence of baseline liver metastases both in fulvestrant monotherapy and in combination therapy with taselisib treatment group. Furthermore, interaction effect for the combination of fulvestrant with taselisib was estimated, which supports the additive or potential hypothesis for synergistic combination of fulvestrant with taselisib in postmenopausal women with ER+/HER2- advanced or metastatic breast cancer. These results have important implications for understanding and quantitating the effectiveness of combination treatment approaches and shed light on the complex interplay of individual patient characteristics and treatment responses, which highlights the importance of model informed drug development for targeted cancer therapy. 146 Chapter 5: Conclusions 5.1 Summary of Research Findings PI3K/AKT/mTOR signaling is considered as a master intracellular regulator for many cancer types. Massive efforts have been dedicated to the development of drugs targeting PI3K signaling, however, the number of approved inhibitors remains limited. The overall aim of this thesis was to acquire a better understanding of the PI3K/AKT/mTOR pathway response. Developed semi-mechanistic PK-PD models integrated and characterize dynamic relationship between exposure of targeted drugs, modulation of PD biomarkers/tumor triggered by inhibition of PI3K/AKT/mTOR pathway and estimated longitudinal response including emergence of tumor resistance in patients. In this thesis the translatability of the preclinical analysis to the clinical target was evaluated which provides quantitative metrics for assessing similarities and differences between preclinical and clinical methods, measurements, and results. This information will enhance the value of future preclinical translational dose-finding and dose optimization studies to accelerate clinical drug development. Furthermore, clinical longitudinal exposure-tumor growth inhibition models were developed to assess the intensity and time-course of drug effects on tumor response. These models provided metrics that highlights the differences in efficacy and emergence of treatment resistance of targeted-drugs with different mechanisms of action, and provided insights into the impact of combination therapies and individualize responses to these treatments. 147 5.2 PI3K/AKT/mTOR Pathway Significance Cancer remains a significant global health challenge. The PI3K pathway is central to cancer, and the deregulated activation of the PI3K/AKT/mTOR pathway on various levels of signaling is detected in many different types of cancers (10). The PI3K/AKT/mTOR signaling pathway is essential for numerous fundamental cellular functions such as cell differentiation, growth, proliferation, mobility, and metabolism (53, 85). Somatic alterations and genetic amplifications causing activation of this pathway are frequently found in cancer, for instance, common PI3K pathway genetic alterations is the mutation of PIK3CA which have been reported in approximately 40% of breast cancers (93, 94), 17% to 33% of cervical, 39% of endometrial, and 12% of ovarian cancers (133-137). The PI3K/AKT/mTOR pathway plays essential roles not only in cell survival, but also in tumor metastasis, tumor environment, and angiogenesis (152). As a result, there has been a significant effort to develop therapeutics that target critical nodes of the pathway (19). 5.3 PI3K/AKT/mTOR Drug Development Challenges Targeted oncology drug development is challenging because of the diverse nature of cancer (tumors heterogeneity) and possible emergence of tumor resistance in patients. Despite massive efforts that has been dedicated to the development of drugs targeting PI3K signaling, the number of approved inhibitors remains limited, mainly due to poor drug tolerability, intrinsic and/or acquired drug resistance, and signaling feedback loops which neutralize PI3K inhibition (12, 14, 85, 138, 139). Traditionally, the goal of Phase 1 and 2 studies is to assess drug tolerability and safety (Phase 1) and over-all efficacy in specific population (Phase 2). There are typically limited data collected at these stages of drug development with high variability. Additionally, Phase 1 148 and 2 clinical trials are designed based on dose finding and efficacy experiments (proof of mechanism of action) that are conducted at preclinical stages of drug development, where the extent and duration of target modulation is quantified by measuring xenografts tumor tissue biomarkers. The use of translational pharmacokinetics (PK)-pharmacodynamic (PD) modeling of preclinical efficacy data to identify clinically active doses in patients is increasing common. However, enhancing the predictivity of the tools employed to assess the effectiveness of a drug candidate is the main challenge of translational PK-PD analyses (59). There is limited to no retrospective analysis to evaluate the performance of translational PK-PD modeling of preclinical data. Furthermore, the clinical efficacy of PI3K or dual PI3K-mTOR inhibitors as monotherapy has demonstrated modest outcomes, prompting a shift towards exploring combination therapies to circumvent resistance mechanisms. Ongoing clinical investigations are exploring various drug combinations, including those targeting dual inhibition of the PI3K-mTOR pathway as well as inhibition of parallel pathways, and both targeted and non-targeted approaches (140). 149 5.4 Research Contributions and Impact The overall aim of this thesis was to acquire a better understanding of the PI3K-AKT-mTOR pathway response to enhance drug development by developing semi-mechanistic pharmacokinetic-pharmacodynamic models. Developed models, integrated and characterized the dynamic relationship between exposure of targeted drugs, modulation of PD biomarkers/tumor triggered by inhibition of PI3K/AKT/mTOR pathway and estimated longitudinal response including possible emergence of tumor resistance in patients with cancer. 5.4.1 Significance of Research Findings This dissertation comprises my research to develop quantitative pharmacokinetic-pharmacodynamic modeling framework for evaluating time-varying treatment effects of targeted PI3K-AKT-mTOR oncology therapeutics during drug development. Summary of the key findings and impact of each specific chapter is provided in Table 5.1. 150 Table 5.1 Key findings and impact of each specific study Study Novelty/Impact Application Chapter 2: Retrospective Assessment of the Translational Pharmacokinetic-Pharmacodynamic Modeling Performance: A Case Study with Apitolisib, A Dual PI3K/mTOR inhibitor Based on our knowledge this is the first comprehensive retrospective assessment of the translational pharmacokinetic-pharmacodynamic modeling performance for oncology therapeutics utilizing preclinical and two Phase 1 clinical trials data. Current study compares the similarities and differences between preclinical and clinical methods, measurements, and results for development of novel targeted oncology compounds. Selection/prioritization of drug candidates Enhance the value of future preclinical translational dose-finding and dose optimization studies to accelerate clinical drug development Chapter 3: Quantitative Assessment of Drug Efficacy and Emergence of Resistance in Patients with Metastatic Renal Cell Carcinoma Using a Longitudinal Exposure-Tumor Growth Inhibition Model: Apitolisib (dual PI3K/mTORC1/2 inhibitor) versus Everolimus (mTORC1 inhibitor) Based on our knowledge, this is the first study which quantitatively assess and compares efficacy decay of mTORC1 inhibitor (everolimus) vs dual pan-PI3K and mTORC1/2 inhibitor (apitolisib) in patients with metastatic renal cell carcinoma using longitudinal exposure-tumor growth inhibition model. Difference in efficacy decay estimated for these two targeted drugs (with different mechanisms of action) was associated with emergence of tumor resistance. Enhancing understanding of PI3K-AKT-mTOR pathway modulations and response in terms of: Tumor growth inhibition (efficacy) and treatment decay/tumor resistance over time (i.e. indicative of efficacy duration and extent of compensatory feedback loops or target mutation due to drug specific mechanism of action) Dose and patients’ selection Early informed decision-making in clinical development based on assessment of intensity and time-course of drug effects on tumor response, and assessments of early markers of effect (i.e. covariates) Chapter 4: Quantitative Characterization of the Effects of Fulvestrant Alone or in Combination with Taselisib (PI3Kinase Inhibitor) on Longitudinal Tumor Growth in Patients with Estrogen Receptor-positive, HER2-negative, PIK3CA-mutant, Advanced or Metastatic Breast Cancer Longitudinal TGI models were developed to assess effect of estrogen receptor (ER) inhibitor (fulvestrant, selective estrogen receptor down-regulator) alone vs in combination with PI3K inhibitor (taselisib) on tumor dynamics relative to patients’ characteristics. Based on our knowledge this is the first in-vivo in human study that estimated interaction effect for the combination of two targeted drugs, which supports the additive or potential synergistic effect of the combination of PI3K inhibitor with ER inhibitor. 151 5.4.2 Translational Pharmacokinetic-Pharmacodynamic Models Retrospective assessment of the preclinical and clinical Pharmacokinetic-Pharmacodynamic-Efficacy modeling performance with apitolisib (a dual PI3K/mTOR inhibitor) relates to the main challenge of translational PK-PD analyses, which is enhancing the predictivity of the tools employed to assess the effectiveness of a drug candidate at preclinical stages of drug development. There is limited to no retrospective analysis to evaluate the performance of translational PK-PD modeling of preclinical data. In this thesis, the analysis aids in the understanding of the value of preclinical translational dose-finding and dose optimization studies in the context of “clinical drug development”. Initial clinical trials are designed based on dose finding and efficacy experiments (proof of mechanism of action) that are conducted at preclinical stages of drug development, where the extent and duration of target modulation is quantified by measuring xenografts tumor tissue biomarkers. Typically, in Phase 1 studies, for patients’ convenience surrogate plasma biomarkers are collected, since these biomarkers are non-invasive to obtain and can be easily collected through a blood test. In this thesis, we did a retrospective assessment and compared the similarities and differences of the type of data that is typically collected in Phase 1 studies (surrogate plasma biomarker) vs xenografts studies (tumor tissue biomarker). With implementation of model informed drug development, these differences/similarities and their correlation to treatment effect can be identified and characterized. Therefore, disease mechanism-based biomarkers that are indicative of a relevant biological aspect of cancer can serve as additional surrogate end-points during the drug development process and bridge preclinical studies efficacy to clinical response. 152 Integrated Pharmacokinetics-Pharmacodynamic-Efficacy models developed for xenografts bearing human renal cell adenocarcinoma (RCC) and patients with solid tumors show a steep sigmoid curve is linking %pAkt inhibition to tumor growth inhibition. These models quantified a minimum 35% to 45% pAkt modulation threshold (relative to baseline) for tumor shrinkage in patients based on platelet-rich plasma surrogate matrix and in xenografts based on tumor tissue matrix. Based on this relationship between target modulation and antitumor efficacy, it appeared that a constant pAkt inhibition of 61% and 65% would be necessary to achieve tumor stasis in xenografts and patients, respectably. There are limitations and assumptions associated with this analysis that were described in Chapter 2. Overall, the preclinical and clinical developed Integrated Pharmacokinetics-Pharmacodynamic-Efficacy models bring together the information from PK, PD, and efficacy studies to provide a more complete understanding of the relationship between drug dose, drug concentration, and therapeutic response, and help to bridge the gap between xenograft and human studies for development of more effective cancer treatments. 5.4.3 Longitudinal Exposure-Tumor Growth Inhibition Models The use of longitudinal exposure-tumor growth inhibition (TGI) models has emerged as a valuable tool in clinical drug development to provide a quantitative framework in assessing drug efficacy in cancer patients. The fundamental principle underlying longitudinal exposure-TGI models is the integration of pharmacokinetic data with tumor growth inhibition dynamics. By quantifying drug concentrations in plasma, alongside tumor size measurements over time, these models enable the estimation of critical parameters such as the rate of tumor growth and drug efficacy in the form of tumor shrinkage. More recently, longitudinal exposure-TGI models have been used to quantitatively characterize the effects of drug resistance. Furthermore, it has been 153 shown that faster tumor growth rate often correlates with a higher likelihood of disease progression and shorter progression-free survival (PFS) or overall survival (OS), and TGI metrics can be a significant predictor of PFS or OS (82, 83). In this thesis, an integrated sequential longitudinal exposure-tumor growth inhibition model was developed based on longitudinal tumor size data of patients with metastatic renal cell carcinoma (mRCC) enrolled in ROVER clinical trial. The ROVER trial, a randomized Phase 2 clinical study, aimed to directly compare the efficacy of simultaneously targeting multiple nodes within the PI3K/mTOR signaling pathway (apitolisib) with the isolated inhibition of mTORC1 (everolimus). The model assessed the disparity in overall efficacy between the two drugs and quantified efficacy decay caused by emergence of resistance. The model estimated on-treatment tumor growth rate constant was 1.7-fold higher for apitolisib compared to everolimus. Estimated half-life for loss of treatment effect over time for everolimus was 16.1 weeks compared to 7.72 weeks for apitolisib suggesting a faster rate of tumor re-growth for apitolisib patients likely due to the emergence of resistance. This modeling approach offers valuable insights into the potential limitations of pan-PI3K and mTOR dual inhibition strategies in a clinical context for mRCC treatment and emphasizes the importance of model informed drug development for targeted cancer therapy. Additionally, in the clinical setting, a multifaceted approach is essential for targeted cancer treatment, one that not only explores the effectiveness of individual treatments but also delves into the potential gains in therapeutic outcome that can be achieved through combination therapies. In particular, breast cancer is a formidable adversary in the field of oncology, with 154 various subtypes presenting unique challenges for clinicians and researchers. Among these, estrogen receptor-positive (ER+), phosphatidylinositol-4,5-bisphosphate 3-kinase catalytic subunit alpha (PIK3CA)-mutant, human epidermal growth factor receptor 2 negative (HER2-) advanced breast cancer stands as a particularly intricate clinical indication, since approximately 40% of ER+/HER2-breast carcinomas present mutations in the PIK3CA gene. In this thesis, longitudinal tumor growth inhibition (TGI) models were developed to characterize tumor response over time in postmenopausal women with ER+/HER2- advanced or metastatic breast cancer undergoing treatment with fulvestrant alone or in combination with the PI3K inhibitor, taselisib. Impact of clinically relevant covariates on TGI metrics was assessed to identify patient subsets most likely to benefit from treatment with fulvestrant monotherapy or combination with taselisib. Overall, additive/potentially synergistic anti-tumor effects were observed in patients treated with the taselisib-fulvestrant combination. These results have important implications for understanding the therapeutic impact of combination treatment approaches and individualize responses to these treatments. 5.5 Research Limitations Early clinical trials are designed based on dose finding and efficacy experiments (proof of mechanism of action) that are conducted at preclinical stages of drug development, where the extent and duration of target modulation is quantified by measuring xenografts tumor tissue biomarkers. Typically, in Phase 1 studies, surrogate plasma biomarkers are collected for patient convenience since these biomarkers are less invasive to obtain and can be easily collected through a blood test. In this thesis, our objective was to perform a retrospective assessment and compare quantitative similarities and differences between the type of data that is typically 155 collected in Phase 1 studies (surrogate plasma biomarker) versus data collected from preclinical xenografts studies (tumor tissue biomarker). One of the limitations of our retrospective assessment of translational pharmacokinetic-pharmacodynamic models is the assumption of similarities in tumor response between xenograft mice implanted with cancer cells line of human origin and patients. Subcutaneous tumors implanted in xenograft mice may not reflect the heterogeneity of tumors observed in patients with metastatic tumors. Another assumption of the translational modeling is the presumption of similar drug distribution in the subcutaneous tumor environment of xenograft models and human tumors (42, 43). In this analysis, we assumed that drug distribution is similar, despite reported differences in tumor vasculature and transport in xenograft versus human tumors (44). Furthermore, longitudinal exposure-tumor growth inhibition model developed based on ROVER Phase 2 clinical trial has limitations on its ability to conduct accurate covariate assessments on TGI metrics (i.e. model will be over-parameterize to conduct accurate covariate assessment based on all clinically relevant covariates). In general, Phase 1-2 oncology clinical trials face a critical limitation in their ability to assess the efficacy of new compounds due to the limited number of patients enrolled. However, by leveraging model-informed drug development (MIDD), general trends within the dataset can be assessed to provide meaningful insights from the available data and enable a deeper understanding of drug behavior and efficacy. 156 5.6 Future Directions Despite major research aimed at discovering and developing novel and effective anticancer drugs, oncology drug development is a lengthy and costly process, with high attrition rates (141), and unmet medical needs across a wide range of diseases. In recent years, repurposing drugs has emerged as a promising strategy in pharmaceutical research and development. This innovative approach involves identifying new therapeutic applications for existing drugs, which have already undergone rigorous testing for safety and efficacy. By leveraging the wealth of data available on these compounds, researchers can expedite the drug discovery process, reduce costs, and potentially bring new treatments to market more quickly. Utilizing established libraries of clinical drugs combined with substantial advancements in disease biology, genomics, proteomics, transcriptomics, and bioinformatics, has accelerated the rate of activity-based, literature-based and in silico drugs repurposing (141). This approach not only enhances safety but also reduces costs (141). For repurposing drugs, considering the animal models at preclinical stages of drug development, Patient-Derived Xenograft (PDX) models in translational cancer research have potential applications in personalized medicine. PDX models involve implanting tumor tissue directly from a patient into immunodeficient mice, allowing the tumor to grow in a surrogate host. These models are used in preclinical research to better mimic human cancer biology and response to treatments, providing valuable insights into cancer progression and therapy efficacy. Since tumor tissue is directly obtained from patients and implanted into immunodeficient mice, PDX models retain the heterogeneity and complexity of the original patient tumor, including stromal components. In contrast, human cell-based inoculated xenografts where tumor cells isolated from 157 patients are cultured in vitro and then injected into immunodeficient mice, therefore these cell-based xenografts models usually consist of a homogeneous population of tumor cells and lack the tumor microenvironment found in PDX models. Furthermore, with regard to tumor growth dynamics, in the PDX models, tumors grow in a manner that closely resembles the growth patterns observed in patients, including tumor architecture and vascularization. In contrast, human cell-based inoculated xenografts, tumor growth may be more uniform and faster due to the absence of stromal components and the presence of a higher initial cell density. Overall, generally PDX models are considered to better recapitulate complexity of patient tumors and biology for drug response, making them valuable tools for preclinical drug screening and personalized medicine. Apitolisib (GDC-0980) is dual PI3K/mTOR inhibitor, which can induce apoptosis of cancer cells and inhibit cancer cell growth (53). It is an orally available agent that targets PI3K and mTORC1/2 in the PI3K/AKT/mTOR signaling pathway. Phase 1 and 2 clinical trials of apitolisib in patients with different cancer types (Phase 1) and patients with metastatic renal cell carcinoma (Phase 2) was discussed in Chapters 2 and 3 of this thesis. As was discussed in Chapter 3, the results of the Phase 2 study demonstrated that the PI3K/mTORC1/mTORC2 inhibitor, apitolisib, significantly underperformed in comparison to the mTORC1 inhibitor, everolimus in mRCC population. However, it is noteworthy that apitolisib strongest anti-tumor effect was observed in breast, prostate, and lung cancer cell lines (36). Metastatic renal cell carcinoma is often more challenging to treat compared to breast cancer. Metastatic RCC tends to be more aggressive and is biologically complex with various subtypes, making it difficult to develop effective targeted therapies. 158 A future study could evaluate repurposing apitolisib for treatment of metastatic/advanced breast cancer utilizing PDX models. Based on published results of apitolisib cell-line potency (36), for repurposing apitolisib, estrogen receptor-positive, HER2-negative, PIK3CA-mutant, breast cancer indication could be evaluated in PDX models by directly utilizing patient’s tumor fragments. Initially anti-tumor activity of apitolisib monotherapy at clinically relevant doses would be evaluated in tumor tissues and plasma (surrogate matrix) by collecting relevant biomarkers of interest such as pAkt, p4EBP1, pS6K and pS6 from patient-derived xenografts. Additionally, plasma circulating tumor DNA (ctDNA) can be collected from PDX models as a translational surrogate to assess efficacy of apitolisib in inhibiting the pathway and further use as tool for selection of patients and combination therapy. Furthermore, plasma and tumor tissue concentrations of apitolisib would be collected from PDX models to stablish the link and quantify the correlation between exposure of drug (measured in both plasma and tumor tissue) and the extent of inhibition measured in the pathway via collection of relevant biomarkers (tumor tissue/surrogate plasma), ctDNA and tumor volumes. Circulating tumor DNA (ctDNA) is small fragments of DNA that are released into the bloodstream by cancer cells as they die and break apart. These fragments carry genetic information specific to the tumor from which they originated. In clinical trials, ctDNA is used in monitoring treatment response. Changes in ctDNA levels can indicate how well a treatment is working or if cancer is progressing, providing real-time feedback on treatment efficacy. ctDNA analysis can also reveal genetic changes in tumors over time, including the development of resistance to treatment or the emergence of new mutations, hence it can be use in selection of combinational targeted therapy. ctDNA analysis can help with identifying patients who are more 159 likely to benefit from specific treatments (patient stratification in clinical trials), allowing for more personalized and targeted therapy approaches. Overall, ctDNA analysis in clinical trials offers a non-invasive and dynamic approach to monitoring cancer status and treatment response, which can lead to improved patient outcomes and more efficient drug development processes. Currently, a Phase 3 clinical trial (NCT05501886) evaluating efficacy and safety of gedatolisib, another dual PI3K/mTOR inhibitor, in combination with fulvestrant, and with or without palbociclib for the treatment of patients with locally advanced or metastatic HR+/HER2- breast cancer following progression on or after CDK4/6 and aromatase inhibitor therapy. Therefore, a future study with MIDD approaches could evaluate combination of apitolisib (dual PI3K/mTOR inhibitor) with fulvestrant and palbociclib in PDX models at clinically relevant doses. Tumor heterogeneity is a major challenge for drug development, and changes in heterogeneity are thought to contribute to anticancer treatment resistance (142). Current longitudinal exposure-tumor growth inhibition (TGI) model used in Chapter 3 could be enhanced by modification to joint model framework. Tumor growth inhibition joint modeling of tumor volumes and ctDNA (circulating tumor DNA) involves integrating data from both measurements to better understand the dynamics of tumor response to treatment (i.e. ctDNA provides valuable insight into tumor volumes and conversely, tumor volumes offer informative insight through ctDNA). This approach allows for a more comprehensive assessment of treatment efficacy, and quantitating efficacy decay over time (i.e. emergence of tumor resistance). This joint translational longitudinal exposure-TGI model by providing insights into the dynamic relationship between tumor burden, tumor mutation and exposure of drugs provides model informed platform for 160 selection of combinational targeted therapies and dosing optimization; since ctDNA within peripheral blood plasma provides non-invasive access to cancer-specific somatic mutations (143, 144). Utilizing patients apitolisib PK collected in Phase 1, a joint translational longitudinal exposure-TGI model could be developed to evaluate repurposing of apitolisib for estrogen receptor-positive, HER2-negative, PIK3CA-mutant, metastatic breast cancer indication. 5.7 Concluding Remarks The PI3K/AKT/mTOR pathway stands as one of the critical signaling cascades within the field of cellular physiology and is considered as a master intracellular regulator for many cancer types. This thesis underscores the significance of model informed drug development for targeted PI3K/AKT/mTOR cancer therapy throughout the drug development lifecycle from preclinical to Phase 1, 2 and 3. Pharmacometrics models including translational pharmacokinetic-pharmacodynamic models utilized here are important quantitative tools that can provide a better understanding of drug disposition, biomarker (or tumor) response and efficacy. These models quantitatively characterize drug disposition, inter-relate drug concentrations and its effect on tumor response. Results presented in this thesis, evaluate the translatability of the preclinical analysis to the clinical target and provide information that will enhance the value of future preclinical translational dose-finding and dose optimization studies to accelerate clinical drug development. Furthermore, these results highlight the application of tumor growth inhibition modeling framework to quantify the differences in efficacy and emergence of treatment resistance for targeted-drugs with different mechanism of action, and provides insights into the impact of combination therapies and individualize responses to these treatments. 161 References 1. Siegel RL, Miller KD, Wagle NS, Jemal A. Cancer statistics, 2023. CA: a cancer journal for clinicians. 2023;73(1):17-48. 2. Hutchinson L, Kirk R. High drug attrition rates--where are we going wrong? Nature reviews Clinical oncology. 2011;8(4):189-90. 3. Mullard A. R&D re-balancing act. Nature reviews Drug discovery. 2023;22(4):258. 4. Dowden H, Munro J. Trends in clinical success rates and therapeutic focus. Nature reviews Drug discovery. 2019;18(7):495-6. 5. Jentzsch V, Osipenko L, Scannell JW, Hickman JA. Costs and Causes of Oncology Drug Attrition With the Example of Insulin-Like Growth Factor-1 Receptor Inhibitors. JAMA network open. 2023;6(7):e2324977. 6. Huang M, Shen A, Ding J, Geng M. Molecularly targeted cancer therapy: some lessons from the past decade. Trends in pharmacological sciences. 2014;35(1):41-50. 7. U.S. Food and Drug Administration. Project Optimus. Reforming the dose optimization and dose selection paradigm in oncology. 2023 [Available from: https://www.fda.gov/about-fda/oncology-center-excellence/project-optimus. 8. Falzone L, Salomone S, Libra M. Evolution of Cancer Pharmacological Treatments at the Turn of the Third Millennium. Front Pharmacol. 2018;9:1300. 9. Targeted Therapy to Treat Cancer. National Cancer Institute; Available from: https://www.cancer.gov/about-cancer/treatment/types/targeted-therapies. Updated 2022 May 31. 10. Polivka J, Jr., Janku F. Molecular targets for cancer therapy in the PI3K/AKT/mTOR pathway. Pharmacology & therapeutics. 2014;142(2):164-75. 11. Yang J, Nie J, Ma X, Wei Y, Peng Y, Wei X. Targeting PI3K in cancer: mechanisms and advances in clinical trials. Molecular cancer. 2019;18(1):26. 162 12. Vanhaesebroeck B, Perry MWD, Brown JR, Andre F, Okkenhaug K. PI3K inhibitors are finally coming of age. Nature reviews Drug discovery. 2021;20(10):741-69. 13. Dolgin E. Cancer drug approvals and setbacks in 2022. Nature cancer. 2022;3(12):1406-8. 14. Hanker AB, Kaklamani V, Arteaga CL. Challenges for the Clinical Development of PI3K Inhibitors: Strategies to Improve Their Impact in Solid Tumors. Cancer discovery. 2019;9(4):482-91. 15. Madabushi R, Seo P, Zhao L, Tegenge M, Zhu H. Review: Role of Model-Informed Drug Development Approaches in the Lifecycle of Drug Development and Regulatory Decision-Making. Pharmaceutical research. 2022;39(8):1669-80. 16. Wagner JG. History of pharmacokinetics. Pharmacology & therapeutics. 1981;12(3):537-62. 17. Felmlee MA, Morris ME, Mager DE. Mechanism-based pharmacodynamic modeling. Methods in molecular biology (Clifton, NJ). 2012;929:583-600. 18. Rajman I. PK/PD modelling and simulations: utility in drug development. Drug discovery today. 2008;13(7-8):341-6. 19. Josephs DH, Sarker D. Pharmacodynamic Biomarker Development for PI3K Pathway Therapeutics. Translational oncogenomics. 2015;7(Suppl 1):33-49. 20. Park JW, Kerbel RS, Kelloff GJ, Barrett JC, Chabner BA, Parkinson DR, et al. Rationale for biomarkers and surrogate end points in mechanism-driven oncology drug development. Clinical cancer research : an official journal of the American Association for Cancer Research. 2004;10(11):3885-96. 21. Jackson RC. Pharmacodynamic modelling of biomarker data in oncology. ISRN pharmacology. 2012;2012:590626. 163 22. Orrell D, Fernandez E. Using predictive mathematical models to optimise the scheduling of anti-cancer drugs. Innovations in Pharmaceutical Technology. 2010;33:58–62. 23. Hansson EK, Amantea MA, Westwood P, Milligan PA, Houk BE, French J, et al. PKPD Modeling of VEGF, sVEGFR-2, sVEGFR-3, and sKIT as Predictors of Tumor Dynamics and Overall Survival Following Sunitinib Treatment in GIST. CPT Pharmacometrics Syst Pharmacol. 2013;2(11):e84. 24. Ribba B, Kaloshi G, Peyre M, Ricard D, Calvez V, Tod M, et al. A tumor growth inhibition model for low-grade glioma treated with chemotherapy or radiotherapy. Clinical cancer research : an official journal of the American Association for Cancer Research. 2012;18(18):5071-80. 25. Zhu AZ. Quantitative translational modeling to facilitate preclinical to clinical efficacy & toxicity translation in oncology. Future science OA. 2018;4(5):FSO306. 26. Sheiner LB. The population approach to pharmacokinetic data analysis: rationale and standard data analysis methods. Drug metabolism reviews. 1984;15(1-2):153-71. 27. Bruno R, Lu JF, Sun YN, Claret L. A modeling and simulation framework to support early clinical drug development decisions in oncology. Journal of clinical pharmacology. 2011;51(1):6-8. 28. Claret L, Girard P, Zuideveld KP. A longitudinal model for tumor size measurements in clinical oncology studies,PAGE 15. 2006. 29. Claret L, Girard P, Hoff PM, Van Cutsem E, Zuideveld KP, Jorga K, et al. Model-based prediction of phase III overall survival in colorectal cancer on the basis of phase II tumor dynamics. Journal of clinical oncology : official journal of the American Society of Clinical Oncology. 2009;27(25):4103-8. 30. Eisenhauer EA, Therasse P, Bogaerts J, Schwartz LH, Sargent D, Ford R, et al. New response evaluation criteria in solid tumours: revised RECIST guideline (version 1.1). European journal of cancer. 2009;45(2):228-47. 164 31. Ribba B, Holford NH, Magni P, Troconiz I, Gueorguieva I, Girard P, et al. A review of mixed-effects models of tumor growth and effects of anticancer drug treatment used in population analysis. CPT Pharmacometrics Syst Pharmacol. 2014;3(5):e113. 32. U.S. Food and Drug Administration. Guidance document. Optimizing the Dosage of Human Prescription Drugs and Biological Products for the Treatment of Oncologic Diseases 2023 [Available from: <https://www.fda.gov/regulatory-information/search-fda-guidance-documents/optimizing-dosage-human-prescription-drugs-and-biological-products-treatment-oncologic-diseases>. 33. Bueno L, de Alwis DP, Pitou C, Yingling J, Lahn M, Glatt S, et al. Semi-mechanistic modelling of the tumour growth inhibitory effects of LY2157299, a new type I receptor TGF-beta kinase antagonist, in mice. European journal of cancer. 2008;44(1):142-50. 34. Wong H, Belvin M, Herter S, Hoeflich KP, Murray LJ, Wong L, et al. Pharmacodynamics of 2-[4-[(1E)-1-(hydroxyimino)-2,3-dihydro-1H-inden-5-yl]-3-(pyridine-4-yl)-1H-pyrazol-1-yl]ethan-1-ol (GDC-0879), a potent and selective B-Raf kinase inhibitor: understanding relationships between systemic concentrations, phosphorylated mitogen-activated protein kinase kinase 1 inhibition, and efficacy. The Journal of pharmacology and experimental therapeutics. 2009;329(1):360-7. 35. Owonikoko TK, Khuri FR. Targeting the PI3K/AKT/mTOR pathway: biomarkers of success and tribulation. American Society of Clinical Oncology educational book American Society of Clinical Oncology Annual Meeting. 2013. 36. Wallin JJ, Edgar KA, Guan J, Berry M, Prior WW, Lee L, et al. GDC-0980 is a novel class I PI3K/mTOR kinase inhibitor with robust activity in cancer models driven by the PI3K pathway. Molecular cancer therapeutics. 2011;10(12):2426-36. 37. Dolly SO, Wagner AJ, Bendell JC, Kindler HL, Krug LM, Seiwert TY, et al. Phase I Study of Apitolisib (GDC-0980), Dual Phosphatidylinositol-3-Kinase and Mammalian Target of Rapamycin Kinase Inhibitor, in Patients with Advanced Solid Tumors. Clinical cancer research : an official journal of the American Association for Cancer Research. 2016;22(12):2874-84. 165 38. Salphati L, Pang J, Plise EG, Lee LB, Olivero AG, Prior WW, et al. Preclinical assessment of the absorption and disposition of the phosphatidylinositol 3-kinase/mammalian target of rapamycin inhibitor GDC-0980 and prediction of its pharmacokinetics and efficacy in human. Drug metabolism and disposition: the biological fate of chemicals. 2012;40(9):1785-96. 39. Therasse P, Arbuck SG, Eisenhauer EA, Wanders J, Kaplan RS, Rubinstein L, et al. New guidelines to evaluate the response to treatment in solid tumors. European Organization for Research and Treatment of Cancer, National Cancer Institute of the United States, National Cancer Institute of Canada. Journal of the National Cancer Institute. 2000;92(3):205-16. 40. Byrne MJ, Nowak AK. Modified RECIST criteria for assessment of response in malignant pleural mesothelioma. Annals of oncology : official journal of the European Society for Medical Oncology. 2004;15(2):257-60. 41. Salphati L, Wong H, Belvin M, Bradford D, Edgar KA, Prior WW, et al. Pharmacokinetic-pharmacodynamic modeling of tumor growth inhibition and biomarker modulation by the novel phosphatidylinositol 3-kinase inhibitor GDC-0941. Drug metabolism and disposition: the biological fate of chemicals. 2010;38(9):1436-42. 42. Wong H, Vernillet L, Peterson A, Ware JA, Lee L, Martini JF, et al. Bridging the gap between preclinical and clinical studies using pharmacokinetic-pharmacodynamic modeling: an analysis of GDC-0973, a MEK inhibitor. Clinical cancer research : an official journal of the American Association for Cancer Research. 2012;18(11):3090-9. 43. Yamazaki S, Vicini P, Shen Z, Zou HY, Lee J, Li Q, et al. Pharmacokinetic/pharmacodynamic modeling of crizotinib for anaplastic lymphoma kinase inhibition and antitumor efficacy in human tumor xenograft mouse models. The Journal of pharmacology and experimental therapeutics. 2012;340(3):549-57. 44. Jang SH, Wientjes MG, Lu D, Au JL. Drug delivery and transport to solid tumors. Pharmaceutical research. 2003;20(9):1337-50. 45. Beal S, Boeckmann L, Bauer R, Sheiner L. NONMEM User’s Guides. (1989–2009). NONMEM User’s Guides (1989–2009). Elliot City: Icon Development Solutions; 2009. 166 46. R Core Team (2019). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria2019. 47. Goldmacher GV, Conklin J. The use of tumour volumetrics to assess response to therapy in anticancer clinical trials. British journal of clinical pharmacology. 2012;73(6):846-54. 48. Tanaka C, O'Reilly T, Kovarik JM, Shand N, Hazell K, Judson I, et al. Identifying optimal biologic doses of everolimus (RAD001) in patients with cancer based on the modeling of preclinical and clinical pharmacokinetic and pharmacodynamic data. Journal of clinical oncology : official journal of the American Society of Clinical Oncology. 2008;26(10):1596-602. 49. Yamazaki S, Skaptason J, Romero D, Lee JH, Zou HY, Christensen JG, et al. Pharmacokinetic-pharmacodynamic modeling of biomarker response and tumor growth inhibition to an orally available cMet kinase inhibitor in human tumor xenograft mouse models. Drug metabolism and disposition: the biological fate of chemicals. 2008;36(7):1267-74. 50. Yates JW, Dudley P, Cheng J, D'Cruz C, Davies BR. Validation of a predictive modeling approach to demonstrate the relative efficacy of three different schedules of the AKT inhibitor AZD5363. Cancer chemotherapy and pharmacology. 2015;76(2):343-56. 51. Dayneka NL, Garg V, Jusko WJ. Comparison of four basic models of indirect pharmacodynamic responses. Journal of pharmacokinetics and biopharmaceutics. 1993;21(4):457-78. 52. Mager DE, Wyska E, Jusko WJ. Diversity of mechanism-based pharmacodynamic models. Drug metabolism and disposition: the biological fate of chemicals. 2003;31(5):510-8. 53. Sutherlin DP, Bao L, Berry M, Castanedo G, Chuckowree I, Dotson J, et al. Discovery of a potent, selective, and orally available class I phosphatidylinositol 3-kinase (PI3K)/mammalian target of rapamycin (mTOR) kinase inhibitor (GDC-0980) for the treatment of cancer. Journal of medicinal chemistry. 2011;54(21):7579-87. 54. Sarker D, Ang JE, Baird R, Kristeleit R, Shah K, Moreno V, et al. First-in-human phase I study of pictilisib (GDC-0941), a potent pan-class I phosphatidylinositol-3-kinase (PI3K) 167 inhibitor, in patients with advanced solid tumors. Clinical cancer research : an official journal of the American Association for Cancer Research. 2015;21(1):77-86. 55. Tarantelli C, Lupia A, Stathis A, Bertoni F. Is There a Role for Dual PI3K/mTOR Inhibitors for Patients Affected with Lymphoma? International journal of molecular sciences. 2020;21(3). 56. Wong H, Alicke B, West KA, Pacheco P, La H, Januario T, et al. Pharmacokinetic-pharmacodynamic analysis of vismodegib in preclinical models of mutational and ligand-dependent Hedgehog pathway activation. Clinical cancer research : an official journal of the American Association for Cancer Research. 2011;17(14):4682-92. 57. Claret L, Gupta M, Han K, Joshi A, Sarapa N, He J, et al. Evaluation of tumor-size response metrics to predict overall survival in Western and Chinese patients with first-line metastatic colorectal cancer. Journal of clinical oncology : official journal of the American Society of Clinical Oncology. 2013;31(17):2110-4. 58. Wong H, Choo EF, Alicke B, Ding X, La H, McNamara E, et al. Antitumor activity of targeted and cytotoxic agents in murine subcutaneous tumor models correlates with clinical response. Clinical cancer research : an official journal of the American Association for Cancer Research. 2012;18(14):3846-55. 59. Stewart AG. Translational Pharmacology. Frontiers in Pharmacology. 2017;8. 60. Motzer RJ, Escudier B, Oudard S, Hutson TE, Porta C, Bracarda S, et al. Phase 3 trial of everolimus for metastatic renal cell carcinoma : final results and analysis of prognostic factors. Cancer. 2010;116(18):4256-65. 61. Houghton PJ. Everolimus. Clinical cancer research : an official journal of the American Association for Cancer Research. 2010;16(5):1368-72. 62. Salazar R, Garcia-Carbonero R, Libutti SK, Hendifar AE, Custodio A, Guimbaud R, et al. Phase II Study of BEZ235 versus Everolimus in Patients with Mammalian Target of Rapamycin Inhibitor-Naive Advanced Pancreatic Neuroendocrine Tumors. Oncologist. 2018;23(7):766-e90. 168 63. Meric-Bernstam F, Akcakanat A, Chen H, Do KA, Sangai T, Adkins F, et al. PIK3CA/PTEN mutations and Akt activation as markers of sensitivity to allosteric mTOR inhibitors. Clinical cancer research : an official journal of the American Association for Cancer Research. 2012;18(6):1777-89. 64. Tabernero J, Rojo F, Calvo E, Burris H, Judson I, Hazell K, et al. Dose- and schedule-dependent inhibition of the mammalian target of rapamycin pathway with everolimus: a phase I tumor pharmacodynamic study in patients with advanced solid tumors. Journal of clinical oncology : official journal of the American Society of Clinical Oncology. 2008;26(10):1603-10. 65. Wolin EM. PI3K/Akt/mTOR pathway inhibitors in the therapy of pancreatic neuroendocrine tumors. Cancer Lett. 2013;335(1):1-8. 66. Yao JC, Shah MH, Ito T, Bohas CL, Wolin EM, Van Cutsem E, et al. Everolimus for advanced pancreatic neuroendocrine tumors. N Engl J Med. 2011;364(6):514-23. 67. Bendell JC, Kurkjian C, Infante JR, Bauer TM, Burris HA, 3rd, Greco FA, et al. A phase 1 study of the sachet formulation of the oral dual PI3K/mTOR inhibitor BEZ235 given twice daily (BID) in patients with advanced solid tumors. Invest New Drugs. 2015;33(2):463-71. 68. Markman B, Tabernero J, Krop I, Shapiro GI, Siu L, Chen LC, et al. Phase I safety, pharmacokinetic, and pharmacodynamic study of the oral phosphatidylinositol-3-kinase and mTOR inhibitor BGT226 in patients with advanced solid tumors. Annals of oncology : official journal of the European Society for Medical Oncology. 2012;23(9):2399-408. 69. Papadopoulos KP, Tabernero J, Markman B, Patnaik A, Tolcher AW, Baselga J, et al. Phase I safety, pharmacokinetic, and pharmacodynamic study of SAR245409 (XL765), a novel, orally administered PI3K/mTOR inhibitor in patients with advanced solid tumors. Clinical cancer research : an official journal of the American Association for Cancer Research. 2014;20(9):2445-56. 70. Powles T, Lackner MR, Oudard S, Escudier B, Ralph C, Brown JE, et al. Randomized Open-Label Phase II Trial of Apitolisib (GDC-0980), a Novel Inhibitor of the PI3K/Mammalian Target of Rapamycin Pathway, Versus Everolimus in Patients With Metastatic Renal Cell 169 Carcinoma. Journal of clinical oncology : official journal of the American Society of Clinical Oncology. 2016;34(14):1660-8. 71. Wise-Draper TM, Moorthy G, Salkeni MA, Karim NA, Thomas HE, Mercer CA, et al. A Phase Ib Study of the Dual PI3K/mTOR Inhibitor Dactolisib (BEZ235) Combined with Everolimus in Patients with Advanced Solid Malignancies. Target Oncol. 2017;12(3):323-32. 72. FDA. U.S.Food and Drug Administration. Drugs@FDA: FDA-Approved Drugs. https://www.accessdata.fda.gov/scripts/cder/daf/index.cfm?event=overview.process&ApplNo=022334 2009 [ 73. Bergstrand M, Hooker AC, Wallin JE, Karlsson MO. Prediction-corrected visual predictive checks for diagnosing nonlinear mixed-effects models. AAPS J. 2011;13(2):143-51. 74. Karlsson MO, Holford NA, editors. Tutorial on visual predictive checks (Abstract 1434). Population Approach Group Europe (PAGE); 2008; Marseille, France. 75. Beal SL, Sheiner L, Boeckmann AJ, Bauer RJ. NONMEM 7.4 Users Guides (ICON plc, Gaithersburg, MD). https://www.scienceopen.com/document?vid=7bf48f4e-0bb4-4719-abe3-090ca42463be 1989-2019 [ 76. Savic RM, Karlsson MO. Importance of shrinkage in empirical bayes estimates for diagnostics: problems and solutions. Aaps j. 2009;11(3):558-69. 77. Cho DC, Cohen MB, Panka DJ, Collins M, Ghebremichael M, Atkins MB, et al. The efficacy of the novel dual PI3-kinase/mTOR inhibitor NVP-BEZ235 compared with rapamycin in renal cell carcinoma. Clinical cancer research : an official journal of the American Association for Cancer Research. 2010;16(14):3628-38. 78. Serra V, Scaltriti M, Prudkin L, Eichhorn PJ, Ibrahim YH, Chandarlapaty S, et al. PI3K inhibition results in enhanced HER signaling and acquired ERK dependency in HER2-overexpressing breast cancer. Oncogene. 2011;30(22):2547-57. 170 79. Negrier S, Gravis G, Perol D, Chevreau C, Delva R, Bay JO, et al. Temsirolimus and bevacizumab, or sunitinib, or interferon alfa and bevacizumab for patients with advanced renal cell carcinoma (TORAVA): a randomised phase 2 trial. Lancet Oncol. 2011;12(7):673-80. 80. Rini BI, Bellmunt J, Clancy J, Wang K, Niethammer AG, Hariharan S, et al. Randomized phase III trial of temsirolimus and bevacizumab versus interferon alfa and bevacizumab in metastatic renal cell carcinoma: INTORACT trial. Journal of clinical oncology : official journal of the American Society of Clinical Oncology. 2014;32(8):752-9. 81. Bauer TM, Patel MR, Infante JR. Targeting PI3 kinase in cancer. Pharmacology & therapeutics. 2015;146:53-60. 82. Chan P, Marchand M, Yoshida K, Vadhavkar S, Wang N, Lin A, et al. Prediction of overall survival in patients across solid tumors following atezolizumab treatments: A tumor growth inhibition-overall survival modeling framework. CPT Pharmacometrics Syst Pharmacol. 2021;10(10):1171-82. 83. Bruno R, Marchand M, Yoshida K, Chan P, Li H, Zou W, et al. Tumor Dynamic Model-Based Decision Support for Phase Ib/II Combination Studies: A Retrospective Assessment Based on Resampling of the Phase III Study IMpower150. Clinical cancer research : an official journal of the American Association for Cancer Research. 2023;29(6):1047-55. 84. Fruman DA, Chiu H, Hopkins BD, Bagrodia S, Cantley LC, Abraham RT. The PI3K Pathway in Human Disease. Cell. 2017;170(4):605-35. 85. Hopkins BD, Pauli C, Du X, Wang DG, Li X, Wu D, et al. Suppression of insulin feedback enhances the efficacy of PI3K inhibitors. Nature. 2018;560(7719):499-503. 86. Stein A, Wang W, Carter AA, Chiparus O, Hollaender N, Kim H, et al. Dynamic tumor modeling of the dose-response relationship for everolimus in metastatic renal cell carcinoma using data from the phase 3 RECORD-1 trial. BMC Cancer. 2012;12:311. 87. Rocca A, Maltoni R, Bravaccini S, Donati C, Andreis D. Clinical utility of fulvestrant in the treatment of breast cancer: a report on the emerging clinical evidence. Cancer Manag Res. 2018;10:3083-99. 171 88. Osborne CK, Schiff R. Mechanisms of endocrine resistance in breast cancer. Annu Rev Med. 2011;62:233-47. 89. Engelman JA, Luo J, Cantley LC. The evolution of phosphatidylinositol 3-kinases as regulators of growth and metabolism. Nat Rev Genet. 2006;7(8):606-19. 90. Miller TW, Rexer BN, Garrett JT, Arteaga CL. Mutations in the phosphatidylinositol 3-kinase pathway: role in tumor progression and therapeutic implications in breast cancer. Breast Cancer Res. 2011;13(6):224. 91. Vasan N, Toska E, Scaltriti M. Overview of the relevance of PI3K pathway in HR-positive breast cancer. Ann Oncol. 2019;30(Suppl_10):x3-x11. 92. Whitman M, Downes CP, Keeler M, Keller T, Cantley L. Type I phosphatidylinositol kinase makes a novel inositol phospholipid, phosphatidylinositol-3-phosphate. Nature. 1988;332(6165):644-6. 93. Campbell IG, Russell SE, Choong DY, Montgomery KG, Ciavarella ML, Hooi CS, et al. Mutation of the PIK3CA gene in ovarian and breast cancer. Cancer Res. 2004;64(21):7678-81. 94. Mollon L, Agullar A, Anderson E, Joni D. Abstract 1207: A systematic literature review of the prevalence of PIK3CA mutations and mutation hotspots in HR+/HER2- metastatic breast cancer. Can Research. 2018;78:1207. 95. Edgar KA, Song K, Schmidt S, al. e. The PI3K inhibitor, taselisib (GDC-0032), has enhanced potency in PIK3CA mutant models through a unique mechanism of action. Abstract 370. Cancer Res. 2016;76. 96. Olivero A, Heffron T, Baumgardner M, Belvin M, Ross L, Blaquiere N, et al. Discovery of GDC-0032: A beta-sparing PI3K inhibitor active against PIK3CA mutant tumors. Cancer Research. 2013;73:DDT02-1. 97. Wallin JJ, Edgar KA, Guan J, al. e. The PI3K inhibitor GDC-0032 is selectively potent against PIK3CA mutant breast cancer cell lines and tumors. Abstract P2-17-01. Caner Res. 2013;73. 172 98. Dent S, Cortes J, Im YH, Dieras V, Harbeck N, Krop IE, et al. Phase III randomized study of taselisib or placebo with fulvestrant in estrogen receptor-positive, PIK3CA-mutant, HER2-negative, advanced breast cancer: the SANDPIPER trial. Annals of oncology : official journal of the European Society for Medical Oncology. 2021;32(2):197-207. 99. Jonsson E, Harling K, editors. Increasing the efficiency of the covariate search algorithm in the SCM. (Abstract). Population Approach Group Europe (PAGE) 2018; Montreux, Switzerland. 100. Beal SS, Boeckmann L, Bauer RJ, Sheiner LB. NONMEM User’s Guides. (1989–2009). https://www.semanticscholar.org/paper/NONMEM-User%E2%80%99s-Guides.-(1989%E2%80%932009)-Beal-Boeckmann/1964357daa9975ac959840262a810b2e0b39c8f4. 2009 [ 101. R Core Team (2019) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/. 2019 [ 102. Yamamura J, Kamigaki S, Fujita J, Osato H, Komoike Y. The Difference in Prognostic Outcomes Between De Novo Stage IV and Recurrent Metastatic Patients with Hormone Receptor-positive, HER2-negative Breast Cancer. In Vivo. 2018;32(2):353-8. 103. Nathan MR, Schmid P. A Review of Fulvestrant in Breast Cancer. Oncol Ther. 2017;5(1):17-29. 104. Van Tine BA, Crowder RJ, Ellis MJ. ER and PI3K independently modulate endocrine resistance in ER-positive breast cancer. Cancer discovery. 2011;1(4):287-8. 105. Cancer Genome Atlas N. Comprehensive molecular portraits of human breast tumours. Nature. 2012;490(7418):61-70. 106. Bosch A, Li Z, Bergamaschi A, Ellis H, Toska E, Prat A, et al. PI3K inhibition results in enhanced estrogen receptor function and dependence in hormone receptor-positive breast cancer. Sci Transl Med. 2015;7(283):283ra51. 173 107. Miller TW, Balko JM, Fox EM, Ghazoui Z, Dunbier A, Anderson H, et al. ERalpha-dependent E2F transcription can mediate resistance to estrogen deprivation in human breast cancer. Cancer discovery. 2011;1(4):338-51. 108. Juric D, Krop I, Ramanathan RK, Wilson TR, Ware JA, Sanabria Bohorquez SM, et al. Phase I Dose-Escalation Study of Taselisib, an Oral PI3K Inhibitor, in Patients with Advanced Solid Tumors. Cancer discovery. 2017;7(7):704-15. 109. Juric D, Rodon J, Tabernero J, Janku F, Burris HA, Schellens JHM, et al. Phosphatidylinositol 3-Kinase alpha-Selective Inhibition With Alpelisib (BYL719) in PIK3CA-Altered Solid Tumors: Results From the First-in-Human Study. Journal of clinical oncology : official journal of the American Society of Clinical Oncology. 2018;36(13):1291-9. 110. Baselga J, Dent SF, Cortés J, Im Y-H, Diéras V, Harbeck N, et al. Phase III study of taselisib (GDC-0032) + fulvestrant (FULV) v FULV in patients (pts) with estrogen receptor (ER)-positive, PIK3CA-mutant (MUT), locally advanced or metastatic breast cancer (MBC): Primary analysis from SANDPIPER. Journal of Clinical Oncology. 2018;36(18_suppl):LBA1006-LBA. 111. Gilewski TA, Dang C, Surbone A, et.al. Section 13, Principles of chemotherapy: Chapter 38, Cytokinetics. In: Bast RCJ, Kufe dW, Pollock RE, et.al., Medicine H-FC, editors. 5th ed. ed. Ontario, BC: Decker Inc.; 2000. p. 511-38. 112. Norton L. A Gompertzian model of human breast cancer growth. Cancer Res. 1988;48(24 Pt 1):7067-71. 113. Frances N, Claret L, Bruno R, Iliadis A. Tumor growth modeling from clinical trials reveals synergistic anticancer effect of the capecitabine and docetaxel combination in metastatic breast cancer. Cancer chemotherapy and pharmacology. 2011;68(6):1413-9. 114. D'Souza A, Spicer D, Lu J. Overcoming endocrine resistance in metastatic hormone receptor-positive breast cancer. J Hematol Oncol. 2018;11(1):80. 174 115. Kaminska K, Akrap N, Staaf J, Alves CL, Ehinger A, Ebbesson A, et al. Distinct mechanisms of resistance to fulvestrant treatment dictate level of ER independence and selective response to CDK inhibitors in metastatic breast cancer. Breast Cancer Res. 2021;23(1):26. 116. Razavi P, Chang MT, Xu G, Bandlamudi C, Ross DS, Vasan N, et al. The Genomic Landscape of Endocrine-Resistant Advanced Breast Cancers. Cancer Cell. 2018;34(3):427-38 e6. 117. Garutti M, Griguolo G, Botticelli A, Buzzatti G, De Angelis C, Gerratana L, et al. Definition of High-Risk Early Hormone-Positive HER2-Negative Breast Cancer: A Consensus Review. Cancers (Basel). 2022;14(8). 118. Liu Y, He M, Zuo WJ, Hao S, Wang ZH, Shao ZM. Tumor Size Still Impacts Prognosis in Breast Cancer With Extensive Nodal Involvement. Front Oncol. 2021;11:585613. 119. Papadaki MA, Stoupis G, Theodoropoulos PA, Mavroudis D, Georgoulias V, Agelaki S. Circulating Tumor Cells with Stemness and Epithelial-to-Mesenchymal Transition Features Are Chemoresistant and Predictive of Poor Outcome in Metastatic Breast Cancer. Molecular cancer therapeutics. 2019;18(2):437-47. 120. Goetz MP, O’’Shaughnessy J, Sledge GW, al. e. The benefit of abemaciclib in prognostic subgroups: an exploratory analysis of combined data from the MONARCH 2 and 3 studies. . Cancer Res Conf. 2017;78:1. 121. Bonotto M, Gerratana L, Di Maio M, De Angelis C, Cinausero M, Moroso S, et al. Chemotherapy versus endocrine therapy as first-line treatment in patients with luminal-like HER2-negative metastatic breast cancer: A propensity score analysis. Breast. 2017;31:114-20. 122. Gamucci T, Mentuccia L, Natoli C, Sperduti I, Cassano A, Michelotti A, et al. A Real-World Multicentre Retrospective Study of Paclitaxel-Bevacizumab and Maintenance Therapy as First-Line for HER2-Negative Metastatic Breast Cancer. J Cell Physiol. 2017;232(6):1571-8. 123. Gerratana L, Fanotto V, Bonotto M, Bolzonello S, Minisini AM, Fasola G, et al. Pattern of metastasis and outcome in patients with breast cancer. Clin Exp Metastasis. 2015;32(2):125-33. 175 124. Rugo HS, Cristofanilli M, Loibl S, Harbeck N, DeMichele A, Iwata H, et al. Prognostic Factors for Overall Survival in Patients with Hormone Receptor-Positive Advanced Breast Cancer: Analyses From PALOMA-3. Oncologist. 2021;26(8):e1339-e46. 125. Bravaccini S, Bronte G, Scarpi E, Ravaioli S, Maltoni R, Mangia A, et al. The impact of progesterone receptor expression on prognosis of patients with rapidly proliferating, hormone receptor-positive early breast cancer: a post hoc analysis of the IBIS 3 trial. Ther Adv Med Oncol. 2020;12:1758835919888999. 126. Davey MG, Ryan EJ, Folan PJ, O'Halloran N, Boland MR, Barry MK, et al. The impact of progesterone receptor negativity on oncological outcomes in oestrogen-receptor-positive breast cancer. BJS Open. 2021;5(3). 127. Lashen AG, Toss MS, Mongan NP, Green AR, Rakha EA. The clinical value of progesterone receptor expression in luminal breast cancer: A study of a large cohort with long-term follow-up. Cancer. 2023;129(8):1183-94. 128. Liu S, Chia SK, Mehl E, Leung S, Rajput A, Cheang MC, et al. Progesterone receptor is a significant factor associated with clinical outcomes and effect of adjuvant tamoxifen therapy in breast cancer patients. Breast Cancer Res Treat. 2010;119(1):53-61. 129. Elledge RM, Green S, Pugh R, Allred DC, Clark GM, Hill J, et al. Estrogen receptor (ER) and progesterone receptor (PgR), by ligand-binding assay compared with ER, PgR and pS2, by immuno-histochemistry in predicting response to tamoxifen in metastatic breast cancer: a Southwest Oncology Group Study. Int J Cancer. 2000;89(2):111-7. 130. Regan MM, Viale G, Mastropasqua MG, Maiorano E, Golouh R, Carbone A, et al. Re-evaluating adjuvant breast cancer trials: assessing hormone receptor status by immunohistochemical versus extraction assays. Journal of the National Cancer Institute. 2006;98(21):1571-81. 131. Stendahl M, Ryden L, Nordenskjold B, Jonsson PE, Landberg G, Jirstrom K. High progesterone receptor expression correlates to the effect of adjuvant tamoxifen in premenopausal 176 breast cancer patients. Clinical cancer research : an official journal of the American Association for Cancer Research. 2006;12(15):4614-8. 132. Miller TW, Hennessy BT, Gonzalez-Angulo AM, Fox EM, Mills GB, Chen H, et al. Hyperactivation of phosphatidylinositol-3 kinase promotes escape from hormone dependence in estrogen receptor-positive human breast cancer. J Clin Invest. 2010;120(7):2406-13. 133. Janku F, Wheler JJ, Westin SN, Moulder SL, Naing A, Tsimberidou AM, et al. PI3K/AKT/mTOR inhibitors in patients with breast and gynecologic malignancies harboring PIK3CA mutations. Journal of clinical oncology : official journal of the American Society of Clinical Oncology. 2012;30(8):777-82. 134. Levine DA, Bogomolniy F, Yee CJ, Lash A, Barakat RR, Borgen PI, et al. Frequent mutation of the PIK3CA gene in ovarian and breast cancers. Clinical cancer research : an official journal of the American Association for Cancer Research. 2005;11(8):2875-8. 135. Janku F, Tsimberidou AM, Garrido-Laguna I, Hong DS, Naing A, Falchook GS, et al. PIK3CA, KRAS, and BRAF mutations in patients with advanced cancers treated with PI3K/AKT/mTOR axis inhibitors. Journal of Clinical Oncology. 2010;28(15_suppl):2583-. 136. Miyake T, Yoshino K, Enomoto T, Takata T, Ugaki H, Kim A, et al. PIK3CA gene mutations and amplifications in uterine cancers, identified by methods that avoid confounding by PIK3CA pseudogene sequences. Cancer Lett. 2008;261(1):120-6. 137. Hayes MP, Wang H, Espinal-Witter R, Douglas W, Solomon GJ, Baker SJ, et al. PIK3CA and PTEN mutations in uterine endometrioid carcinoma and complex atypical hyperplasia. Clinical cancer research : an official journal of the American Association for Cancer Research. 2006;12(20 Pt 1):5932-5. 138. Chandarlapaty S, Sawai A, Scaltriti M, Rodrik-Outmezguine V, Grbovic-Huezo O, Serra V, et al. AKT inhibition relieves feedback suppression of receptor tyrosine kinase expression and activity. Cancer Cell. 2011;19(1):58-71. 177 139. Rozengurt E, Soares HP, Sinnet-Smith J. Suppression of feedback loops mediated by PI3K/mTOR induces multiple overactivation of compensatory pathways: an unintended consequence leading to drug resistance. Molecular cancer therapeutics. 2014;13(11):2477-88. 140. Owusu-Brackett N, Shariati M, Meric-Bernstam F. Role of PI3K/AKT/mTOR in Cancer Signaling. In: Badve S, Kumar GL, editors. Predictive Biomarkers in Oncology: Applications in Precision Medicine. Cham: Springer International Publishing; 2019. p. 263-70. 141. Masuda T, Tsuruda Y, Matsumoto Y, Uchida H, Nakayama KI, Mimori K. Drug repositioning in cancer: The current situation in Japan. Cancer science. 2020;111(4):1039-46. 142. Sellami D, Dharan B, Wilke C, Scherer SJ, Hirawat S. Circulating tumor DNA as a novel tool to shape clinical trial designs with the potential to impact outcomes: a focus on PI3K inhibitors. Annals of oncology : official journal of the European Society for Medical Oncology. 2017;28(11):2882-7. 143. Bratman SV, Yang SYC, Iafolla MAJ, Liu Z, Hansen AR, Bedard PL, et al. Personalized circulating tumor DNA analysis as a predictive biomarker in solid tumor patients treated with pembrolizumab. Nature cancer. 2020;1(9):873-81. 144. Corcoran RB, Chabner BA. Application of Cell-free DNA Analysis to Cancer Treatment. N Engl J Med. 2018;379(18):1754-65. 145. Ghosh AP, Marshall CB, Coric T, Shim EH, Kirkman R, Ballestas ME, et al. Point mutations of the mTOR-RHEB pathway in renal cell carcinoma. Oncotarget. 2015;6(20):17895-910. 146. Argani P, Mehra R. Renal cell carcinoma associated with tuberous sclerosis complex (TSC)/mammalian target of rapamycin (MTOR) genetic alterations. Modern Pathology. 2022; 35:296-297. 147. Pezzicoli G, Filoni E, Gernone A, Cosmai L, Rizzo M, Porta C. Playing the Devil’s Advocate: Should We Give a Second Chance to mTOR Inhibition in Renal Clear Cell Carcinoma? – ie Strategies to Revert Resistance to mTOR Inhibitors. Cancer Manag Res. 2021;13:7623-7636 178 148. Gadkar K, Friedrich C, Hurez V, Ruiz ML, Dickmann L, Kumar Jolly M, Schutt L, Jin J, Ware JA, Ramanujan S. Quantitative systems pharmacology model-based investigation of adverse gastrointestinal events associated with prolonged treatment with PI3-kinase inhibitors. CPT Pharmacometrics Syst Pharmacol. 2022;11(5):616-627. 149. Moein A, Jin JY, Wright MR, Wong H. Quantitative Assessment of Drug Efficacy and Emergence of Resistance in Patients with Metastatic Renal Cell Carcinoma Using a Longitudinal Exposure-Tumor Growth Inhibition Model: Apitolisib (Dual PI3K/mTORC1/2 Inhibitor) Versus Everolimus (mTORC1 Inhibitor). J Clin Pharmacol. 2024; Epub ahead of print. 150. Dickler MN, Saura C, Richards DA, Krop IE, Cervantes A, Bedard PL, et al. Phase II Study of Taselisib (GDC-0032) in Combination with Fulvestrant in Patients with HER2-Negative, Hormone Receptor-Positive Advanced Breast Cancer. Clin Cancer Res. 2018;24 (18):4380-4387. 151. Juric D, Saura C, Cervantes A, Kurkjian C, Patel MR, Sachdev J, et al. Abstract PD1-3: Ph1b study of the PI3K inhibitor GDC-0032 in combination with fulvestrant in patients with hormone receptor-positive advanced breast cancer. Cancer Res. 2013;73 (24_Supplement). 152. He Y, Sun MM, Zhang GG, et al. Targeting PI3K/Akt signal transduction for cancer therapy. Signal Transduction and Targeted Therapy. 2021;6:425. 179 Appendices Appendix A: NONMEM Codes for “Retrospective Assessment of the Translational Pharmacokinetic-Pharmacodynamic Modeling Performance: A Case Study with Apitolisib, A Dual PI3K/mTOR inhibitor” I. Preclinical Integrated PK-PD-Efficacy Model $PROBLEM Integrated PK-PD-Efficacy ;---------------------------------- $INPUT ID ; NONMEM identification number TIME ; hr EVID ; NONMEM observation identifier AMT ; mg/kg ADDL ; Additional number of doses II ;Dosing frequency (QD) CMT ; 1=depot, 2=central (plasma), 3=biomarker (pAKT), 4=tumor (SLD) DV ; SLD TBSL ; Individual xenograft Tumor baseline ;---------------------------------- $DATA ;;;;;;;;;;;;;;;;;;;;;; ;---------------------------------- $SUBROUTINES ADVAN13 TOL=7 ;---------------------------------- $MODEL COMP=(DEPOT) COMP=(CENTRAL) COMP=(PAKT) COMP=(TUMOR) ;---------------------------------- $PK CL = 0.387 ;CL/F L/hr/kg V = 1.13 ;V/F L/kg KA = 1.1 ;1/hr 180 S2 = V K20 = CL/V ;pAKT IC50 = 0.403 ;mg/L [403 ug/L = 0.403 mg/L] KIN = 88698 KOUT = KIN/100 HILL = 1 ; γ1 = sigmoidicity factor IMAX = 1 ;Tumor KG = THETA(1)*EXP(ETA(1)) KMAX=THETA(2)*EXP(ETA(2)) KI50=THETA(3) HL = THETA(4) ; γ2= sigmoidicity factor A_0(3)=100 A_0(4)=TBSL ;Tumor Baseline ;----------------------- $DES DADT(1) = -KA*A(1) DADT(2) = KA*A(1) - K20*A(2) CP=A(2)/V IF (CP.GT.0) THEN DADT(3) = KIN*(1-((IMAX*CP**HILL)/(IC50**HILL+CP**HILL)))-KOUT*A(3) ELSE DADT(3) = KIN*(1-((IMAX*CP)/(IC50+CP)))-KOUT*A(3) ENDIF R=100-A(3) IF (R.LT.0) R=0 K=(KMAX*R**HL)/(KI50**HL+R**HL) DADT(4) = KG*A(4) - K*A(4) ;--------------------- 181 $ERROR IPRED = A(4) IRES = DV-IPRED W = IPRED*THETA(5) IF (W.EQ.0) W = 1 IWRES = IRES/W Y= IPRED+W*ERR(1) ;---------------------------------- $THETA (0, 0.00568) ;KG (0, 0.0194) ;KMAX (1, 67.3,100) ;KI50 (1, 9.33, 15) ;HL (γ2) (0, 0.249) ;Proportional error ;---------------------------------- $OMEGA 0.0277 ;KG 0.0525 ;KMAX ;---------------------------------- $SIGMA 1 FIX ;---------------------------------- $EST METHOD=1 INTERACTION MAXEVAL=9999 SIG=3 PRINT=5 NOABORT ;---------------------------------- $COV UNCONDITIONAL PRINT=E MATRIX = S ;---------------------------------- 182 II. Clinical Integrated PK-PD-Efficacy Model $PROBLEM Integrated PK-PD-Efficacy ;---------------------------------- $INPUT ID ; NONMEM identification number TIME ; week EVID ; NONMEM observation identifier AMT ; µg ADDL ; Additional number of doses II ;Dosing frequency (QD) CMT ; 1=depot, 2=plasma, 3=peripheral, 4=biomarker, 5=tumor (SLD) DV ; SLD TBSL ; Individual Tumor baseline ICL ; Individual apparent oral clearance IV1 ; Individual apparent central volume of distribution IV2 ; Individual apparent peripheral volume of distribution IQ ; Individual apparent inter-compartmental clearance (CLd) IKA ; Individual first-order absorption rate constant IALAG1 ; Individual absorption lagged time IEC50 ; Apitolisib IC50 ;---------------------------------- $DATA ;;;;;;;;;;;;;;;;;;;;;; ;---------------------------------- $ABBREVIATED DERIV2=NO ;---------------------------------- $SUBROUTINES ADVAN13 TOL=7 ;---------------------------------- $MODEL COMP=(DEPOT) COMP=(CENTRAL) COMP=(PHERI) COMP=(PAKT) COMP=(TUMOR) ;---------------------------------- 183 $PK CL = ICL*168 ;L/week V1 = IV2 ;L V2 = IV3 ;L Q = IQ*168 ;L/week KA = IKA*168 ;1/week ALAG1 = IALAG1/168 ;week S2 = V1 K20 = CL/V1 K23 = Q/V1 K32 = Q/V2 ;pAKT EC50 = IEC50 ; apitolisib IC50 KIN = 88699 KOUT = KIN/100 HILL = 1 ; γ1 = sigmoidicity factor IMAX = 1 ;Tumor KG = THETA(1)*EXP(ETA(1)) KMAX=THETA(2)*EXP(ETA(2)) KI50=THETA(3)*EXP(ETA(3)) HL = THETA(4)*EXP(ETA(4)) ; γ2= sigmoidicity factor A_0(4)=100 A_0(5)=BSLD ;Tumor Baseline ;----------------------- $DES DADT(1) = -KA*A(1) DADT(2) = KA*A(1) - K20*A(2) - K23*A(2) + K32*A(3) DADT(3) = K23*A(2) - K32*A(3) CP=A(2)/V2 IF (CP.GT.0) THEN DADT(4) = (KIN*168)*(1-((IMAX*CP**HILL)/(EC50**HILL+CP**HILL)))-(KOUT*168)*A(4) ELSE DADT(4) = (KIN*168)*(1-((IMAX*CP)/(EC50+CP)))-(KOUT*168)*A(4) ENDIF R=100-A(4) IF (R.LT.0) R=0 184 K=(KMAX*R**HL)/(KI50**HL+R**HL) DADT(5) = KG*A(5) - K*A(5) ;--------------------- $ERROR IPRED = A(5) IRES = DV-IPRED W = IPRED*THETA(5) IF (W.EQ.0) W = 1 IWRES = IRES/W Y= IPRED+W*ERR(1) ;---------------------------------- $THETA (0, 0.0102) ;KG (0, 0.0149) ;KMAX (1, 58.1,100) ;KI50 (1, 6.52, 15) ;HILL (γ2) (0, 0.141) ;Proportional error $OMEGA 0.5 ;KG 0.5 ;KMAX 0.0225 FIX ;KI50 0.0225 FIX ;HL (γ2) ;---------------------------------- $SIGMA 1 FIX ;---------------------------------- $EST METHOD=1 INTERACTION MAXEVAL=9999 SIG=3 PRINT=5 NOABORT ;---------------------------------- $COV PRINT=E UNCONDITIONAL MATRIX = S ;---------------------------------- 185 Appendix B: NONMEM Code for “Quantitative Assessment of Drug Efficacy and Emergence of Resistance in Patients with Metastatic Renal Cell Carcinoma Using a Longitudinal Exposure-Tumor Growth Inhibition Model: Apitolisib (dual PI3K/mTORC1/2 inhibitor) versus Everolimus (mTORC1 inhibitor)” $PROBLEM Longitudinal Exposure-Tumor Growth Inhibition Model ;---------------------------------- $INPUT ID ; NONMEM identification number TIME ; week (relative to tumor baseline assessments starting from 0) DRUG ; 1= Everolimus, 2= Apitolisib EVID ; NONMEM observation identifier AMT ; actual dosing amount CMT ; 1=depot, 2=central (plasma), 3=peripheral (tissue), 4=tumor (SLD) DV ;SLD ;---------------------------------- $DATA ;;;;;;;;;;;;;; $ABBREV COMRES = 1 $ABBR PROTECT ;---------------------------------- $SUBROUTINES ADVAN13 TOL=7 ;---------------------------------- $MODEL COMP=(DEPOT) ;1 COMP=(CENTRAL) ;2 COMP=(PHERI) ;3 COMP=(TUMOR) ;4 ;---------------------------------- $PK ;;; Everolimus popPK parameters IF(DRUG.EQ.1) CL = 14.8*168 ;CL/F L/hr to L/week IF(DRUG.EQ.1) V1 = 172 ;V1/F L IF(DRUG.EQ.1) V2 = 495 ;V2/F L IF(DRUG.EQ.1) Q = 48*168 ;Q/F L/hr to L/week IF(DRUG.EQ.1) KA = 6.07*168 ;1/hr to 1/week ;;; Apitolisib popPK parameters IF(DRUG.EQ.2) CL = 21.33*168 ;CL/F L/hr to week IF(DRUG.EQ.2) V1 = 210.61 ;V1/F L IF(DRUG.EQ.2) V2 = 639.06 ;V2/F L 186 IF(DRUG.EQ.2) Q = 5.93*168 ;Q/F L/hr to week IF(DRUG.EQ.2) KA = 3.35*168 ;1/hr to week IF(DRUG.EQ.2) ALAG1 = 0.465/168 ;hr to week S2 = V1 K20 = CL/V1 K23 = Q/V1 K32 = Q/V2 ;;;Tumor Metrics TVSLD0 = THETA(1) ; baseline tumor size IF(NEWIND.NE.2) KG1 = 0 IF(NEWIND.NE.2) KS1 = 0 IF(NEWIND.NE.2) RSTHALF1 = 0 IF(NEWIND.NE.2) KG2 = 0 IF(NEWIND.NE.2) KS2 = 0 IF(NEWIND.NE.2) RSTHALF2 = 0 IF(DRUG.EQ.1) KG1 = THETA(2) ; Everolimus net tumor growth rate constant IF(DRUG.EQ.1) KS1 = THETA(3) ; Everolimus tumor shrinkage rate constant IF(DRUG.EQ.1) RSTHALF1 = THETA(4) ; Everolimus T50λ IF(DRUG.EQ.2) KG2 = THETA(5) ; Apitolisib net tumor growth rate constant IF(DRUG.EQ.2) KS2 = THETA(6) ; Apitolisib tumor shrinkage rate constant IF(DRUG.EQ.2) RSTHALF2 = THETA(7) ; Apitolisib T50λ SLD0 = TVSLD0 * EXP(ETA(1)) IF(DRUG.EQ.1) KG =KG1 * EXP(ETA(2)) IF(DRUG.EQ.1) KS =KS1 * EXP(ETA(3)) IF(DRUG.EQ.1) RSTHALF =RSTHALF1 * EXP(ETA(4)) IF(DRUG.EQ.2) KG =KG2 * EXP(ETA(5)) IF(DRUG.EQ.2) KS =KS2 * EXP(ETA(6)) IF(DRUG.EQ.2) RSTHALF =RSTHALF2 * EXP(ETA(7)) LAM = LOG(2)/RSTHALF ; constant accounting for loss of treatment effect over time ; Compartment initialization A_0(1) = 0 A_0(2) = 0 A_0(3) = 0 A_0(4)=SLD0 187 ;----------------------- $DES DADT(1) = -KA*A(1) DADT(2) = KA*A(1) - K20*A(2) - K23*A(2) + K32*A(3) DADT(3) = K23*A(2) - K32*A(3) CP = A(2)/V2 DADT(4) = KG*A(4) - KS*A(4)*CP*(EXP(-LAM*T)) ;--------------------- $ERROR IPRED=F RES1 = SQRT(THETA(8)) Y = F + RES1*ERR(1) W=SQRT(THETA(8)) DEL = 0 IF(W.EQ.0) DEL = 1 IRES = DV - IPRED IWRES = (DV-IPRED)/(W+DEL) ;---------------------------------- $THETA (0, 69.1) ;SLD0 mm (0, 0.00306) ;KG1 1/week (0, 0.313) ;KS1 1/week (0, 23) ;RSTHALF1 week (0, 0.00476) ;KG2 1/week (0, 0.234) ;KS2 1/week (0, 7.73) ;RSTHALF2 week (0, 76.8) ;VARIANCE OF ADD ERROR $OMEGA 0.442 ;SLD0 1.15 ;KG1 1.14 ;KS1 1.2 FIX ;RSTHALF1 1.13 ;KG2 0.84 ;KS2 5.63 ;RSTHALF2 $SIGMA 1 FIX ;---------------------------------- $EST METHOD=1 INTERACTION MAXEVAL=9999 SIG=3 PRINT=5 NOABORT ;---------------------------------- $COV PRINT=E UNCONDITIONAL MATRIX=S ;---------------------------------- 188 Appendix C: NONMEM Codes for “Quantitative Characterization of the Effects of Fulvestrant Alone or in Combination with Taselisib (PI3Kinase Inhibitor) on Longitudinal Tumor Growth in Patients with Estrogen Receptor-positive, HER2-negative, PIK3CA-mutant, Advanced or Metastatic Breast Cancer” I. Base Fulvestrant TGI Model $PROBLEM Base Fulvestrant TGI Model ;---------------------------------- $INPUT ID ; NONMEM identification number TIME ; week EVID ; NONMEM observation identifier CMT ; 1= tumor (SLD) DV ; SLD ;---------------------------------- $DATA ;;;;;;;;;;;;;; ;---------------------------------- $SUBROUTINE ADVAN13 TOL=6 ;---------------------------------- $MODEL COMP=(TUMOR) ;1 ;---------------------------------- $PK ; Tumor Metrics TVSLD0 = THETA(1) ; baseline tumor size TVKG = THETA(2) ; net tumor growth rate constant TVKSF = THETA(3) ; tumor shrinkage rate constant for Fulvestrant TVLAMF = THETA(4) ; λ for Fulvestrant SLD0 = TVSLD0 * EXP(ETA(1)) KG = TVKG * EXP(ETA(2)) KSF = TVKSF * EXP(ETA(3)) LAMF = TVLAMF * EXP(ETA(4)) ; Compartment initialization A_0(1) = SLD0 189 ;----------------------- $DES SLDmx=1000 ; maximum tumor burden estimated then fixed DADT(1)= (KG * LOG(SLDmx/A(1)) * A(1)) - (KSF * EXP(-LAMF*T) * A(1)) ;--------------------- $ERROR IPRED=F IRES = DV - IPRED W=SQRT(THETA(5)) IF(W.EQ.0) W = 1 IWRES = IRES/W Y = IPRED + W*ERR(1) ;---------------------------------- $THETA (0, 35.5) ;SLD0 (0, 0.0015) ;KG (0, 0.00381) ;KSF (0, 0.00636) ;LAMF (0, 23.2) ;VARIANCE OF ADDITIVE ERROR $OMEGA 0.571 ;SLD0 1.91 ;KG 1.82 ;KSF 3.37 ;LAMF $SIGMA 1 FIX ;---------------------------------- $EST METHOD=1 INTERACTION MAXEVAL=9999 SIG=3 PRINT=5 NOABORT ;---------------------------------- $COV PRINT=E UNCONDITIONAL MATRIX=S ;---------------------------------- 190 II. Covariate Fulvestrant TGI Model $PROBLEM Covariate Fulvestrant TGI Model ;---------------------------------- $INPUT ID ; NONMEM identification number TIME ; week EVID ; NONMEM observation identifier CMT ; 1= tumor (SLD) DV ; SLD SLDBL ; baseline tumor size IXRSENDO ; baseline endocrine sensitivity: 0= none sensitive, 1= sensitive LIVER ; baseline liver metastases: 0=no metastases, 1= metastases ;---------------------------------- $DATA ;;;;;;;;;;;;;;;;;;;;;;;;;; ;---------------------------------- $SUBROUTINE ADVAN13 TOL=6 ;---------------------------------- $MODEL COMP=(TUMOR) ;1 ;---------------------------------- $PK ;;; KGSLDBL-DEFINITION START KGSLDBL = ((SLDBL/34.55)**THETA(6)) ;;; KGSLDBL-DEFINITION END ;;; KGIXRSENDO-DEFINITION START IF(IXRSENDO.EQ.1.0000E+00) KGIXRSENDO = 1 ; Most common IF(IXRSENDO.EQ.0.0000E+00) KGIXRSENDO = ( 1 + THETA(7)) ;;; KGIXRSENDO-DEFINITION END ;;; KGLIVER-DEFINITION START IF(LIVER.EQ.1.0000E+00) KGLIVER = 1 ; Most common IF(LIVER.EQ.0.0000E+00) KGLIVER = ( 1 + THETA(8)) ;;; KGLIVER-DEFINITION END ;;; KG-RELATION START KGCOV=KGSLDBL*KGIXRSENDO*KGLIVER ;;; KG-RELATION END TVSLD0 = THETA(1) TVKG = THETA(2) TVKG = KGCOV*TVKG TVKSF = THETA(3) 191 TVLAMF = THETA(4) SLD0 = TVSLD0 * EXP(ETA(1)) KG = TVKG * EXP(ETA(2)) KSF = TVKSF * EXP(ETA(3)) LAMF = TVLAMF * EXP(ETA(4)) ; Compartment initialization A_0(1) = SLD0 ;----------------------- $DES SLDmx=1000 ;estimated then fixed DADT(1)= (KG * LOG(SLDmx/A(1)) * A(1)) - (KSF * EXP(-LAMF*T) * A(1)) ;--------------------- $ERROR IPRED=F IRES = DV - IPRED W=SQRT(THETA(5)) IF(W.EQ.0) W = 1 IWRES = IRES/W Y = IPRED + W*ERR(1) ;---------------------------------- $THETA (0, 36) ;SLD0 (0, 0.00145) ;KG (0, 0.00405) ;KSF (0, 0.00671) ;LAMF (0, 23) ;VARIANCE OF ADDITIVE ERROR (-100, 1.2,100000) ; KGSLDBL1 (-1,0.743, 5) ;KGIXRSENDO (-1,-0.642,5) ;KGLIVER $OMEGA 0.542 ;SLD0 1.04 ;KG 1.31 ;KSF 2.74 ;LAMF $SIGMA 1 FIX ;---------------------------------- $EST METHOD=1 INTERACTION MAXEVAL=9999 SIG=3 PRINT=5 NOABORT ;---------------------------------- $COV PRINT=E UNCONDITIONAL MATRIX=S ;---------------------------------- 192 III. Base Combination Therapy TGI Model $PROBLEM Base Combination Therapy TGI Model ;---------------------------------- $INPUT ID ; NONMEM identification number TIME ; week COMBTX ; 0= Fulvestrant, 1= Fulvestrant+ Taselisib EVID ; NONMEM observation identifier AMT ; actual dosing amount for Taselisib CMT ; 1=depot, 2=central (plasma), 3=peripheral (tissue), 4=tumor (SLD) DV ; SLD PIK3CAST ; PIK3CA mutation status: 0=wild type, 1=mutant ;---------------------------------- $DATA ;;;;;;;;;;;;;;;;;;;;;; ;---------------------------------- $SUBROUTINE ADVAN13 TOL=6 ;---------------------------------- $MODEL COMP=(GDCDEPOT) ;1 COMP=(GDCCENT) ;2 COMP=(GDCPERIPH) ;3 COMP=(TUMOR) ;4 ;---------------------------------- $PK ; Taselisib (GDC-0032) popPK parameters CL = 3.02 * 168 ; Clearance (L/hr) to L/week V2 = 165 ; Central volume (L) V3 = 35.2 ; Peripheral volume (L) Q = 1.57 * 168 ; Inter-compartmental clearance (L/hr) to L/week KA = 1.48 * 168 ; First-order absorption rate constant (1/hr) to 1/week ALAG1 = 0.416/168 ; Absorption Lag (hr) to week K20 = CL/V2 K23 = Q/V2 K32 = Q/V3 193 ; Tumor ;;; KSGPIK3CAST-DEFINITION START IF(PIK3CAST.EQ.1) KSGPIK3CAST = 1 ; Most common IF(PIK3CAST.EQ.0) KSGPIK3CAST = (THETA(8)) ;power ;;; KSGPIK3CAST-DEFINITION END ;;; KSG-RELATION START KSGCOV=KSGPIK3CAST ;;; KSG-RELATION END IF(NEWIND.NE.2) TVKSG = 0 IF(NEWIND.NE.2) TVLAMG = 0 TVSLD0 = THETA(1) ; baseline tumor size TVKG = THETA(2) ; net tumor growth rate constant IF(COMBOTX.EQ.1) TVKSG = THETA(3) ; β (taselisib) TVKSG = KSGCOV*TVKSG TVKSF = THETA(4) ; tumor shrinkage rate constant for Fulvestrant IF(COMBOTX.EQ.1) TVLAMG = THETA(5) ; λ for Taselisib TVLAMF = THETA(6) ; λ for Fulvestrant IF(NEWIND.NE.2) KSG = 0 IF(NEWIND.NE.2) LAMG = 0 SLD0 = TVSLD0 * EXP(ETA(1)) KG = TVKG * EXP(ETA(2)) IF(COMBOTX.EQ.1) KSG= TVKSG * EXP(ETA(3)) KSF = TVKSF * EXP(ETA(4)) IF(COMBOTX.EQ.1) LAMG = TVLAMG * EXP(ETA(5)) LAMF = TVLAMF * EXP(ETA(6)) ; Compartment initialization A_0(1) = 0 A_0(4) = SLD0 ;----------------------- $DES ;;Taselisib (GDC) PK DADT(1) = -KA*A(1) DADT(2) = KA*A(1) - K20*A(2) - K23*A(2) + K32*A(3) DADT(3) = K23*A(2) - K32*A(3) A2 = A(2)/V2 GDC= A2 * EXP(-LAMG*T) ;;Tumor SLDmx=1000 ; maximum tumor burden, estimated then fixed DADT(4)= (KG * LOG(SLDmx/A(4)) * A(4)) - (KSF * EXP(-LAMF*T) * A(4)) - (KG * KSG * GDC * A(4)) 194 ;--------------------- $ERROR IPRED=F IRES = DV - IPRED W=SQRT(THETA(7)) IF(W.EQ.0) W = 1 IWRES = IRES/W Y = IPRED + W*ERR(1) ;---------------------------------- $THETA (0, 37.9) ;SLD0 (0, 0.00282) ;KG (0, 157) ;KSG (0, 0.00695) ;KSF (0, 0.116) ;LAMG (0, 0.0028) ;LAMF (0, 21.7) ;VARIANCE OF ADDITIVE ERROR (0, 0.659,1) ;KSGPIK3CAST $OMEGA 0.533 ;SLD0 1.08 ;KG 0.752 ;KSG 1.03 ;KSF 0.344 ;LAMG 4.16 ;LAMF $SIGMA 1 FIX ;---------------------------------- $EST METHOD=1 INTERACTION MAXEVAL=9999 SIG=3 PRINT=5 NOABORT ;---------------------------------- $COV PRINT=E UNCONDITIONAL MATRIX=S ;---------------------------------- 195 IV. Covariate Combination Therapy TGI Model $SIZES PD=-100 $PROBLEM Covariate Combination Therapy TGI Model ;---------------------------------- $INPUT ID ; NONMEM identification number TIME ; week COMBTX ; 0= Fulvestrant, 1= Fulvestrant+ Taselisib EVID ; NONMEM observation identifier AMT ; actual dosing amount for Taselisib CMT ; 1=depot, 2=central (plasma), 3=peripheral (tissue), 4=tumor (SLD) DV ; SLD PIK3CAST ; PIK3CA mutation status: 0=wild type, 1=mutant SLDBL ; baseline tumor size IXRSENDO ; baseline endocrine sensitivity: 0= none sensitive, 1= sensitive LIVER ; baseline liver metastases: 0=no metastases, 1= metastases ;---------------------------------- $DATA ;;;;;;;;;;;;;;;;;;;;;;; ;---------------------------------- $SUBROUTINE ADVAN13 TOL=6 ;---------------------------------- $MODEL COMP=(GDCDEPOT) ;1 COMP=(GDCCENT) ;2 COMP=(GDCPERIPH) ;3 COMP=(TUMOR) ;4 ;---------------------------------- $PK ; Taselisib popPK parameters CL = 3.02 * 168 ; Clearance (L/hr) to L/week V2 = 165 ; Central volume (L) V3 = 35.2 ; Peripheral volume (L) Q = 1.57 * 168 ; Inter-compartmental clearance (L/hr) to L/week KA = 1.48 * 168 ; First-order absorption rate constant (1/hr) to 1/week ALAG1 = 0.416/168 ; Absorption Lag (hr) to week K20 = CL/V2 K23 = Q/V2 K32 = Q/V3 196 ;------------------KSG------------------------- ;;; KSGPIK3CAST-DEFINITION START IF(PIK3CAST.EQ.1) KSGPIK3CAST = 1 ; Most common IF(PIK3CAST.EQ.0) KSGPIK3CAST = (THETA(8)) ;;; KSGPIK3CAST-DEFINITION END ;;; KSGPRST-DEFINITION START IF(PRST.EQ.1) KSGPRST = 1 ; Most common IF(PRST.EQ.0) KSGPRST = ( 1 + THETA(12)) ;;; KSGPRST-DEFINITION END ;;; KSG-RELATION START KSGCOV=KSGPIK3CAST*KSGPRST ;;; KSG-RELATION END ;-----------KG--------------------------------------------- ;;; KGSLDBL-DEFINITION START KGSLDBL = ((SLDBL/34.55)**THETA(9)) ;;; KGSLDBL-DEFINITION END ;;; KGENDOSEN-DEFINITION START IF(IXRSENDO.EQ.1) KGENDOSEN = 1 ; Most common IF(IXRSENDO.EQ.0) KGENDOSEN = ( 1 + THETA(10)) ;;; KGENDOSEN-DEFINITION END ;;; KGLIVER-DEFINITION START IF(LIVER.EQ.1) KGLIVER = 1 ; Most common IF(LIVER.EQ.0) KGLIVER = ( 1 + THETA(11)) ;;; KGLIVER-DEFINITION END ;;; KG-RELATION START KGCOV=KGSLDBL*KGLIVER*KGENDOSEN ;;; KG-RELATION END ;--------------------------------------------------------- IF(NEWIND.NE.2) TVKSG = 0 IF(NEWIND.NE.2) TVLAMG = 0 TVSLD0 = THETA(1) TVKG = THETA(2) TVKG = KGCOV*TVKG IF(COMBOTX.EQ.1) TVKSG = THETA(3) TVKSG = KSGCOV*TVKSG TVKSF = THETA(4) 197 IF(COMBOTX.EQ.1) TVLAMG = THETA(5) TVLAMF = THETA(6) IF(NEWIND.NE.2) KSG = 0 IF(NEWIND.NE.2) LAMG = 0 SLD0 = TVSLD0 * EXP(ETA(1)) KG = TVKG * EXP(ETA(2)) IF(COMBOTX.EQ.1) KSG= TVKSG * EXP(ETA(3)) KSF = TVKSF * EXP(ETA(4)) IF(COMBOTX.EQ.1) LAMG = TVLAMG * EXP(ETA(5)) LAMF = TVLAMF * EXP(ETA(6)) ; Compartment initialization A_0(1) = 0 A_0(4) = SLD0 ;----------------------- $DES ;;Taselisib (GDC) PK DADT(1) = -KA*A(1) DADT(2) = KA*A(1) - K20*A(2) - K23*A(2) + K32*A(3) DADT(3) = K23*A(2) - K32*A(3) A2 = A(2)/V2 GDC= A2 * EXP(-LAMG*T) ;;Tumor SLDmx=1000 ;estimated then fixed DADT(4)= (KG * LOG(SLDmx/A(4)) * A(4)) - (KSF * EXP(-LAMF*T) * A(4)) - (KG * KSG * GDC * A(4)) ;--------------------- $ERROR IPRED=F IRES = DV - IPRED W=SQRT(THETA(7)) IF(W.EQ.0) W = 1 IWRES = IRES/W Y = IPRED + W*ERR(1) ;---------------------------------- $THETA (0, 38) ;SLD0 (0, 0.0032) ;KG (0, 156) ;KSG (0, 0.00767) ;KSF (0, 0.132) ;LAMG (0, 0.00456) ;LAMF (0, 22) ;VARIANCE OF ADDITIVE ERROR 198 (0.1, 0.659,1) ;KSGPIK3CAST _8 (-5, 0.634,5) ;KGSLDBL _9 (-5, 0.384,5) ;KGENDOSEN _10 (-5, -0.557,5) ;KGLIVER _11 (-5, -0.47,5) ;KSGPRST _12 $OMEGA 0.526 ;SLD0 0.786 ;KG 0.408 ;KSG 1.1 ;KSF 0.452 ;LAMG 2.63 ;LAMF $SIGMA 1 FIX ;---------------------------------- $EST METHOD=1 INTERACTION MAXEVAL=9999 SIG=3 PRINT=5 NOABORT ;---------------------------------- $COV PRINT=E UNCONDITIONAL MATRIX=S ;---------------------------------- 199 V. Interaction TGI Model $SIZES PD=-100 $PROBLEM Interaction TGI Model ;---------------------------------- $INPUT ID ; NONMEM identification number TIME ; week COMBTX ; 0= Fulvestrant, 1= Fulvestrant+ Taselisib EVID ; NONMEM observation identifier AMT ; actual dosing amount for Taselisib CMT ; 1=depot, 2=central (plasma), 3=peripheral (tissue), 4=tumor (SLD) DV ; SLD PIK3CAST ; PIK3CA mutation status: 0=wild type, 1=mutant SLDBL ; baseline tumor size IXRSENDO ; baseline endocrine sensitivity: 0= none sensitive, 1= sensitive LIVER ; baseline liver metastases: 0=no metastases, 1= metastases ;---------------------------------- $DATA ;;;;;;;;;;;;;;;;;;;;;;;;;; ;---------------------------------- $SUBROUTINE ADVAN13 TOL=6 ;---------------------------------- $MODEL COMP=(GDCDEPOT) ;1 COMP=(GDCCENT) ;2 COMP=(GDCPERIPH) ;3 COMP=(TUMOR) ;4 ;---------------------------------- $PK ; Taselisib popPK parameters CL = 3.02 * 168 ; Clearance (L/hr) to L/week V2 = 165 ; Central volume (L) V3 = 35.2 ; Peripheral volume (L) Q = 1.57 * 168 ; Inter-compartmental clearance (L/hr) to L/week KA = 1.48 * 168 ; First-order absorption rate constant (1/hr) to 1/week ALAG1 = 0.416/168 ; Absorption Lag (hr) to week K20 = CL/V2 K23 = Q/V2 K32 = Q/V3 200 ;------------------KSG------------------------- ;;; KSGPIK3CAST-DEFINITION START IF(PIK3CAST.EQ.1) KSGPIK3CAST = 1 ; Most common IF(PIK3CAST.EQ.0) KSGPIK3CAST = (THETA(8)) ;;; KSGPIK3CAST-DEFINITION END ;;; KSGPRST-DEFINITION START IF(PRST.EQ.1) KSGPRST = 1 ; Most common IF(PRST.EQ.0) KSGPRST = ( 1 + THETA(12)) ;;; KSGPRST-DEFINITION END ;;; KSG-RELATION START KSGCOV=KSGPIK3CAST*KSGPRST ;;; KSG-RELATION END ;-----------KG--------------------------------------------- ;;; KGSLDBL-DEFINITION START KGSLDBL = ((SLDBL/34.55)**THETA(9)) ;;; KGSLDBL-DEFINITION END ;;; KGENDOSEN-DEFINITION START IF(IXRSENDO.EQ.1) KGENDOSEN = 1 ; Most common IF(IXRSENDO.EQ.0) KGENDOSEN = ( 1 + THETA(10)) ;;; KGENDOSEN-DEFINITION END ;;; KGLIVER-DEFINITION START IF(LIVER.EQ.1) KGLIVER = 1 ; Most common IF(LIVER.EQ.0) KGLIVER = ( 1 + THETA(11)) ;;; KGLIVER-DEFINITION END ;;; KG-RELATION START KGCOV=KGSLDBL*KGLIVER*KGENDOSEN ;;; KG-RELATION END ;--------------------------------------------------------- IF(NEWIND.NE.2) TVKSG = 0 IF(NEWIND.NE.2) TVLAMG = 0 IF(NEWIND.NE.2) TVINT = 0 TVSLD0 = THETA(1) TVKG = THETA(2) TVKG = KGCOV*TVKG IF(COMBOTX.EQ.1) TVKSG = THETA(3) TVKSG = KSGCOV*TVKSG TVKSF = THETA(4) IF(COMBOTX.EQ.1) TVLAMG = THETA(5) TVLAMF = THETA(6) 201 IF(COMBOTX.EQ.1) TVINT = THETA(13) ; typical interaction fulvestrant and taselisib IF(NEWIND.NE.2) KSG = 0 IF(NEWIND.NE.2) LAMG = 0 IF(NEWIND.NE.2) INT = 0 SLD0 = TVSLD0 * EXP(ETA(1)) KG = TVKG * EXP(ETA(2)) IF(COMBOTX.EQ.1) KSG= TVKSG * EXP(ETA(3)) KSF = TVKSF * EXP(ETA(4)) IF(COMBOTX.EQ.1) LAMG = TVLAMG * EXP(ETA(5)) LAMF = TVLAMF * EXP(ETA(6)) IF(COMBOTX.EQ.1) INT = TVINT * EXP(ETA(7)) ; Compartment initialization A_0(1) = 0 A_0(4) = SLD0 ;----------------------- $DES ;;Taselisib (GDC) PK DADT(1) = -KA*A(1) DADT(2) = KA*A(1) - K20*A(2) - K23*A(2) + K32*A(3) DADT(3) = K23*A(2) - K32*A(3) A2 = A(2)/V2 GDC= A2 * EXP(-LAMG*T) ;;Tumor SLDmx=1000 ;estimated then fixed DADT(4)= (KG * LOG(SLDmx/A(4)) * A(4)) - ((KSF * EXP(-LAMF*T) * A(4)) + (KG * KSG * GDC * A(4))) * INT ;--------------------- $ERROR IPRED=F IRES = DV - IPRED W=SQRT(THETA(7)) IF(W.EQ.0) W = 1 IWRES = IRES/W Y = IPRED + W*ERR(1) ;---------------------------------- 202 $THETA (0, 38.1) ;SLD0 (0, 0.00321) ;KG (0, 70.5, 76) ;KSG (0, 0.00764) ;KSF (0, 0.131, 0.135) ;LAMG (0, 0.00453) ;LAMF (0, 22) ;VARIANCE OF ADD ERROR (0.1, 0.661,1) FIX ;KSGPIK3CAST _8 (-5, 0.624,5) FIX ;KGSLDBL _9 (-5, 0.386,5) FIX ;KGENDOSEN _10 (-5, -0.548,5) FIX ;KGLIVER _11 (-5, -0.382,5) FIX ;KSGPRST _12 (1, 1.78) ;INT _13 $OMEGA 0.527 ;SLD0 0.784 ;KG 0.42 ;KSG 1.08 ;KSF 0.455 ;LAMG 2.58 ;LAMF 0.0255 FIX ;INT $SIGMA 1 FIX ;---------------------------------- $EST METHOD=1 INTERACTION MAXEVAL=9999 SIG=3 PRINT=5 NOABORT ;---------------------------------- $COV PRINT=E UNCONDITIONAL MATRIX=S ;----------------------------------
Thesis/Dissertation
eng
Pharmaceutical Sciences
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Wong, Harvey
Quantitative pharmacokinetic-pharmacodynamic modeling to optimize targeted PI3K-AKT-mTOR oncology therapeutics development
Text