Business, Sauder School of
Operations and Logistics (OPLOG), Division of
DSpace
UBCV
Jin, Yiwen
Doctor of Philosophy - PhD
University of British Columbia
This doctoral dissertation comprises two independent essays on healthcare delivery analytics. In the first essay, we investigate the impact of task switching on three angles of emergency department (ED) operations: physician productivity, quality of care, and patient routing using comprehensive data of patient visits and lab tests. We find that a 10% increase in the switching frequency of physicians reduces the number of patients treated per hour by 8.65% - 11.53% on average. However, we find no significant influence on treatment quality. We propose an easily implementable data-driven queue management method to optimally partition patients into two queues to minimize switch cost. Further simulation shows that this method can reduce average waiting time by 38%. In the second essay, we study how surgical and cleaning teams adaptively adjust the service speed in response to real-time deviations from the planned schedules and the further impact on surgical quality. Using a unique surgery data set, we unveil that surgical and cleaning teams speed up when they fall behind schedule and slow down when they get ahead of schedule, with a stronger slowdown effect. We further show that a faster-than-scheduled surgical procedure erodes quality by increasing 30-day readmission and reoperation probabilities. Through a counterfactual analysis, we obtain a convex relationship between readmissions/reoperations and end-of-shift times.
Essays on Healthcare DeliveryAnalyticsbyYiwen JinB.A. Economics and B.S. Mathematics, Wuhan University, 2018A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Business Administration - Management Science)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)July 2024© Yiwen Jin 2024The following individuals certify that they have read, and recommend tothe Faculty of Graduate and Postdoctoral Studies for acceptance, the thesisentitled:Essays on Healthcare Delivery Analyticssubmitted by Yiwen Jin in partial fulfillment of the requirements for thedegree of Doctor of Philosophy in Business Administration - Man-agement Science.Examining Committee:Mahesh Nagarajan, Professor, Sauder School of Business, UBCSupervisorYichuan Ding, Associate Professor, Desautels Faculty of Management, McGillUniversityCo-SupervisorSteven Shechter, Professor, Sauder School of Business, UBCSupervisory Committee MemberYi Qian, Associate Professor, Sauder School of Business, UBCUniversity ExaminerNick Bansback, Professor, School of Population and Public Health, UBCUniversity ExaminerAdditional Supervisory Committee Members:Harish Krishnan, Professor, Sauder School of Business, UBCSupervisory Committee MemberiiAbstractThis doctoral dissertation comprises two independent essays on healthcaredelivery analytics.In the first essay, we investigate the impact of task switching on three anglesof emergency department (ED) operations: physician productivity, qualityof care, and patient routing using comprehensive data of patient visits andlab tests. We find that a 10% increase in the switching frequency of physi-cians reduces the number of patients treated per hour by 8.65% - 11.53% onaverage. However, we find no significant influence on treatment quality. Wepropose an easily implementable data-driven queue management method tooptimally partition patients into two queues to minimize switch cost. Fur-ther simulation shows that this method can reduce average waiting time by38%.In the second essay, we study how surgical and cleaning teams adaptivelyadjust the service speed in response to real-time deviations from the plannedschedules and the further impact on surgical quality. Using a unique surgerydata set, we unveil that surgical and cleaning teams speed up when they fallbehind schedule and slow down when they get ahead of schedule, with astronger slowdown effect. We further show that a faster-than-scheduled sur-gical procedure erodes quality by increasing 30-day readmission and reoper-ation probabilities. Through a counterfactual analysis, we obtain a convexrelationship between readmissions/reoperations and end-of-shift times.iiiLay SummaryThis dissertation spans two research streams: (i) empirical healthcare oper-ations, and (ii) behavioral queueing.Chapter 2 relates to both two streams and chapter 3 relates to the firststream. In these two chapters, we utilize detailed datasets to explore howhealthcare providers behave in various complex healthcare service sites andwhat are the potential outcomes on service efficiency and quality. With theseempirical findings, we propose operational solutions to improve healthcareservice delivery accordingly. In chapter 2, we propose a data-driven queuemanagement method in which we demonstrate how to optimally route pa-tients to two queues such that the switch costs can be minimized. In chapter3, we quantify the efficiency-quality frontier for hospital managers to helpthem achieve desired quality goals.ivPrefaceChapter 2 and 3 of this dissertation are now under revision and to be submit-ted back to journals. The research in chapter 3 has been approved by UBCChildren’s & Women’s Research Ethics Board with the number: H21-00785.Chapter 2 is co-authored with Yige Duan, Yichuan Ding, Mahesh Nagarajan,Garth Hunte. Chapter 3 is co-authored with Yichuan Ding, Steven Shechter,Jugpal Arneja.I was the leading author in the two chapters and was involved in cleaningand organizing the data, running the analyses, developing the models andresults, and writing the manuscripts. My co-authors offered crucial guidanceand feedback, and they invested considerable effort at different stages of thework.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 The Cost of Task Switching: Evidence from Emergency De-partments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Clinical Setting and Data . . . . . . . . . . . . . . . . . . . . 102.3.1 The Care Delivery Process . . . . . . . . . . . . . . . 102.3.2 Identifying the Clean Period . . . . . . . . . . . . . . 132.3.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Empirical Methods . . . . . . . . . . . . . . . . . . . . . . . 172.4.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.2 Instrumental Variable . . . . . . . . . . . . . . . . . . 172.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5.1 The Effect of Task Switching on Physician Productiv-ity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5.2 Effect Heterogeneity . . . . . . . . . . . . . . . . . . . 202.5.3 Estimation by CCS Pairs: Identifying Costly Switches 23viTable of Contents2.6 A Data-driven Approach for Queue Management in ED . . . 242.6.1 Queue Management and Max Bisection . . . . . . . . 242.6.2 Simulation under Two-Queue ED System . . . . . . . 302.7 Effects of Task Switching on Quality and Routing . . . . . . 322.7.1 Quality of Care . . . . . . . . . . . . . . . . . . . . . 322.7.2 Patient Routing . . . . . . . . . . . . . . . . . . . . . 322.8 Managerial Implications . . . . . . . . . . . . . . . . . . . . . 352.9 Conclusions and Future Research . . . . . . . . . . . . . . . 363 Adaptive Server Behavior to Schedule Deviations and ItsConsequences: Evidence from Operating Rooms . . . . . . 383.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.1.1 Contribution . . . . . . . . . . . . . . . . . . . . . . . 423.2 Literature Background . . . . . . . . . . . . . . . . . . . . . 433.2.1 Healthcare Provider Productivity . . . . . . . . . . . 433.2.2 Surgical Speed and Quality . . . . . . . . . . . . . . . 453.3 Hypothesis Development . . . . . . . . . . . . . . . . . . . . 463.4 Clinical Setting and Data . . . . . . . . . . . . . . . . . . . . 483.4.1 Surgery Stages and Shift Scheduling . . . . . . . . . . 483.4.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.5 Empirical Methods for Clinical Teams’ Responsive Behaviour 543.6 Estimation Results and Interpretations . . . . . . . . . . . . 563.6.1 Main Results . . . . . . . . . . . . . . . . . . . . . . . 563.6.2 Heterogeneity Across Surgeon Seniority . . . . . . . . 583.7 Exploration on Surgical Quality . . . . . . . . . . . . . . . . 613.7.1 Empirical Methods on Quality . . . . . . . . . . . . . 613.7.2 Estimation Results . . . . . . . . . . . . . . . . . . . 633.8 Counterfactual Study . . . . . . . . . . . . . . . . . . . . . . 653.9 Conclusions and Future Research . . . . . . . . . . . . . . . 674 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73AppendicesA Appendix for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . 87A.1 Additional Tables and Figures . . . . . . . . . . . . . . . . . 87A.1.1 OLS Estimates . . . . . . . . . . . . . . . . . . . . . . 87viiTable of ContentsA.1.2 Robustness Checks . . . . . . . . . . . . . . . . . . . 87A.1.3 Switch Cost in the Fast Track . . . . . . . . . . . . . 91A.1.4 Effect Heterogeneity across Physicians . . . . . . . . . 95A.1.5 Effect Heterogeneity across CCS Pairs . . . . . . . . . 96A.1.6 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . 97A.2 Computation Steps in Simulation . . . . . . . . . . . . . . . 98B Appendix for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . 99B.1 GMM Estimation . . . . . . . . . . . . . . . . . . . . . . . . 99B.2 Robustness Checks . . . . . . . . . . . . . . . . . . . . . . . . 102B.2.1 Dynamic Panel Model Specification Tests . . . . . . . 102B.2.2 Sample Inclusion Criterion . . . . . . . . . . . . . . . 104B.2.3 IV Specification Tests . . . . . . . . . . . . . . . . . . 107viiiList of Tables2.1 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . 162.2 Effect of Task Switching on PPH . . . . . . . . . . . . . . . . 212.3 Effect Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . 222.4 Two-Queue Simulation Results . . . . . . . . . . . . . . . . . 312.5 Effect of Task Switching on Quality of Care . . . . . . . . . . 332.6 Effect of Task Switching on Patient Routing . . . . . . . . . . 343.1 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . 533.2 GMM Estimation Results . . . . . . . . . . . . . . . . . . . . 573.3 Heterogeneity of Responses in Surgery Stage between SurgeonSeniority Groups . . . . . . . . . . . . . . . . . . . . . . . . . 603.4 Impact of Relative Procedure and Turnover Duration on Post-surgical Risks . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.5 Results of the Counterfactual Analysis . . . . . . . . . . . . . 67A.1 Effect of Task Switching on PPH: OLS Estimates . . . . . . . 88A.2 Alternative Patient Type Definition and Sampling Method . . 93A.3 Effect of Task Switching on PPH in Fast-track of ED B . . . 94A.4 Significant CCS Pairs Estimates in ED A . . . . . . . . . . . 96A.5 Significant CCS Pairs Estimates in ED B . . . . . . . . . . . 96B.1 FE-OLS Estimation Results . . . . . . . . . . . . . . . . . . . 103B.2 Specification Tests for Main Model . . . . . . . . . . . . . . . 105B.3 Estimates for Different Surgeon Seniority Group . . . . . . . 106B.4 Robustness with Add-on Cases Estimation Results . . . . . . 107B.5 Robustness with Cancellations Estimation Results . . . . . . 108B.6 Effects of RPD on Read/Reop with HOS . . . . . . . . . . . . 109B.7 Effect of RPD on Readmissions and Reoperations with DSS . 110ixList of Figures2.1 Typical ED Care Delivery Process . . . . . . . . . . . . . . . 112.2 ED Physician Shift Structure and Clean Period . . . . . . . . 142.3 Relationship between SL and switching frequency in ED A . 182.4 Relationship between SL and switching frequency in ED B . . 192.5 Graph of Patient Types . . . . . . . . . . . . . . . . . . . . . 272.6 CCS Graph Max-Bisection Results for ED A . . . . . . . . . 282.7 CCS Graph Max-Bisection Results for ED B . . . . . . . . . 293.1 OR Shift Structure . . . . . . . . . . . . . . . . . . . . . . . . 403.2 Clinical Personnel Responses to Real-time Schedule Devia-tions in OR Shifts and Subsequent Impact on Quality . . . . 403.3 An Example of an OR Slate . . . . . . . . . . . . . . . . . . . 493.4 Surgical and Cleaning Teams’ Responsive Behavior . . . . . . 593.5 Surgical Quality and End-of-Shift Time . . . . . . . . . . . . 66A.1 Distribution of Patient Triage in the Refined Sample vs. En-tire Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89A.2 Distribution of Patient Sex in the Refined Sample vs. EntireSample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90A.3 Distribution of Patient Age in the Refined Sample vs. EntireSample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91A.4 Distribution of Patient CCS in the Refined Sample vs. EntireSample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92A.5 Switch Cost Coefficients Across Top Five ED Physicians . . . 95xAcknowledgementsMy journey through the PhD is an adventure, and I am grateful to haveshared this experience with remarkable individuals.I would like to express my deepest appreciation to my supervisor, Prof.Yichuan Ding, for his tremendous support and encouragement. His exper-tise, understanding, and patience added considerably to my academic career.He is willing to devote his time and effort so generously. I am extremelygrateful for his mentorship.My sincere thanks go to Prof. Mahesh Nagarajan and Prof. Steven Shechter,whose continuous support and guidance are extremely important in my aca-demic training. Their rigorous standards and encouragement helped me torefine my thinking and brought things to a higher level, which pushed meto become a better researcher.I also want to thank my physician co-authors, Dr. Garth Hunte and Dr. Jug-pal Arneja, for their valuable suggestions and insights as frontline healthcareproviders that helped improve this thesis. I am grateful to Prof. HarishKrishnan and Prof. Chris Ryan for taking the time to provide beneficialfeedback on my projects and presentations.My sincere thanks to Elaine Cho and Rita Quill for being so helpful and en-suring that things are managed smoothly. Special thanks go to my friendsand peer PhD students at Sauder School of Business. Their kindness pro-vided a sense of belonging and relief.Lastly, I am deeply indebted to my parents and grandparents, who have pro-vided me with unfailing support and continuous encouragement throughoutmy years of study. This accomplishment would not have been possible with-out them. I cannot forget to acknowledge my fiancée, Minjia Li. Her love,understanding and encouragement when the times got tough have been asource of motivation that I could always count on. Minjia, thank you forbeing there every step of the way.xiChapter 1IntroductionHealthcare bears paramount importance, directly influencing the well-beingof individuals and communities. However, it is also a sector fraught withcomplex challenges. In the United States, the 2022 healthcare expenditurereaches a staggering $ 4.4 trillion, or more than $ 12,000 per person, repre-senting about 20% of the country’s GDP. Meanwhile, healthcare spendingin Canada is $ 331 billion, or $ 8,563 per person. Despite these significantexpenditures, both countries continue to grapple with escalating costs, in-efficiencies, and disparities in access and quality of care. This situation isfurther exacerbated by two factors: 1) the COVID-19 pandemic in the pastthree years has levied unprecedented strain on healthcare systems world-wide; 2) by 2030, 1 in 6 people in the world will be aged 60 years or over,which will significantly increase the demand for healthcare services. Thereis an urgent need for better healthcare delivery.The complexity of healthcare service systems leads to various factors in theservice delivery process that may influence healthcare providers’ efficiencyand patients’ treatment quality. There also exist many noises that bring biasto the estimation. These phenomena are particularly prominent in highlyacute and load-intensive sites, such as emergency departments (ED) andoperating rooms (OR). In my research, I collaborate with frontline physi-cians and surgeons to explore the behavior of healthcare providers in theseservice sites. In this process, I utilize data-driven methods to improve health-care delivery and generate meaningful insights to inform better policy anddecision-making in collaboration with frontline healthcare practitioners.The dissertation includes two essays that follow the previously mentionedstreams. We briefly introduce each of them in what follows.In the first essay, we explore ED physicians’ behavior when serving patientsand the further implications on the entire ED system. ED physicians treatpatients with different symptoms and constantly switch between tasks. Herewe propose two research questions: 1) How will task switching impact ED1Chapter 1. Introductionoperations? 2) What are the potential operational solutions? Specifically,we investigate the impact of task switching on three angles of ED operations:physician productivity, quality of care, and patient routing. In this analysis,we utilize a comprehensive dataset of patient visits and lab tests.To address the estimation bias due to measurement errors and endogenouspatient selection, we refine the sample period and construct an instrumen-tal variable (IV) called switching likelihood, which exploits the exogenouscomposition of waiting patients. With this IV, our estimates show that, atdifferent EDs, a 10% increase in the switching frequency of physicians re-duces the number of patients treated per hour by 8.65% - 11.53% on average.Task switching negatively impacts ED physician productivity. However, wefind no significant influence on treatment quality measured by 7 and 30-dayrevisit-and-admission rate. On patient routing, we find physicians presentswitch-averse behavior when picking patients.With the empirical results, we then devise an easily implementable data-driven queue management method to optimally partition patients into twoqueues. Task switching negatively impacts ED physician productivity, andthis impact is more prominent for certain patient type pairs. Being aware ofthe heterogeneous impact on physician productivity among different patienttype pairs, we partition patients into two clusters (queues) to minimize theadverse effects of task switching. We find that it is equivalent with solvinga max-bisection problem in a certain graph. Based on the simulation ofimplementing the proposed two-queue system in our collaborating EDs, wefind that the average waiting time can be reduced by up to 38%. Thismethod can considerably reduce ED congestion and patient waiting times.In the second essay, we study how clinical teams adaptively respond to real-time deviations from the planned operating room schedules and the associ-ated consequences of these responses. Specifically, we investigate whetherclinical personnel adjust their service speed when they are ahead of or be-hind the original schedule and whether this affects patient readmissions andreoperations.Schedules and disruptions are ubiquitous in various sectors, such as health-care, transportation, and project management. The operating room is atypical healthcare site that functions with detailed schedules. Collaboratingwith surgeons from a primary children’s hospital in Vancouver, we study howsurgical and cleaning teams adaptively adjust the service speed in responseto real-time deviations from the planned OR schedules and the further im-pact on surgical quality of these responses, using a unique surgery data set2Chapter 1. Introductionthat includes actual and scheduled surgery time stamps.We identify a new type of adaptive server behavior within schedules, whichcomplements the existing scheduling and behavioral queueing literature. Wealso contribute to the literature on surgical speed and quality. We find thatsurgical and cleaning teams speed up when they fall behind schedule andslow down when they get ahead of schedule, with the slowdown exhibitinga stronger effect. Quantitatively, surgical teams expedite the surgery byan average of 5.6% when facing one standard deviation (SD) delay in theplanned start for that surgery, whereas they take on average 10.5% longerwhen they are one SD ahead of schedule. In the turnover times, cleaningteams accelerate by 10.3% (slow down by 22.1%) on average when they areone SD ahead of (behind) schedule.We then leverage the deviation from the scheduled start as an IV to addressendogeneity issues in estimating the impact of surgical speed on surgicalquality. We present a causal study that a faster-than-scheduled procedureduration erodes surgical quality by increasing 30-day readmission and reop-eration probabilities. Through a counterfactual analysis, we quantify andobtain a convex relationship between readmissions/reoperations and end-of-shift (EOS) time differences, which can assist hospital managers in schedul-ing surgeries to achieve desired efficiency-quality trade-offs.3Chapter 2The Cost of Task Switching:Evidence from EmergencyDepartments2.1 IntroductionRecent technological advancements and economic growth have given rise toan increase in skilled and complex jobs, replacing routine and monotonouspositions [1–3]. As a result, workers are now required to frequently per-form and transition between various tasks [4]. However, this trend poseschallenges, as psychological studies have demonstrated that task switchingimposes additional cognitive burdens, prolongs task completion times, andincreases performance errors [5–8]. Consequently, the cost of task switching(also known as switch cost) has become an increasingly crucial determinantof worker productivity.Despite the psychological experiments conducted, there remains limited ev-idence concerning the impact of task switching on workplace productivity.Studies investigating this phenomenon face challenges in measuring taskswitching, as detailed diary data on tasks performed during everyday workis often unavailable or too expensive to gather. Furthermore, task switch-ing frequently occurs endogenously [9], resulting in biased estimates. Thesecomplications hinder the evaluation of task switching consequences, partic-ularly from a causal perspective.In this study, we investigate the influence of task switching on the produc-tivity of emergency department (ED) physicians. As jacks of all trades, EDphysicians possess a wide array of medical knowledge, practice various clin-ical skills, and treat patients presenting diverse medical symptoms. Due tothe variability in patients’ symptoms and treatment approaches, physiciansare compelled to switch tasks regularly. Additionally, ED physicians work42.1. Introductionindividually and face a high volume of incoming patients their shifts. Thesefactors establish EDs as an ideal setting to examine task switching and itseffects on physician productivity.We leverage the administrative data of patient visits and lab tests fromtwo large EDs on the west coast of Canada. To identify task switching, wecategorize patients into different types based on their chief complaint systems(CCSs), which are recorded by a triage nurse upon the patient’s arrival atthe ED. For each physician, we measure task switching by calculating theswitching frequency, defined as the number of patients with a differing typefrom the preceding picked patient relative to the total number of patientstreated by the physician within a specific time frame. We then quantify theswitch cost by examining how switching frequency impacts service speed andquality. Additionally, we explore the effects of task switching on physicians’routing decisions.Our analysis, however, encounters two primary challenges. The first chal-lenge pertains to the measurement of physician service speed. Since our datadoes not capture every detailed activity of physicians, there is no direct mea-sure of the actual time a doctor spends on each patient. Specifically, EDphysicians frequently face interruptions from reentrant patients and multi-tasking [10]. The second challenge lies in addressing the endogeneity issueduring the estimation process. In our collaborating EDs, physicians selectpatients to treat when they become available, rather than being assignedpatients by others. This grants physicians considerable discretion in patientselection. Consequently, the observed sequence of patient types is subjectto selection bias, as physicians may strategically choose patients. If physi-cians aim to minimize switch cost by prioritizing patients of the same type,ordinary least squares (OLS) estimates will likely underestimate the actualimpact of task switching [11].To address the first challenge, we refine the sample period to a clean periodand employ the number of patients treated per hour (PPH) as a measureof physician service speed. Leveraging a comprehensive and unique lab testdataset, we obtain the earliest lab result time for each physician’s shift byidentifying the minimum lab result release time among two patient groups:(1) patients selected by the focal physician earlier in the day, and (2) pa-tients picked by other ED physicians earlier in the day whose shifts haveconcluded by the lab result release time. The second group encompassesall potential hand-over patients. We then define the clean period as theduration from the start of the shift to the earliest lab result time for each52.1. Introductionphysician. During the clean period, physicians primarily perform initialassessments (IA) for new patients, with reentrant interruptions being virtu-ally absent as no lab results have been returned yet. Meanwhile, the PPHmeasures a physician’s average efficiency over a time period, effectively av-eraging out patient-specific measurement errors and noises. Notably, thePPH is unaffected by physicians’ batch-picking and multitasking behavior.We divide the obtained clean period into several 30-minute blocks, for whichwe compute the PPH.We address the second challenge by proposing an instrumental variable (IV)as we utilize the switching likelihood (SL) as the IV. SL is the ratio ofunique types to the queue length at the beginning of each 30-minute block.By design, SL is positively correlated with the physician’s actual switch-ing frequency and independent from the focal patient’s unobserved physicalattributes. Importantly, it capitalizes on the type composition of waitingpatients determined prior to patient selection in the subsequent stage. Thisallows for exogenous variation in patient-type switching, enabling us to dis-tinguish the switch cost from the endogenous patient selection process.Our analysis reveals that across different EDs, a higher switching frequencyleads to decreased physician productivity. Specifically, holding others con-stant, a 10% increase in the switching frequency results in an average re-duction of 0.41 to 0.47 patients treated per hour, or an 8.65% to 11.53%decrease in PPH at the two EDs. The estimated cost is statistically signifi-cant and robust across alternative specifications. Additionally, we find thatphysicians exhibit switch-aversion, meaning they strategically select patientsof the same type to circumvent task switching. However, task switching hasminimal impact on treatment quality, as measured by 7- and 30-day revisit-and-readmission (RAD) rates. These findings suggest that task switchingprimarily influences the efficiency of ED operations, while physicians manageto reduce task switching (possibly subconsciously rather than intentionally)without significantly affecting service quality.As an operational solution, we propose a practical, data-driven queue man-agement method that leverages the identified switch cost heterogeneity amongdifferent CCS pairs to optimally partition patients into two queues. Ourqueue redesign minimizes intra-queue switching costs and maximizes inter-queue switching costs to mitigate the negative impact of task switching onED efficiency. We demonstrate that designing such a two-queue system isequivalent to solving a max bisection problem, which can be addressed usingsemi-definite programming (SDP) relaxation [12, 13]. Through simulation,62.1. Introductionwe further show that physicians’ productivity improves under the proposedtwo-queue system, resulting in a more substantial reduction in patient wait-ing times and ED congestion compared to current practices. Our findingsindicate that the average PPH at both EDs increases by 3.25% to 6.19% us-ing this new design, translating to a 38.16% to 39.66% reduction in averagepatient waiting time.Our study makes several contributions. First, we illustrate that task switch-ing is costly for emergency care delivery by impairing physician productiv-ity. Our estimates indicate that task switching reduces ED physician servicespeed. Due to the queueing system’s externality, task switching’s negativeimpact can be more significant at the ED system level compared to thepatient level. We also find evidence that ED physicians tend to prioritizepatients without task switching in the routing stage. Although this maypartially alleviate the switch cost, the estimated impact of task switchingremains sizeable and robust.Second, we propose an implementable data-driven queue management methodin ED based on heterogeneous switch cost estimates. To mitigate the nega-tive impact of task switching, we partition patients into two queues so thatpatients with inexpensive switching costs are clustered into the same queue.This method is general and can easily be extended to incorporate other pa-tient demographics. Through a simulation study, we find that implementingsuch a two-queue system can reduce average patient waiting time by up to40%. This will yield a substantial improvement if implemented in our col-laborating ED.Third, the identification strategy developed in this paper may appeal toother empirical researchers interested in ED operations. By exploiting thelab test data, we propose a new approach to identify a clean period inwhich physicians are almost free from interruptions from reentrant patients,a primary challenge in estimating the ED physician’s productivity. We alsopropose an IV to address endogeneity due to physicians’ strategic patientselection. This IV can be easily constructed in commonly used ED data setsand generalized to other ED-related studies.The remainder of our paper is organized as follows. The next section reviewsthe literature related to our work. Section 3.4 describes the ED backgroundinformation and the data we use. Section 3.5 formulates the empirical mod-els. The main results are presented in Section 3.6. Then Section 3.8 proposesa data-driven queue management method and present simulation results. InSection 2.7, we explore the influence of task switching on the quality of care72.2. Literature Reviewand patient routing decisions. Finally, Section 2.8 discusses the managerialimplications. Section 3.9 concludes.2.2 Literature ReviewOur paper is related to five strands of literature. First, we contribute tohealthcare management studies on physician productivity. From a queueingtheoretic perspective, EDs can be modeled as a system with state-dependentservice rate [14, 15]. As such, existing research has investigated various fac-tors affecting productivity and efficiency in ED, including queue length [16],shift schedules [17, 18], triage [19] and peer pressure [20, 21]. They alsopropose alternative designs of the care delivery system regarding physicianshift scheduling [22, 23], new triage policies [24], and waiting time predic-tion and announcement [25–27]. [28] provides an overview of studies onworker productivity from different angles. We complement the above liter-ature by identifying the switch cost as a novel factor influencing physicianproductivity and system performance.Second, our paper is related to research on multitasking [10, 29] and inter-ruptions [30, 31]. [10] shows that a physician’s productivity has an invertedU-shape response to her on-hand patients indicating the multitasking level.Our paper complements this finding by showing that the patient mix and theservice sequence also matter—a physician becomes more productive whenhe consecutively sees patients sharing the same type. Since we are con-cerned with the IA time the physician spends on each individual patient,we use a different measure of physician productivity from [10]. Regardinginterruptions, note that it is different psychological notion than task switch-ing as interruptions represent distinct cognitive demands and disruptions.Task switching, as an executive function, involves voluntarily or involun-tarily shifting attention and cognitive resources between tasks [5, 32, 33].This cognitive flexibility enables individuals to adapt to new task demands.Interruptions, however, entail unexpected breaks that introduce new tasks,often involuntarily [34]. These disruptions, such as phone calls or messages,necessitate a temporary shift in attention before resuming the interruptedtask [34–36]. While both task switching and interruptions demand atten-tional and cognitive shifts, the primary distinction lies in the voluntary orinvoluntary nature of these shifts. Our paper complements this thread ofexisting literature by examining the impact of task switching on focal taskservice speed.82.2. Literature ReviewOur research is also related to task specialization [37, 38] and task varietyand their effects on productivity [39–41]. Conceptually, task specializationand task variety are cumulative, and their effects on productivity dampenor exacerbate over time. However, task switching is an instantaneous event,and its effect is relatively transitory. Note that task variety also differs fromour ”frequency of task switching.” To illustrate, consider two job sequencesconsisting of two job types: 1-2-1-2-1-2-1-2-1-2 and 1-1-1-1-1-2-2-2-2-2. Bothsequences have the same ”variety of tasks” but exhibit distinct task switchingfrequencies. Existing research also shows that task performance only benefitsfrom experience on related tasks [42–44]. Some researchers explore taskpooling and its impacts on healthcare service efficiency and quality [45, 46].Our subsequent queue design also connects to this thread.Fourth, our paper connects to a growing body of research on discretionarytask routing. [47] show that ED physicians route patients according to theirwaiting time and triage acuity codes, but [48] find that the arrival of lowacuity patients may delay the treatment of high acuity patients. Related toour paper, [49] examine how varying workload conditions lead individuals toself-select tasks from a larger set of available tasks in the ED context, focus-ing on the short-term and long-term effects of such behavior. Their studycenters on physicians’ inclination to choose easier patients when workloadsare heavier. This definition of ”task switching” differs from ours, as easierpatients may have the same or different types as previous patients. Fur-thermore, they find that this behavior improves throughput for the currentshift but hurt long-term productivity in the future. However, we focus onthe the influence of task switching on the focal task. [9] examine how ra-diological physicians sequence tasks given a preassigned workload and howthat will impact productivity. They find that endogenously circumventingtask switching by grouping similar tasks impedes productivity. Althoughthey posit that exogenously grouping similar tasks could be beneficial. Inour paper, we find that most ED physicians have a tendency to prioritizetasks of similar types, resulting in task switching arising from a combinationof endogenous and exogenous behavior. In this context, we show that taskswitching still negatively impacts productivity.Finally, we contribute to the literature on the efficiency-quality trade-off inservice queues. [50] review a broad scope of papers in behavioral queuingresearch. They quantitatively identify the total system welfare as the prod-uct of customers’ net utility and system throughput. These two componentsrepresent the system operation efficiency and service quality, respectively.[51] review and show that a vital triptych of quality measures is structure,92.3. Clinical Setting and Dataprocess, and outcome in healthcare analytics. [52] study the trifecta amongefficiency, quality ,and patient experience in hospitals. In addition, [53]investigate when and how server-level quality metrics differ from customer-experienced metrics and the effect of such judgment. Our paper investigatesthe potential trade-off between the time and quality of care delivery due totask switching and finds that switch cost materializes in the dimension oftime mostly.2.3 Clinical Setting and DataOur study takes place at two major EDs in Vancouver, Canada. Both EDsprovide emergency care for thousands of patients each month. ED A op-erates from 8 AM to 8 PM seven days a week, while ED B functions ona 24/7 basis. ED physicians work independently, treating patients with awide range of demographics and medical conditions. A typical physician’sshift lasts for seven to eight hours.2.3.1 The Care Delivery ProcessFigure 2.1 illustrates the treatment process when a patient visits an ED.Upon arrival, a triage nurse attends to the patient, collecting their demo-graphic and clinical information, evaluating the medical situation, and as-signing a triage acuity code ranging from 1 (resuscitation) to 5 (nonurgent).The nurse also classifies the patient’s symptoms into a chief complaint ac-cording to the a specified list [54]. These information are recorded in anonline system that physicians can easily access. Patients with a triage codeof 1 are sent directly to physicians for urgent treatment (which accountfor less than 0.5% of all visits), while others typically wait in the waitingroom until an available physician selects and meets them. When available,physicians scan the online patient information and pick the next patientfrom the waiting room. A physician then meets with the selected patientin the treatment room for an initial assessment (IA), which is the focus ofour study. Although there is no explicit selection rule, it has been shownthat physicians consider both the patient’s waiting time and triage code.Specifically, physicians attempt to adhere to a fractile response objective,which outlines a triage-specific target waiting time and a target percentageof patients to be seen within that time frame [47, 55]. However, the highvolume of patients often makes it challenging for ED physicians to complywith this objective.102.3. Clinical Setting and DataIn order to acquire a more precise measure of physician productivity, weexamine the detailed activities ED physicians engage in during a patient’slength of stay at the EDs. As depicted in Figure 2.1, a physician’s activitiescan be categorized into two stages.1. Initial Assessment (IA): A physician selects a patient by scanning in-formation in the patient care information system. The physician needsto physically find the selected patient, talk to the patient, make diag-nostic decisions, order lab tests, and charting. After the first meeting,the patient is put under observation, during which the physician canchart for the patient and work on other patients.2. Follow-up Services (FS): A physician provides follow-up assessmentand consultation when a patient’s lab test results are available or whenthe patient’s observation period ends. In the former case, the physicianreviews the lab results with the patient. Then the physician decideswhether to discharge or admit the patient to an inpatient unit.The specific sequence of the aforementioned events may differ from case tocase. For instance, lab tests are occasionally ordered before the diagnosisbased on the physician’s review of the patient’s information from the patientportal prior to talking to the patient.Figure 2.1: Typical ED Care Delivery ProcessIn summary, physicians closely attend to patients during the IA period,which serves as a suitable indicator of ED physicians’ service speed. Con-versely, the FS period is subject to various disturbances, such as reentrant112.3. Clinical Setting and Datainterruptions from previous patients or requests to review lab test results.As a result, our study primarily investigates the impact of task switchingon the duration of the IA period.Note that in the existing literature (e.g., 19, 56, 57), the service time mayrefer to the pick-to-discharge (P2D) time, i.e., the interval between whena physician selects a patient and when that patient is discharged home oradmitted to an inpatient unit. However, the P2D duration of an individualpatient is far from an accurate measure of the actual time a physician spendson the patient. This is because the majority of a patient’s P2D duration(on average, more than three hours) is spent waiting for lab results, duringwhich the physician may spend most of their time treating other patients[10].To gather firsthand evidence supporting the use of IA in our study, weconducted a time-and-motion study by shadowing physician shifts at one ofthe two EDs. As external observers, we recorded a physician’s time spent oneach individual activity using a stopwatch and interviewed several healthcareworkers to gather additional information. In total, we shadowed two shiftsfor four hours each and observed the treatments of 22 patients. The averageIA time per patient in our shadowing study is 13.3 minutes, and the averagetime for each FS is 3.6 minutes.The time-and-motion study provided valuable insights into the care deliveryprocess. First, using the P2D time to measure a physician’s actual timespent on each patient would result in a significant overestimation. This isbecause, during most of the P2D duration, patients are waiting for lab resultsor disposition decisions, which require minimal input from the physician.Second, the time-and-motion study demonstrates that the service processcan be best described by a single-server reentrant queue [58–60]. Afterbeing selected, a patient will progress throughIA→ waiting→ FS→ waiting→ FS→ . . .until being discharged or admitted. In this process, waiting and FS mayrepeat multiple times. Third, most of the actual service time is spent inthe IA stage. The majority of the physician’s work, including selectingand locating the patient, diagnosing the problem, ordering lab tests, andcharting, is completed during IA, and physicians need time to familiarizethemselves with the patient’s clinical condition. In contrast, the FS time ismuch shorter because the physician has already gained an understanding ofthe patient’s situation.122.3. Clinical Setting and Data2.3.2 Identifying the Clean PeriodIn this study, we focus on how task switching impacts physician produc-tivity during the IA period, for which we adopt a series of cleaning andidentification strategies. To distinguish IA from the overall P2D time, weexploit a unique lab test data set with timestamps of the request, perfor-mance, and release of all lab tests (blood, urine, stool, ECG, X-ray, CTscan, etc.) Within each physician’s shift, we define the earliest lab resulttime as the minimum lab result release time among two patient groups: (1)patients picked by the focal ED physician at an earlier time of the day and(2) patients picked by other ED physicians earlier in the day whose shiftshave ended by the lab result release time. The second group encompassesall patients who could potentially be handed over to the focal physician byother physicians who have completed their shifts. By defining the earliestlab result time in this manner, we ensure that the focal physician will notreceive any lab test results for potential reentrant patients, including thosethey have seen earlier and those who might be handed over to them by otherphysicians who have completed their shifts. We refer to the period betweenthe shift start time (i.e., the time to pick the first patient in a shift) andthe earliest lab result time as the clean period. In Figure 2.2, we present adiagram to depict how we obtain the clean period.Based on our discussions with ED physician collaborators and our own ex-tensive experiences as patients visiting the ED, a physician generally willnot meet a patient again before receiving updates about the patient’s labtest results after ordering lab tests. In fact, even when a patient’s lab resultsare out, the physician may process other jobs first before responding to thelab results. For example, according to Figure 2.2, the physician may firstconduct IA for patient n+ 1 before responding to the lab results of patient2. The above definition of the earliest lab result time guarantees that duringthe clean period, they are unlikely to spend time on reentrant patients (pa-tients who have already met the focal physician or other physicians). Whilethere may be exceptional cases, such as a physician needing to speak to areentrant patient again due to forgetting something or a reentrant patient’shealth suddenly deteriorating, these instances are rare in daily operations.Interruptions or multitasking could also be caused by the arrival of triage-1patients with preemptive. However, such interruptions can be captured inour empirical analysis using the timestamps of treatment for the triage-1patients. Furthermore, triage-1 patients only account for less than 0.5% ofthe total patient volume, so including or excluding these cases would not132.3. Clinical Setting and Datachange our results.We also assess the representativeness of the refined sample. We explore thedistribution of patient demographics in the refined sample and the entiresample in Appendix A.1.2. The results indicate that the patients used inour study are representative of ED operations.Figure 2.2: ED Physician Shift Structure and Clean Period2.3.3 DataOur primary dataset encompasses all patient visits to the two EDs fromApril 2013 to March 2016. ED B has a distinct regular/fast track system,while ED A operates a single track where patients of all types are pooledtogether. Following [47], we focus on ED A and the regular track for EDB in the main model and include the results of the ED B fast track as arobustness check in Appendix A.1.The data set contains rich information about patient characteristics such asgender, age, homelessness, arriving transportation, triage acuity code, andchief complaints. A total of 163 chief complaint categories (CCC) are iden-tified under 15 chief complaint systems (CCS) (for example, cardiovascularor gastrointestinal). In the baseline analysis, we define task switching aswhether the focal and preceding picked patients of the same physician havedifferent CCSs. The focal patient is named switcher. In section A.1, we alsoconsider alternative definitions of task switching. Additionally, we definethe waiting time of a patient as the difference between the arrival time and142.3. Clinical Setting and Datathe calling time [26, 47], and we use the revisit-and-readmission (RAD) ratesin 7 or 30 days as measures of service quality [61, 62].We measure physician productivity using patients treated per hour (PPH)[23, 63] during the clean period, in which potential noises from reentrantpatients are eliminated. As a variable at a more aggregate level, PPH is ro-bust to physician multitasking and batch-picking behavior at the beginningof physician shifts. It also averages out random errors. To calculate PPH,we partition the refined clean period into multiple 30-minute blocks, withthe last block rounded upward (to include the portion beyond the earliestlab result time). The PPH of each 30-minute block represents the numberof service cycles (pick-to-pick period) contained in that block divided by30 minutes. Service cycles that are censored by the 30-minute cutoffs arecounted as half of a normal cycle, based on the assumption that censoringtimes are independent of patient pick times. We also remove blocks duringwhich no patient is waiting in the ED. This ensures that PPH does notoverestimate physician productivity due to potential idling times.Table 3.1 summarizes the key variables in the refined sample. The samplewe use for analysis includes 3,559 and 4,879 shifts for the two EDs, andthe sample period ranges from 1.08 to 1.19 hours on average. Overall, weobtain 7,845 30-minute blocks as observations for ED A and 10,521 blocksfor ED B. The average numbers of patients served are 2.391 and 2.031 per30 minutes, equivalent to 4.783 and 4.062 patients per hour. The average 7and 30-day RAD probabilities are 0.02 and 0.045 for ED A and 0.033 and0.083 for ED B. Among all patients at the two EDs, 13.3% and 26.8% ofpatients are admitted to an inpatient unit, respectively.To measure task switching, we compute the switching frequency by tak-ing the ratio of the number of switchers among the picked patients in eachblock, which serves as a proxy for switching intensity in a certain block.The average switching frequencies at the two EDs are 0.865 and 0.839, re-spectively, suggesting that task switching is common in ED services. Theaverage switching likelihoods (which is the instrumental variable we use,refer to Section 3.5) at the two EDs are 0.809 and 0.758, respectively.Regarding other ED- and patient-level variables, the average numbers ofwaiting patients (queue length) at the two EDs are 4.52 and 5.15, and theaverage numbers of patients being served (ED load) are 10.76 and 25.9,respectively. We use this variable to control for ED bed constraints. Theaverage age of patients is around 50, and the gender distribution is relativelyeven. Moreover, the two EDs differ significantly in the proportion of patients152.3. Clinical Setting and Dataarriving by ambulance. This is because ED B is larger and serves as amajor ambulance destination. We also include the proportion of five groupsof patients with different waiting times. ED physicians see most patientswithin 60 minutes of waiting time, while only about 17% of all patients areseen in 15 minutes. Most patients have intermediate triage levels (triagecodes 2, 3, and 4).Table 2.1: Summary StatisticsVariables ED A ED BMean (S.D.) Mean (S.D.)Patients treated in each block 2.391 (1.106) 2.031 (0.95)PPH 4.783 (2.212) 4.062 (1.9)7-day RAD 0.020(0.103) 0.033 (0.141)30-day RAD 0.045 (0.152) 0.083 (0.216)Inpatient admission 0.133 (0.256) 0.268 (0.35)Switching frequency 0.865 (0.255) 0.839 (0.299)Switching likelihood 0.809 (0.196) 0.758 (0.216)Average queue length 4.520 (2.803) 5.152 (3.444)ED load 10.76 (5.083) 25.94 (7.119)Patient age 53.48 (15.58) 49.74 (15.14)Female patient 0.538 (0.357) 0.447 (0.387)Arrival by ambulance 0.125 (0.244) 0.389 (0.38)Triage code 3.309 (0.505) 2.899 (0.522)<15 minutes 0.170 (0.300) 0.160 (0.306)15–30 minutes 0.369 (0.389) 0.326 (0.393)30–60 minutes 0.333 (0.382) 0.306 (0.384)60–120 minutes 0.156 (0.314) 0.195 (0.339)S120 minutes 0.021 (0.121) 0.052 (0.193)Physicians 57 60Shifts 3,559 4,87930-minute blocks 7,845 10,521Average length of clean period 1.078 hr 1.192 hr162.4. Empirical Methods2.4 Empirical Methods2.4.1 ModelConsider ED physician shifts indexed by i = 1P 2P · · · P I where I is the totalnumber of shifts (3,559 for ED A and 4,879 for ED B). Each 30-min blockin shift i is indexed by t = 1P 2P · · · P Ni, until the earliest release of lab testresults. In each block, we assume the following linear model:PPHit = δ · SFit + x⊤itβ + Fi +Dit + uit. (2.1)The dependent variable PPHit is the extrapolated number of patients seenper hour. The key explanatory variable SFit is the switching frequency.The parameter of interest, δ, reflects the effect of task switching on PPH.Covariates in xit include the average queue length and ED load within theblock; the average age and triage level of treated patients; the proportion oftreated patients in each waiting time range; the share of female, homeless,and arriving by ambulance patients; and the share of patients in each CCS.Fi denotes physician fixed effects and day-of-week fixed effects that do notvary within each shift i. Dit stands for the clock hour fixed effects of thestart of block. Lastly, uit is the unobserved error term.Estimating Equation (2.1) using OLS yields a biased estimate of δ becausethe switching frequency can be correlated with the error uit. One causeof such correlation is the physician’s endogenous selection of patients [11],where the likelihood of selecting a specific patient depends on the patient’sattributes [9, 49]. In Section 2.7, we show that physicians are likely awareof the switch cost and tend to avoid selecting patients with a different type.2.4.2 Instrumental VariableTo correct the sample selection bias, we exploit the exogenous compositionof waiting patients to construct a variable called switching likelihood (SL) asthe IV for switching frequency. Specifically, let J (iP t) be the set of waitingpatients at the starting time of block t of shift i. We define SL as thenumber of unique types in J (iP t) divided by the total number of waitingpatients, |J (iP t)|. As shown in Figure 2.3, SL is positively correlated withswitching frequency: The more unique types among waiting patients at thebeginning of the shift, the more likely the physician will switch betweentypes in subsequent treatment. For example, suppose J (iP t) consists ofthree patients and each has a distinct type. Then the SL equals one and the172.4. Empirical Methodsphysician will likely switch tasks between every two patients. In contrast, ifall patients had the same type, the switching likelihood would be zero andthe physician would hardly switch tasks.Moreover, we argue that our IV satisfies the exclusion restriction, i.e. itaffects the PPH only through task switching. By construction, SL onlydepends on pre-determined composition of waiting patients who arrive onaverage 40 minutes before the block begins. Thus, it is uncorrelated withunobserved factors during the block that contemporaneously affects PPH.On the other hand, waiting patients who are not selected for treatmentshould not affect physicians’ productivity with respect to the patients beingtreated. In particular, since physicians already prioritize the most acute pa-tients at the beginning of the shift, we do not expect further interruptionsfrom other waiting patients. If anything, interruptions arise from previ-ously treated patients or patients with time-varying medical conditions, butboth are uncorrelated with the type composition of waiting patients at thebeginning of the shift.Figure 2.3: Relationship between SL and switching frequency in ED AWith the IV, we estimate the following equations using limited informationmaximum likelihood (LIML), which has better finite sample properties than182.5. ResultsFigure 2.4: Relationship between SL and switching frequency in ED Btwo-stage least squares [64]:PPHit = δ · SFit + x⊤itβ + Fi +Dt + uitP (2.2)SFit = α · SLit + x⊤itγ + Fi +Dt + ϵit. (2.3)It is worth mentioning that our IV approach shares a similar spirit with [9],who examine discretionary task routing and estimate the impact of devia-tion from first-come-first-serve (FCFS) on the image-reading speed of radi-ologists. Their IV for deviation is based on an indicator of whether thereis a chance to deviate from a prescribed sequence of images. Analogously,our IV can be interpreted as the extent to which a physician may avoidtask switching. If the SL is high and most patients have distinct types, thephysician has little chance to avoid task switching.2.5 Results2.5.1 The Effect of Task Switching on PhysicianProductivityTable 3.2 presents estimates of Equation (2.2). The first row displays es-timates of δ, representing the cost of task switching on the PPH of ED192.5. Resultsphysicians. For the two EDs, the estimates are -4.139 and -4.685, respec-tively, both of which are statistically significant. Consequently, a 10%increase in switching frequency results in an expected PPH reduction of4.139 × 0.1 = 0.41 and 4.685 × 0.1 = 0.47 for the respective EDs. Thesereductions correspond to 8.65% and 11.53% decreases in PPH relative tothe sample means (see Table 3.1). This indicates that task switching leadsto substantial efficiency losses in ED operations.In comparison, Table A.1 in Appendix A.1.1 presents the OLS estimates ofEquation (2.1). Compared with the LIML estimates, the OLS estimates of δare much smaller and statistically insignificant. These results indicate thatphysicians’ discretionary selection of patients would bias the OLS estimatesand therefore justify our use of IV. Besides, the bottom of Table 3.2 showsthe Wald F statistics. At both EDs, we reject the null hypothesis that theIV is only weakly correlated with switching frequency. This further enhancesthe validity of our IV.We perform several robustness checks for the switch cost estimates. Theresults are reported in Appendix A.1.2. In particular, our estimates arerobust to alternative definitions of patient types (CCS × triage codes andCCC) and alternative levels of aggregation (by shift versus 30-minute block).In Appendix A.1.3, we estimate the switch cost at the fast track of EDB. Although the patient mix differs between regular and fast tracks, bothsamples exhibit sizeable and statistically significant switch cost.2.5.2 Effect HeterogeneityBesides the main effect, we also estimate heterogeneous switch costs acrosspatients and other environmental factors. Specifically, we examine the mod-erating effects of the following factors: patient age, triage level, arrival byambulance, and day-of-week. We modify Equation (2.1) with an additionalterm interacting with the switching frequency with one of the moderatorsonce at a time. The new regression model is given byPPHit = δ · SFit + δw · (SFit ×Wit) + x⊤itβ + Fi +Dt + uitP (2.4)where Wit is the moderator of interest. Other covariates and fixed effectsremain the same.We estimate Equation (2.4) by LIML using SLit and SLit ×Wit as IVs forSFit and SFit ×Wit, respectively. The estimated δ and δw are reported inTable 2.3. It is worth noting that we control for the main effects of other202.5. ResultsTable 2.2: Effect of Task Switching on PPHED A ED BSwitching frequency -4.139*** -4.685***(1.041) (0.993)Average queue length 0.092*** 0.031***(0.015) (0.011)Average ED load 0.015* 0.022***(0.008) (0.005)Average age -0.003 -0.001(0.002) (0.002)Average triage 0.423*** 0.046(0.073) (0.055)Female proportion -0.009 -0.046(0.066) (0.054)Homeless proportion 0.023 -0.099(0.369) (0.145)Ambulance arrival proportion -0.024 0.021(0.097) (0.075)Waiting time 15-30 min 0.596*** 0.711***(0.101) (0.061)Waiting time 30-60 min 0.760*** 1.052***(0.135) (0.077)Waiting time 60-120 min 0.746*** 1.156***(0.158) (0.096)Waiting time S 120 min 0.602* 1.375***(0.322) (0.192)Fixed effects:Clock hour Included IncludedPhysician Included IncludedDay-of-week Included IncludedObservations 7,845 10,521Kleibergen-Paap rk Wald F statistic 177.8 45.29Notes: Estimated by LIML. All estimates control for physician fixed effects, day-of-the-week fixed effects and clock-hour fixed effects. The results for the share of patients in eachCCS are omitted from the table due to size constraint. Robust standard errors clusteredby physicians in parentheses (* p < 0.1, ** p < 0.05, *** p < 0.01).212.5. ResultsTable 2.3: Effect HeterogeneityVariables ED A ED BPanel ASwitching frequency -4.157*** -4.674***(1.050) (0.989)Switching frequency× average age 0.025 0.011(0.061) (0.061)Kleibergen-Paap rk Wald F statistic 8.081 17.14Panel BSwitching frequency -3.967*** -4.636***(1.034) (1.020)Switching frequency× average triage -2.578 -0.747(2.093) (1.718)Kleibergen-Paap rk Wald F statistic 16.97 10.98Panel CSwitching frequency -4.364*** -4.348**(1.145) (1.360)Switching frequency× ambulance arrival 2.350 -0.848(2.706) (2.360)Kleibergen-Paap rk Wald F statistic 8.680 11.88Panel DSwitching frequency -4.176*** -4.750***(1.136) (1.107)Switching frequency × visit on weekend 0.127 0.260(1.219) (1.534)Kleibergen-Paap rk Wald F statistic 65.45 21.28Fixed effects:Clock hour Included IncludedPhysician Included IncludedDay-of-week Included IncludedObservations 7,845 10,521Notes: Estimated by LIML. All estimates control for explanatory variables xit and zitand fixed effects Fi and Dt. The omitted ones from the table are due to size constraints.In panels A and B, we demean average age and triage level to zero mean. In panels Cand D, we explore how switch cost varies with ambulance arrival proportions and withweekdays/weekends. Robust standard errors clustered by physician in parentheses (*p < 0.1, ** p < 0.05, *** p < 0.01).222.5. Resultsmoderators in each regression. For example, when we estimate the hetero-geneous switch costs in age, other factors are controlled as unchanged. Assuch, the effect heterogeneity along different moderators does not confoundeach other. We find that almost all interactive terms are small and statis-tically insignificant at both EDs. Therefore, the switch cost exhibits littlevariation across patient characteristics and the ED environment.Furthermore, we explore the heterogeneity of switch costs across individualphysicians. For this analysis, we concentrate on the top five physicians ateach ED, ranked by the total number of patients seen. Together, thesetop five physicians account for 33.1% and 20.9% of the samples at the twoEDs, respectively. Figure A.5 in Appendix A.1.4 displays estimates of δfrom Equation (2.2), using the clean periods of each top five physician. Theproductivity of most physicians is adversely affected by task switching, withthe magnitude of this impact varying considerably among these physicians.2.5.3 Estimation by CCS Pairs: Identifying Costly SwitchesThus far, we have assumed that all switches have the same impact on PPH,and we estimate the aggregated switch cost on physicians’ PPH in Equa-tion (2.1). However, the magnitude of switch costs may vary for differenttask combinations. This is in line with our observations from physician col-laborators, who have noted that certain CCS pairs are more similar than oth-ers in terms of treatment approaches and required resources. For instance,the switch cost between Respiratory and OB-GYN (Obstetrics/Gynecology)is larger than that between Gastrointestinal and Genitourinary, as the lat-ter pair requires similar equipment and treatment methods compared to theformer.To estimate such heterogeneous switch costs, we utilize the CCS of patientsbefore and after each switch to construct switch pairs. We allow task switch-ing to be asymmetric, i.e., switching from one CCS to another can be moreor less costly than switching in the reverse direction. In total, we obtain13 × 12 = 156 distinct switch pairs (permutations of 13 CCSs) at the twoEDs, respectively. Here we cluster three most scarce CCS types into onecategory. We then estimate the following model:PPHit =∑m,nδm,n · SFm,nit + x⊤itβ + Fi +Dt + uitP (2.5)where m and n denote the CCS of the preceding and the focal patients,respectively. The variable SFm,nit represents the frequency of switching be-232.6. A Data-driven Approach for Queue Management in EDtween pair (mPn) in block t of physician-shift i. The parameter of interest,δm,n, represents the switch cost associated with CCS pair (mPn). A negativeδm,n represents a reduction in PPH due to task switching, and we assumeδm,m = 0.Our estimation leads to three primary conclusions. First, among the sta-tistically significant pairs δm,n (5% significance level), most are negativeand only one to two pairs are positively significant. Second, a considerablenumber of switch pairs exhibit small switch costs, as the estimates are notstatistically distinguishable from zero. Third, among pairs that do exhibitsignificant switch costs, the magnitudes vary considerably across differentpairs. In Appendix A.1.5, we report the estimates of all significant pairs atboth EDs.2.6 A Data-driven Approach for QueueManagement in ED2.6.1 Queue Management and Max BisectionThe empirical results presented in Section 3.6 indicate that task switchingnegatively impacts physician productivity (PPH), and that this impact isheterogeneous, with the magnitude varying based on the CCS pairs beforeand after each switch. These findings inspire us to redesign the queueingsystem in the ED to mitigate the impact of task switching. Specifically, weexplore the idea of dividing patients in the ED into two queues and assigningeach ED physician to one of the queues. Physicians will only see patientsfrom a different queue when their current queue is empty. Utilizing a data-driven method, we search for the optimal partition of patients into the twoqueues to minimize the total cost from intra-queue switching and maximizethe total cost from inter-queue switching. This approach will substantiallyreduce the expected switch cost because inter-queue task switching occursmuch less frequently than intra-queue task switching, according to our pri-ority rule.Several EDs have adopted a two-queue system. For instance, [45] studiedthe ED of a Kaiser Permanente Medical Center and demonstrated that pa-tients’ length-of-stay in the ED was significantly reduced in a two-queuesystem compared to a single-queue system. Our collaborating ED B alsodivides the ED into a fast track and a regular track, routing patients pri-marily by their triage acuity scores. Each physician is assigned to one of242.6. A Data-driven Approach for Queue Management in EDthe tracks and prioritizes patients within the same track. The administra-tor of that ED is optimistic to incorporating additional patient attributes,such as CCS, into the criteria that are used to partition the patients intotwo tracks. Consequently, the method we study here has the potential forimplementation in our collaborating ED.We propose a data-driven method to partition patients into two queuesbased on their CCS, in accordance with the findings from our empiricalresults in Section 2.5.3, which indicate that CCS pairs are predictors forthe magnitude of switch costs. This method can be easily customized toincorporate other patient attributes, such as the combination of triage acuityscores, age, and chief complaint categories. Furthermore, we stipulate thatafter partitioning, the two queues should have equal visit volumes, aligningwith the current practice wherein the total visits in the fast track and regulartrack are comparable (i.e., 48% vs. 52%). The method can also be extendedto partitioning patients into subsets of varying sizes, though the procedureswill become more complex.The main idea of our method is to construct a weighted graph, where avertex represents each patient visit, and the switch cost from one visit toanother is represented by the cost (weight) on the associated directed arc.In this setup, maximizing the total inter-queue switch cost is equivalent tofinding a max-bisection on the weighted graph.We formulate a weighted undirected graph G = (kPZP ω(·P ·)), where eachvertex i ∈ k represents a unit mass of patients with the same CCS (i.e.,300 patient visits with a CCS in our case). Let m(i) denote the index ofthe CCS associated with vertex i. We first calculate the following value forany unordered pair of vertices iP j based on the average switch cost for bothdirections:ω′(iP j) =12(−δ̂m(i),m(j) − δ̂m(j),m(i))P (2.6)where δ̂m(i),m(j) represents the reduction in PPH led by a task switchingfrom CCS m(i) to m(j); see Equation (2.5) for the interpretation of thecoefficient δ̂m,n. Note that when m(i) = m(j), that is, two vertices belongto the same CCS group, it follows from δ̂m,m that ω′(iP j) = 0. Also, if theswitch cost in both directions is not significantly different from zero, we setthat ω′(iP j) = 0. Since the significant estimates include a few positive ones(see Table A.4) which may result in a negative ω′(iP j), we devise the weight(cost) of the graph G, ω(iP j), such that all pairs of vertices are equippedwith non-negative costs. Concretely, we obtain ω(iP j) by shifting ω′(iP j)252.6. A Data-driven Approach for Queue Management in EDupward:ω(iP j) = ω′(iP j) +⌈max{∣∣all negative ω′(iP j)∣∣}⌉ (2.7)We further note that shifting all weights by a constant does not change theoptimal solution when solving the problem. We then define the edge setas Z := {{iP j}| ω(iP j)}. As an illustrative diagram, Figure 2.5 presents apart of the graph with four CCS types. The dotted lines represent the edgesconnecting with other CCS types.We aim to search for a bisection of the patient population into two queuesso that the expected intra-queue switch cost is minimized. To formulate theintra-queue switch cost, we need to calculate the frequency for each pair ofpatients consecutively picked by the same doctor in a shift. However, welack data on how patients with different CCSs would be sequenced underthe newly proposed two-queue system in the ED. For tractability, we assumethat in a doctor’s shift, a sequence of patients (with random length) will beuniformly sampled from the population, regardless of their CCS. In otherwords, each patient visit is added to a sequence with an equal probability.Consequently, any patient pair will appear in a sequence with equal proba-bility. This enables us to formulate the problem of minimizing the expectedintra-queue switch cost (or equivalently, maximizing the inter-queue switchcost) as an integer programming (IP). See the subsequent Proposition. Theproof is attached in Appendix A.1.6.Proposition 1 Suppose the sequences of patients seen in each shift areuniformly sampled from the population. Then the bisection that maximizesthe total inter-queue switch cost is a solution to the following IP:max(i,j)∈ eE12∑(1− yiyj)ω(iP j)subject to∑iNjyiyj ≤ −nR2Pyi ∈ {−1P 1}P ∀i.(2.8)We apply the Frize and Jerrum approach [13] to solve the max-bisection,which is built on the SDP relaxation method [12]. The optimization compu-tation is performed through Julia [65]. The SDP relaxation of Equation (2.8)262.6. A Data-driven Approach for Queue Management in EDFigure 2.5: Graph of Patient Typesis as follows.max12∑iNjwij (1− vi · vj)subject to∑iNjvi · vj ≤ −nR2vj ∈ SnP ∀j ∈ k(2.9)where k is the set of all vertices in the graph G and Sn = {x ∈ Rn : |x| = 1}stands for the unit sphere in n dimensions.We present the obtained bisection results using different colors in Figure 2.6.The values associated with each edge represent the Equation (2.6) from orig-inal estimates. For ED A, we assign six CCS types to one queue, includingmental (MEN), skin (SKI), genitourinary (GEN), neurology (NEU), oph-thalmology (OPH), gastrointestinal (GAS), and assign all else to the otherone. For ED B, we obtain six CCS types in one queue using similar method,which are: cardiovascular (CAR), orthopedics (ORT), neurology (NEU),general and minor (GNR), genitourinary (GEN), substance misuse (SUB),272.6. A Data-driven Approach for Queue Management in EDFigure 2.6: CCS Graph Max-Bisection Results for ED A282.6. A Data-driven Approach for Queue Management in EDFigure 2.7: CCS Graph Max-Bisection Results for ED B292.6. A Data-driven Approach for Queue Management in EDand all other CCS types belong to the other queue.2.6.2 Simulation under Two-Queue ED SystemWe conduct a simulation study to demonstrate how our proposed two-queuesystem enhances ED efficiency. In the counterfactual scenario, we assumethat doctors in each shift will be dedicated to serving one queue and willonly serve another queue when the assigned queue is empty. This priorityrule is also used in our collaborating ED B with a regular and fast track.To mimic the actual system, we need to define the patient selection rulein the simulated scenario. At a high level, we aim to preserve the orderof patients being selected as in the original scenario so that the differencebetween the simulation and the original scenarios can be solely attributedto the patient clustering practice. This can be accomplished in most caseswhere physicians face the original choice set. In the counterfactual scenario,we allow the physician to pick the same patient as they did in the originalscenario. However, due to the introduction of the two-queue system and themodification of the PPH, the choice sets seen by the doctor may differ fromthe original ones. Consequently, we determine the choice using the revealedpreference as follows. Suppose we observe a physician selecting patient Vfrom a choice set VPWPCP · · ·. We can infer that patient V has a higherpriority over others, i.e., V ≻ W, V ≻ C... We then obtain the closure ofthis partial order by transitivity, e.g., if patient W is later selected from anew choice set WPCPD, we infer W ≻ D, and thus V ≻ D. For the remainingpatients, their relative order is imputed by first-come-first-serve to minimizemodifications to the choice set.Next, we reconstruct the initial assessment time for each patient accordingto the original data, while factoring in the impact of task switching underthe simulated patient service sequences; see Appendix A.2 for the details ofthe reconstruction procedure. The simulation analysis is performed for thebusy periods of ED operations, specifically from 10 am to 6 pm for ED Aand from 10 am to 10 pm for ED B. We simulate 58,531 patient visits in4,347 shifts in ED A, and 83,149 patient visits in 6,938 shifts in ED B.Table 2.4 presents the results of the simulation study. As the baseline, panelA displays the average PPH, patient waiting time, and waiting census (num-ber of patients counted every 10 minutes) in the actual scenario. Panel Bshows the same metrics in the simulated scenario, and panel C reports themean differences between panels A and B, along with the significance under302.6. A Data-driven Approach for Queue Management in EDTable 2.4: Two-Queue Simulation ResultsVariables ED A ED BPanel A. Actual ScenarioPPH 3.381 2.898Waiting time 44.10 43.78Waiting census 4.682 4.471Panel B. Simulated ScenarioPPH 3.491 3.077Waiting time 27.27 26.42Waiting census 3.275 3.075Panel C. Differences∆ PPH 0.110*** 0.179***∆ Waiting time -16.83*** -17.36***∆ Waiting census -1.407*** -1.397***Patient visits 58,531 83,149Physician shifts 4,347 6,938Notes: Panel A reports the average PPH, waiting time, and waiting census in the actualscenario, and Panel B reports the counterfactual scenario values. Panel C summarizes themean differences and reports the two-sample t-tests significance (* p < 0.1, ** p < 0.05,*** p < 0.01).two-sample t-tests. We find significant efficiency gains from clustering pa-tients into two queues. Across the two EDs, the average PPH is increased by0.11 and 0.179, which equal 3.25% and 6.19% of the original levels and arestatistically significant. Furthermore, the average waiting time is reducedby 16.83 and 17.36 minutes (38.16% and 39.66%), and the average waitingcensus by 1.407 and 1.397 (30.04% and 31.23%), respectively. All thesedifferences are statistically significant. Additionally, we also find that theproportion of patients affected by task switching will further decrease from85% to 76.7% - 78.7%. As a result, we conclude that the impact of taskswitching on the ED system, as measured by waiting time and the waitingcensus, is roughly seven times greater than that on the physician level mea-sured by PPH. This is because any faster (or slower) treatment will have aripple effect on multiple subsequent patients waiting to be treated.In summary, our simulation study demonstrates the performance improve-312.7. Effects of Task Switching on Quality and Routingment achieved by implementing a two-queue system in the studied EDs.Under our data-driven queue management method, we are able to allevi-ate the switch cost on physician productivity. Although the improvementin individual physicians’ productivity is moderate, the ripple effect on theED system is seven times larger. Therefore, mitigating the impact of taskswitches will significantly reduce patient waiting time and ED congestion.2.7 Effects of Task Switching on Quality andRouting2.7.1 Quality of CareWe have uncovered a significant switch cost on the efficiency of ED physi-cians. Consequently, it is natural to consider that task switching could alsoimpact the quality of their work. We utilize 7/30-day RAD rates and in-patient admissions as proxies for this. Therefore, we consider the followinglinear modelrit = δ · sit + x⊤itβ) + z⊤itβ2 + Fi +Dt + uitP (2.10)where rit represents the share of revisit and readmission in 7 and 30 days,and the share of inpatient admission upon the focal visit among patientsselected in block (iP t). We still include the explanatory variables xit andzit, and fixed effects Fi and Dt, as in Equation (2.1).As demonstrated in Panels A and B of Table 2.5, task switching has minimaland statistically insignificant impacts on both RAD shares. Furthermore, wefind little connection between inpatient admission and switcher proportion(Panel C).Nonetheless, we must exercise caution when interpreting the aforementionedestimates. If physicians are aware of the switch cost, they may counteract theadverse effects on quality by exerting additional effort and allocating extratime for diagnosis and other remedial procedures. As such, our estimates arebetter understood as the outcome of physicians’ trade-off between efficiencyand quality in the presence of the switch cost.2.7.2 Patient RoutingWe explore whether physicians consider the switch cost when selecting pa-tients. [47] have demonstrated that physicians’ routing decisions exhibit322.7. Effects of Task Switching on Quality and RoutingTable 2.5: Effect of Task Switching on Quality of CareED A ED BPanel A. RAD in 7 daysSwitching frequency -0.0011 -0.0031(0.0060) (0.0044)Panel B. RAD in 30 daysSwitching frequency -0.0095 0.0075(0.0075) (0.0071)Panel C. Inpatient admissionSwitching frequency 0.0079 -0.0087(0.0112) (0.0119)Fixed effects:Clock hour Included IncludedPhysician Included IncludedDay-of-week Included IncludedObservations 7,845 10,521Notes: Estimated by fixed effects OLS. Estimates of other regressors in Equation (2.10)are omitted from the table due to size constraint. Robust standard errors clustered byphysicians reported in parentheses (* p < 0.1, ** p < 0.05, *** p < 0.01).an effort to minimize the average waiting cost of patients, specifically byprioritizing patients with more severe clinical conditions and longer wait-ing times. Furthermore, [49] find that physicians tend to choose patientswith shorter expected processing times. Given that task switching reducesPPH and negatively impacts physician productivity, physicians might alsoprioritize patients of the same type as their preceding patients.To explore physicians’ choice patterns, we adopt a conditional logistic model.Instead of using 30-min blocks, we focus on the individual patient selectionprocess. Suppose the physician’s utility from selecting patient j is givenby jj = Z⊤j ζ + Dj. + vj , which depends on the patient’s characteristics,Zj , whether task switching is required, Dj , and an unobserved error vjfollowing the type-I extreme value distribution [66]. As such, the probabilityof choosing patient j from the choice set J (iP t) is given byPr {selecting j} =exp(Z⊤j ζ +Dj.)∑k∈J (i,t)exp(Z⊤k ζ +Dk.) . (2.11)332.7. Effects of Task Switching on Quality and RoutingThe coefficient of interest, . captures the impact of task switching on thechoice probability. If . < 0, patients with a switched type will be selectedwith lower priority. Following [47], we let Zj include a triage-specific, piece-wise linear function of waiting time. The intuition is that the marginalwaiting cost differs by triage levels and whether the waiting time has ex-ceeded the target physicians want to achieve.Table 2.6: Effect of Task Switching on Patient RoutingVariables ED A ED BDifferent type 0.871*** 0.974*(0.018) (0.015)Triage 2 0.031*** 0.009***(0.018) (0.001)Triage 3 0.024*** 0.007***(0.014) (0.001)Triage 4 0.054*** 0.018***(0.028) (0.002)Triage 5 0.140*** 0.090***(0.076) (0.015)Waiting time × triage 1 1.127** 0.997(0.061) (0.002)Waiting time × triage 2 1.398*** 1.352***(0.014) (0.010)Waiting time × triage 3 1.148*** 1.143***(0.003) (0.002)Waiting time × triage 4 1.077*** 1.062***(0.002) (0.002)Waiting time × triage 5 1.039*** 1.023***(0.002) (0.002)Observations 340,258 406,521Pseudo R2 0.25 0.23Notes: Conditional logit models estimated by maximum likelihood. Dependent variable:indicator of selected patients. The estimates of age, gender, homeless, arrival mode, andpatient CCS are omitted from the table due to size constraint. Coefficients converted toodds ratios. Robust standard errors clustered by physicians in parentheses (* p < 0.1, **p < 0.05, *** p < 0.01).We estimate coefficients in Equation (2.11) using maximum likelihood andcluster standard errors by physicians. Table 2.6 presents the estimates con-342.8. Managerial Implicationsverted to odds ratios (exponential of the original estimates). We discoverthat the effects of task switching on choice probability are negative andstatistically significant at both EDs, corresponding to odds ratios between0.871 and 0.974. Holding everything else constant, the odds of selectinga patient of a different type are 87.1% – 97.4% of the odds of selecting apatient of the same type. The results suggest that physicians exhibit switch-aversion when choosing patients. During the selection process, they preferpatients with the same characteristics as the previously picked patient. Thisfinding also supports our use of IV, as physicians’ strategic patient selectioncontributes to sample selection bias.2.8 Managerial ImplicationsWe summarize the managerial insights from our study to assist ED managersand healthcare practitioners in enhancing operational efficiency.First, our study examines task switching as a prevalent phenomenon in emer-gency departments and identifies a substantial switch cost on the efficiencyof ED physicians. We find that at different EDs, a 10% increase in switch-ing frequency across patient CCS types reduces the average PPH by 8.65%- 11.53%. However, we do not find evidence that task switching affects thequality of care, which might be due to the limited methods of measuringcare quality. While efforts to reduce task switching may offer significantvalue, researchers and ED managers should remain aware of the potentialrisk of compromised care quality. Further research is necessary to explorethe impact of task switching on care quality.In reality, it is impossible to eliminate task switching due to the complexityof ED activities and the diversity of ED patients. However, several strate-gies can be employed to mitigate the impact of task switching. In additionto the proposed data-driven method of partitioning patients into differentqueues, we can introduce the pod system to ED workers [67, 68]. Thisarrangement can enhance inter-professional communication efficiency andalleviate potential delays caused by task switching. For instance, if physi-cians encounter a new patient type and require information, they will havequick access to nearby information resources. Furthermore, the computersystem can highlight waiting patients of the same type as the focal patient tohelp physicians avoid task switching. Ultimately, physicians must carefullybalance the switch cost against other factors (e.g., acuteness, waiting time)when making patient prioritization decisions.352.9. Conclusions and Future ResearchMoreover, our empirical evidence reveals that ED physicians exhibit switchaversion. Holding everything else constant, the odds of selecting a same-typepatient can be twice as high as that of selecting a different-type patient. Ac-cording to our discussions with ED physicians, such switch-averse behavioris typically subconscious. If ED managers could increase physicians’ aware-ness of the task switching problem, physicians could make better trade-offsin patient routing and enhance their service efficiency.2.9 Conclusions and Future ResearchAlthough experimental research on task switching is abundant, less is knownabout the impact of task switching in real workplaces. In this paper, we in-vestigate the task switching behavior of ED physicians to bridge this gap.Emergency departments are well-known for being extremely busy and heav-ily loaded most of the time. ED patients also present with heterogeneousclinical conditions. Consequently, physicians must provide a variety of medi-cal care at a fast pace and suffer from productivity loss due to task switching.Our analysis reveals that a 10% increase in switching frequency leads to an8.65% and 11.53% decrease in PPH on average, and physicians try to avoidtask switching when selecting patients. On the flip side, task switching doesnot have significant impact on treatment quality.By investigating the heterogeneity among different CCS pairs, we propose adata-driven queue management method to mitigate the switch costs in EDs.We use the classical max-bisection algorithm to partition patients into twoqueues based on their CCSs, minimizing the total intra-queue switch costs.The subsequent simulation shows that under the two-queue system, EDphysician productivity can be improved, and as a result, the average waitingtime of ED patients can be reduced by about 40%. This improvement canbe achieved without adding substantial extra resources.Our study has broad implications for occupations and industries beyondhealthcare. Task switching is prevalent in both the service and productionsectors of the economy, and it is ubiquitous in human lives. It is anticipatedthat people’s work will become more complex, more flexible, and less spe-cialized in specific tasks in the future. However, human brains may still notbe prepared for intensive task switching, multitasking, or interrupted work-ing environments [1–3]. As such, the cost of task switching may become anincreasingly important factor impeding workplace productivity. The nega-tive impact of task switching also underscores the importance of managerial362.9. Conclusions and Future Researchpractices to counteract it, including alternative work arrangements, organi-zational structures, and technological assistance to enhance the productivityof future jobs [69].We conclude our paper by suggesting several directions for future research.Our paper focuses on ED physicians’ task switches across patient typesand the consequences on productivity. Future studies can investigate taskswitching within a patient’s treatment but across different activities, de-velop alternative measures for task switching, or examine the switch coston physicians’ mental stress, work sustainability, patient satisfaction, andtreatment quality. Additionally, since we do not observe physician charac-teristics in our data, future research could study determinants of the switchcost at the physician level. As task switching leads to fewer patients treatedand reduced fee-for-service earnings in a time unit, it is crucial to quantifythe monetary value of the switch cost. Future research may compare taskswitching, multitasking, and work interruptions in a unified setting and in-vestigate how workers respond. Since task switching is costly, jobs requiringfrequent task switching may have to pay a wage premium to compensate forthe resulting disutility may also be considered.37Chapter 3Adaptive Server Behavior toSchedule Deviations and ItsConsequences: Evidencefrom Operating Rooms3.1 IntroductionAlthough service providers strive to complete scheduled activities on time,deviations are inevitable, and the actual progress may run behind or aheadof schedule. For example, 40% - 70% of construction projects have under-gone delays in different countries [70], while up to 28% of projects have beencompleted earlier than the due dates [71]. In the airline industry, approxi-mately 20% of flights are delayed [72, 73]. Delays in medical appointmentshave been widely reported [74, 75], and the situation was recently exacer-bated by the COVID-19 pandemic [76].Service providers’ responses to schedule deviations may vary, and we cat-egorize them into three types using terminologies borrowed from biology[77]. The first type is negative (balancing) feedback, which describes ser-vice providers who attempt to reverse schedule deviations by speeding upwhen facing delays and slowing down when ahead of schedule. For exam-ple, in project and airline management, where schedule disruptions arisefrequently, responses include expediting activities to catch up when behindschedule [78–80]. The second type of feedback mechanism is positive feed-back, which describes service providers who react to deviations by furtheramplifying them. One example is Brooks’ Law in software project man-agement, where delayed progress of software development leads to furtherdelays [81]. The third possibility is that there does not appear an apparentresponse; i.e., service providers adhere to their original tempo in each task,383.1. Introductionregardless if they are running behind or ahead of schedule.The three response types have different implications for total service du-ration and system throughput. We refer to this immediate effect as thefirst-order impact. Moreover, service duration changes may affect the qual-ity of service delivered. We refer to this as the second-order impact. Forinstance, pilots accelerate more to save time when flights are delayed at thecost of increased fuel burn and carbon emissions [82]. Construction projectscan also be rushed to catch up with the project deadlines, but often at thecost of poorer project quality, such as rework [83] or reduced safety of theworkers [84, 85].In this paper, we explore service providers’ adaptive behavior and their firstand second order impact in a critical healthcare setting–the operating room(OR). Delays are pervasive in ORs, with approximately 70% of surgical pro-cedures experiencing them [75]. OR delays lead to longer patient wait timesand possible cancellations, which greatly inconvenience patients and theircaregivers. On the other hand, surgeries that finish earlier than scheduledmay result in idle surgery teams, wasting costly healthcare resources [86].The most significant difference between ORs and other healthcare servicesites is that there is almost no chance for walk-in patients because most op-erations are pre-arranged appointments made several months earlier. Emer-gent cases can be added to shifts at the last minute, but that only happensfor about 6.8% of all OR shifts from our data. As a result, the serviceproviders in ORs, which include the surgical teams and the cleaning teams(with some overlap in their staff), are readily aware of schedule deviationsby comparing the actual and planned surgery start times.Knowing how the surgical and cleaning teams respond to schedule deviationscan help OR managers better predict procedure duration, improve patientexperience, and estimate the potential risk associated with the responses[87]. Researchers have attempted to understand surgical teams’ responsemechanisms by surveying or interviewing surgeons. Nevertheless, no con-sensus has been reached – there are results in support of positive feedback[88], negative feedback [89], and no feedback [90].Instead of relying on subjective survey results, we take an econometric ap-proach to investigate adaptive behavior and its effects. Using a uniquesurgical data set including both the actual and planned enter and exit ORtimes, we were able to calculate the actual and planned procedure duration(from enter to exit) and the turnover duration (from exit to next case’s en-393.1. IntroductionFigure 3.1: OR Shift StructureFigure 3.2: Clinical Personnel Responses to Real-time Schedule Deviationsin OR Shifts and Subsequent Impact on Qualityter) as shown in Figure 3.1. We develop empirical methods to investigatehow surgical and cleaning teams respond to schedule deviations. The re-sponses by surgical and cleaning teams can be quantified by changes in theprocedure or turnover duration (i.e., cleaning and preparation), respectively,as a result of the difference between actual and planned start and end times.To the best of our knowledge, this is the first study to use surgical data andeconometric methods to investigate the response behavior of surgical andcleaning teams to real-time schedule updates in the OR. We find that bothsurgical and cleaning teams speed up when falling behind and slow downwhen getting ahead of schedule, with the slowdown exhibiting a strongereffect.While keeping schedules on time is often desirable, attempts to do so mightcome with a cost, such as compromised service quality. A rich literaturefinds a positive correlation between the duration of surgical procedures andpost-surgical complication rates [91]. However, most studies only demon-403.1. Introductionstrate a correlative instead of a causal relationship between these measures.Furthermore, researchers acknowledge that the findings of such correlationare limited due to the inability to adjust for potential confounders [92]. Thisleaves the identification of a causal effect an open question. For example,complications during surgeries tend to both increase the surgical durationas well as increase post-surgical complication risks. In addition, certainsurgical procedures, such as distraction osteogenesis [93], are confoundersas they correlate with longer procedure duration and higher complicationrates. Using data on 30-day post-surgical readmissions and reoperations,we address the endogeneity issue by designing an instrumental variable (IV)that helps identify the causal impact of procedure duration on surgical qual-ity. The validity of our IV builds on the surgical teams’ adaptive behaviorthat we identify. After correcting for the bias with the IV, we find thatfaster surgical procedures lead to higher readmission and reoperation proba-bilities. Figure 3.2 summarizes the different responsive behavior of surgicaland cleaning teams in ORs and the subsequent influence on surgical quality.To investigate these two questions, we leverage a comprehensive administra-tive data set that includes 7,868 surgery cases from April, 2018, to October,2019, in a primary children’s hospital in Canada. The data records eachsurgery case’s actual and scheduled start and end times. Surgeons and thebooking office of the hospital take charge of the scheduling process of eachcase at most times [94], and the surgical teams are informed of the plannedstart and end times of all cases at least one day earlier. By comparing theactual and planned time schedules for each surgical case, we obtain (1) rel-ative procedure duration (RPD), which is the difference between the actualprocedure duration and the planned one, (2) deviation from the scheduledstart (DSS), which is the difference between the actual start time of thesurgery and the planned one, (3) relative turnover duration (RTD) and (4)deviation from the scheduled end (DSE) of the procedure. Overall 62% ofthe operations experience delayed start compared with schedules, which cor-responds to positive DSS values. Based on these quantities, we estimate theimpact of DSS on subsequent surgical duration (i.e., RPD) and the impactof DSE on subsequent turnover duration (i.e., RTD).We adopt several empirical strategies in this study. First, to identify howsurgical and cleaning teams respond to real-time deviations from the orig-inal schedule, the standard ordinary least squares (OLS) method does notwork. Because the DSS for the focal surgery is correlated with the RPDof the previous surgeries in the same shift, the OLS estimator is biased[95]. A similar rationale applies to DSE and RTD. To address this issue,413.1. Introductionwe formulate an auto-regression in which a linear transformation addressesthe above correlation. The general moment method (GMM) estimator ofdynamic panel models is applied in which the high-order lagged regressorsserve as instruments to derive an unbiased estimator [96].The GMM estimator shows that surgical and cleaning teams speed up whenthey fall behind and slow down when they are ahead of schedule. Specifically,when a surgery case has one standard deviation (SD) delayed start thanplanned (23.03 minutes), the surgical team would expedite the focal surgeryby 5.6% on average relative to the median procedure duration. For one SDdelayed start (15.88 minutes), the focal surgery will be prolonged by 10.5%.At the turnover stage, the cleaning teams speed up by 10.3% when facinga SD (26.87 minutes) delayed exit and slow down by 22.1% when facinga SD (18.89 minutes) early exit. The responses of cleaning teams in theturnover stage are more intense than surgical teams and the slowdown effectis stronger. Second, to address the potential endogeneity in estimating theimpact of surgical duration on quality, we utilize DSS as an IV. Accordingto the IV-probit model, an increment of procedure duration results in lower30-day readmission (reoperation) probabilities. We did not use IV whenestimating the impact of the preceding RTD on the quality of the subsequentsurgery because there is less endogeneity concern in the estimation. Theestimation results show that the preceding RTD has no significant impacton quality.To gain a comprehensive understanding of the influence of surgery speedupand slowdown on OR shift end times and surgical quality, we conduct acounterfactual analysis. We unveil a convex relation between these twoquantities, which depicts the efficiency-quality trade-off frontier in the cur-rent OR. We conclude that reducing the gap between actual and plannedshift end times can be achieved at the cost of a higher average 30-day read-mission and reoperation probabilities or vice-versa.3.1.1 ContributionOur study contributes to healthcare management and service operationsliterature in the following aspects.First, we identify healthcare providers’ responsive behavior to real-timeschedule deviations in the OR setting, which complements the vast liter-ature on adaptive server behavior in operations management. We find thatthe balancing feedback behavior exists for both surgical and cleaning teams.423.2. Literature BackgroundBased on discussions with our clinical co-authors, reasons for this may in-clude wanting to avoid potential add-on cases or working overtime. Thisfinding can help surgeons and OR managers, especially those working in asocialized healthcare system like Canada, better predict surgery completiontimes and improve shift planning. Our findings encourage policymakers toreevaluate and develop incentive schemes for surgical teams within a social-ized healthcare system, where they currently receive a nearly fixed salary.Second, our study provides new insights regarding the causal relationshipbetween surgical duration and quality, which is known to be difficult dueto various confounders that bring endogeneity to the estimation process.We find that after addressing endogeneity, faster-than-scheduled surgerieslead to increased post-surgical complication rates, which is contrary to thecorrelative findings in the medical literature that longer surgical durationis associated with poorer quality outcomes. We propose an IV to addressthis challenge, which has a high level of generality and the potential to beapplied to other service settings to study the quality-speed relation.Finally, we propose an auto-regressive model to address the serial corre-lation of procedure duration within the same shift. We utilize the GMMestimator from dynamic panel models with the high-order lagged regressorsas instruments to derive an unbiased estimator. This allows us to applythese statistical methods to explore the behavioral characteristics of serviceproviders. These methods may find other applications in queueing models,where serial correlations are common when customers are served in sequence.The rest of the paper is organized as follows. Section 3.2 reviews the litera-ture related to our work. Section 3.3 discusses the formation of hypotheses.Section 3.4 describes the healthcare context and structure of the data set,and Section 3.5 formulates the model and the GMM estimation method.Section 3.6 presents the estimation results and heterogeneity analysis. Sec-tion 3.7 discusses the impact on surgical quality and the IV-probit estimationresults. Section 3.8 summarizes the counterfactual analysis. Finally, Section3.9 concludes the findings and provides managerial insights.3.2 Literature Background3.2.1 Healthcare Provider ProductivityOur research contributes to the expanding body of empirical literature thatexplores the relationship between operational factors and healthcare providers’433.2. Literature Backgroundproductivity. [16] find that hospital workers accelerate the service rate as theload increases initially, while they decrease the service rate as the load con-tinues to increase or remains high after a certain period. They also provideevidence that such a high load of overwork curtails the quality of care. [97]propose a queueing model to study how delay experienced by a patient im-pacts service times in intensive care units. [98] explore the effect of hospitaloccupancy level on patient length-of-stay (LOS). They identify a “satura-tion effect” for hospital employees, as they cannot speed up to overcomethe workload when the occupancy level is high. [94] conduct an exploratorystudy of the surgeons’ decision process of scheduling surgery cases and iden-tify different priority structures of decision making. [99] study how patientlength-of-stay (LOS) in a clinic varies with hour-of-day, and they find theLOS tends to be larger early in the day while reduces later. Their findingsdiverge from ours because our study focuses on how service duration is af-fected by deviations from the original schedule, as opposed to examining thetime of day. [100] also find a negative impact of surgeon workload on boththe efficiency and quality of cardiac surgeries and propose a mixed integerprogram to incorporate these factors in surgery scheduling. Other papersdiscuss how behavioral factors influence the productivity and performance ofservice providers [28, 101–103]. Researchers also investigate how scheduledworkload impacts turnover times between surgeries [104] whereas they findno significant relationship.Besides the influence of workload and other healthcare sites’ environmentalfactors, doctors’ experience and team structure have also been investigated.[105] explore how surgeons’ experience in focal and related tasks influencetheir performance. They find that a surgeon’s focal experience has a greatereffect on surgeon performance. [106] study the influence of surgery team’sfamiliarity on team productivity. They find that a high dispersion of pair-wise team familiarity (measured by the standard deviation of the numberof past collaborations) lowers productivity in cardiac surgeries. [107] studysurgeons’ learning and forgetting with new surgical device versions and theresulting impact on surgery duration and quality. They identify significantproductivity and quality costs associated with the first use of new devices. [9]explore how radiological doctors deviate from the prescribed task sequenceat discretion when they read images, which erodes productivity.Our research adds to this stream of research by examining how real-time de-viations from schedules influence both the efficiency and quality of surgeries.We analyze the effects of real-time discrepancies between actual occurrencesand planned schedules, which sets our study apart from other research in443.2. Literature Backgroundthe field. By dissecting the dynamics of shifts, we offer a novel perspectivefor understanding operating room behavior.3.2.2 Surgical Speed and QualityOur research also relates to the general topic of healthcare efficiency-qualitytrade-offs. In operations management, [51] review papers on healthcare de-livery quality and summarize the most commonly used service quality met-rics in healthcare settings. They show that a critical combination of qualitymeasures is structure, process, and outcome. [52] study the relationshipamong efficiency, quality, and patient experience in hospitals.In the medical literature, a vast body of research is associated with thistopic. A correlative study by [108] utilizing National Surgical Quality Im-provement Project (NSQIP) data shows a correlation between surgical dura-tion and complications. Longer surgery time than the statewide establishedstandard is associated with higher risk. [109] explore post-surgical complica-tions of plastic surgery and find that increased operative time is a commonrisk factor for plastic surgeries. [110] find that operation duration is cor-related with complications for posterior retroperitoneoscopic adrenalectomyprocedures. A survey paper based on a literature review and meta-analysisby [91] propose that prolonged surgery duration leads to an increased riskof complications.While the aforementioned medical examples indicate that longer operationdurations are correlated with poorer patient outcomes, the literature alsopresents other findings on this topic. In a retrospective analysis of abdom-inal and colorectal surgeries, [111] find that longer surgery duration doesnot lead to a significant increase in complications. [112] find no correlationbetween the surgery duration and the incidence of complications in an or-thopedic procedure. [93] review 30 papers on hand surgery and explore theduration of treatment and complication rates. They find that the durationdoes not have a significant odds ratio for post-surgical complications. [113]systematically review the preoperative and intraoperative factors associatedwith post-surgical complication risks and also influence procedure duration.Most of the studies in this thread focus on a correlative relationship insteadof a causal connection. We contribute to them by proposing an IV to tackleunobservable confounders when carrying out a causal analysis between sur-gical duration and quality. Our approach enables us to address this questionwith a causal perspective.453.3. Hypothesis Development3.3 Hypothesis DevelopmentSchedules are designed to enhance productivity and punctuality. However,discrepancies between actual and planned start/end times are bound to ariseonce schedules are announced. In ORs, the clinical teams review the sched-ules a day in advance and remain cognizant of their progress in relation to theplanned timeline throughout the day. In our analysis, we draw upon first-hand insights from surgeons and corroborating evidence from the literatureto formulate plausible hypotheses regarding their responses to deviationsbetween actual and planned start times.The firsthand experience comes from the interviews with our surgeon col-laborator and the supporting staff. We verify the following practices in thehospital. 1) There is a culture that strives to avoid canceling surgeries whenrunning late, as patients have typically waited for a year or longer. Con-sequently, the surgical and cleaning teams have to work overtime, insteadof canceling the case at the end of shift when they cannot finish on time.This practice supports the conjecture that both teams speed up when facedwith delays to circumvent working overtime. 2) On the flip side, besidesthe scheduled elective cases, emergent add-on cases are likely to be assignedto shifts that are finishing or have finished earlier than scheduled by themanager. However, such extra operative cases do not result in increasedfinancial compensation under the socialized health system. From an in-centive perspective, this supports both team’s slowdown behavior, meaningthey decelerate when ahead of schedule to avoid extra add-on cases.We also find corroborating evidence from the literature that supports thesurgical teams’ responsive behavior as described above. According to in-terviews conducted with 23 surgeons, [89] show that surgeons feel obligedto demonstrate good time management of ORs when faced with time con-straints such as the scheduled shift. They also find a psychological reasonthat surgeons want to build a good reputation for “good sense of time andschedules.” This finding reveals another motive that explains the delay-speedup behavior. Conversely, if they are ahead of schedule, they feel lesspressured and naturally slow down to stay close to the planned schedule.This phenomenon is referred to as “situationally responsive slowing-downmoment” [88], which complements the incentive reason behind the slowingdown behavior of surgical teams. Combining these findings, we propose thefollowing hypothesis on surgical teams’ responsive behavior.Hypothesis 1A. Surgical teams speed up when they fall behind schedule,463.3. Hypothesis Developmentand they slow down when they are ahead of schedule in the surgery stage.For cleaning teams, we also learn that they typically receive indicationsfrom surgical teams when falling behind or ahead of schedule at the end ofa procedure. The cleaning teams then act accordingly during the turnoverstage to minimize deviations from schedules, demonstrating both speedup(when delayed) and slowdown (when getting ahead). Additionally, clean-ing teams share concerns about not canceling surgeries and avoiding extraadd-on cases, similar to surgical teams. Overall, we propose the followinghypothesis on cleaning teams’ responsive behavior.Hypothesis 1B. Cleaning teams speed up when falling behind and slowdown when being ahead in the turnover stage.In line with Hypotheses 1A and 1B, both surgical and cleaning teams ex-hibit a balancing feedback response in their service speed when encounteringdeviations from the pre-established schedule.Addressing our second research question, we consider the consequences of al-tering surgery durations. Substantial evidence in medical research suggeststhat extended operative durations correlate with increased post-surgicalcomplication risks. [91] review 66 related studies and conclude that the likeli-hood of complications rises significantly with prolonged operative durations.Specifically, they find a 14% increase in the likelihood of complications forevery additional 30 minutes of operating time. However, the underlyingmechanism for this finding remains uncertain since various factors in pro-longed surgeries can lead to post-surgical complications. Common examplesinclude increasing microbial exposure and associated infections, tissue re-traction, and bleeding. In light of this literature, we propose the followinghypothesis.Hypothesis 2A. All else equal, a longer procedure time is associated withan increased post-surgical risk.However, the analyses in the existing literature on this topic have a cru-cial flaw: they are primarily correlative instead of causal. As mentionedin [91], correlative analyses suffer from the inability to adjust for potentialconfounders, which may lead to biased results. For example, a specific pro-cedure called distraction osteogenesis is associated with both longer surgicalduration and higher complication rates, making it an endogenous confounderbetween procedure duration and complications [93]. The anesthesia step ofmechanical ventilation is another potential confounder that influences cer-tain post-surgical complications while adding to procedure duration [114].473.4. Clinical Setting and DataWe deduce that there are multiple sources of confounders in the relationshipbetween surgical speed and quality, and they cannot be ignored. We alsoconclude that these confounders tend to increase both surgical duration andcomplication risk levels.Apart from the influence of confounders, we observe that performing pro-cedures faster may increase the likelihood of making mistakes in surgeryprocedures [115, 116], which may further lead to rising post-surgical compli-cation risks. [117] study the impact of operating time on patient outcomesin knee surgeries and find that shortening procedures is associated withan increased risk of post-surgical revisions. The reason is that surgeonsaim to reduce operative time by improving efficiency, potentially leading tocompromises in surgical technique. Consequently, we propose the followingopposite hypothesis.Hypothesis 2B. All else equal, a shorter procedure time leads to an in-creased post-surgical risk when endogeneity is addressed.3.4 Clinical Setting and DataOur study is carried out at a prominent children’s hospital in Canada. Thehospital serves approximately 9,700 patients annually and employs 119 sur-geons across ten different clinical departments. The hospital has 13 avail-able operating rooms, with nine being utilized simultaneously. The primaryworking hours of the hospital are on weekdays, although some emergencycases may be performed during weekends.3.4.1 Surgery Stages and Shift SchedulingBefore delving into the details of the data set, we first introduce the com-position of the surgical and cleaning teams, the surgery process, and thescheduling of an OR shift. The surgical team consists of medical staff indifferent areas, with the mix depending on the procedure type. The teamoften includes a surgeon, an anesthesiologist, a physician assistant, and afew nurses. The surgeon leads the team while the other supporting profes-sionals assist the surgeon before, during, and after the surgery. The cleaningteam, comprising cleaning staff, nurses, and technicians, is responsible forthe turnover stage between two consecutive cases. They clean the OR thor-oughly after the previous patient exits and prepare the room for the nextsurgery.483.4. Clinical Setting and DataFigure 3.1 depicts the breakdown of a typical surgical procedure and thepatient pathway. Upon arrival on the surgery day (the epoch of enteringthe department in the diagram), nurses attend to the patient, assessingtheir condition for surgery by measuring vital signs and performing otherpreparations. The patient is then taken to the designated OR. The pro-cedure duration refers to the total time a patient spends in the OR. Oncethe procedure is completed and the patient exits, the cleaning team startsworking. This period (from the previous exit to the next patient’s entrance)constitutes the turnover connecting two consecutive surgeries.The shift’s start time, marked by the commencement of the first surgery,is typically scheduled for either 7:45 am or 8:20 am. Occasionally, shiftsmay begin later due to additional training or administrative tasks. Priorto the shift’s start, the surgical team receives a comprehensive briefing onthe day’s surgical schedule, even though the schedule is usually sent to theteam several days in advance. The shift is usually scheduled to end between3:15 pm - 3:45 pm. Patients with operations scheduled for that day willbe notified a few days earlier and typically arrive about two to three hoursbefore their scheduled surgery start times.Scheduling surgeries in a hospital is a complex and lengthy process managedby a centralized booking office. There are nine ORs for regular shifts and twoadditional ORs for emergent add-on cases. Usually, each OR is assigned toa sole surgical team from one department throughout the day (shift). Eachshift typically includes four surgeries. The booking office then contacts thepatient and the surgeon to determine which surgeries will be performedon that date , ensuring the total shift length close to eight hours. TheFigure 3.3: An Example of an OR Slatebooking office then drafts an OR slate for each surgery day in an onlinesystem. A surgery slate is a spreadsheet containing essential informationfor each surgery case listed in each row. This information includes plannedstart and end times, planned procedure duration, and a brief procedure493.4. Clinical Setting and Datadescription. It also contains other identifications such as patient name, amedical record number (MRN in Figure 3.3), bed number, and the surgeonin charge. Figure 3.3 presents an example of an OR slate with three surgeriesscheduled for January 12, 2022.We learn from our surgeon collaborators that surgeries are scheduled jointlyby the booking office and the surgeons. The booking office first forecasts theduration of each surgical case’s procedure based on the average of all proce-dures of the same type in the previous calendar year. Surgeons then makeadjustments to these forecasts, taking into account the individual patient’sclinical conditions. The booking office also sets the estimated turnover du-ration to either 20, 25, or 30 minutes, depending on the procedure type. Aschedule is then created by sequencing the surgeries and placing them back-to-back, ensuring the total duration, including procedure time and turnoverduration, fits roughly into an 8-hour shift.The completed day-shift schedule is distributed to the surgical and cleaningteams at least one day before the surgery day so that they are well-informedabout each surgery’s planned start and end time. The finalized schedulesare then recorded in the system and appear in the dataset. Occasionally,some emergency cases are added to the shift on the surgery day withoutnotifying the surgical team in advance. These emergent add-on cases arenot recorded on the slate since they have no advanced schedule. However,they are still recorded in the surgical database. About 7.6% of the shiftscontain add-on cases. We discuss how to handle shifts with add-on cases inSection 3.4.2.3.4.2 DataThe surgery dataset we use is extracted from the hospital’s system, doc-umenting each case’s progress in the OR and hospital from April 2018 toOctober 2019. The dataset includes both the planned and actual start andend times of each surgery. It also contains patients’ demographic informa-tion, such as case type, patient type, age, and surgical procedures.By comparing the actual and planned time schedules for each surgical case,we obtain the difference between the actual and planned procedure dura-tion, which we refer to as the relative procedure duration (RPD). A positive(negative) RPD indicates that the surgery is performed slower (faster) thanplanned. A similar measure has been used in the literature to gauge a surgi-cal team’s speed [118]. We define the deviation from scheduled start (DSS)503.4. Clinical Setting and Dataof surgery as the difference between the actual start time and the plannedone. Thus, a positive (negative) DSS suggests a late (early) start of the focalcase compared to the scheduled. We then obtain the positive and negativeparts of DSS, namely DSS+ and DSS−, to capture the extent of delayed andearly start, respectively. For the turnover stage, we define relative turnoverduration (RTD) as the difference between the actual and scheduled turnoverduration, following our previous definitions. A positive RTD indicates thatthe cleaning team is slower than the planned turnover duration and viceversa. We then define the deviation from scheduled end (DSE) to measurethe difference between the actual and planned end time of the focal surgery.Note that as the turnover starts immediately after a surgery’s end (see Fig-ure 3.1), the end time of the focal surgery is the start time of the turnoverstage. Similar to DSS, we also compute the positive and negative parts ofDSE (DSE+ and DSE−) to measure the scale of delayed (early) end of asurgery.We can also identify sequence shuffling and cancellations by comparing thescheduled sequence with the actual one. Sequence shuffling indicates thatthe actual sequence differs from the scheduled, which is usually caused bya patient’s failure to arrive on time. Some surgeries are canceled mid-shiftand thus will not have actual start and end times, but they can be identifiedfrom the slate.We apply the following exclusion criteria before proceeding with the empir-ical analysis. First, we exclude all cases from the diagnostic department,as they are primarily medical examinations instead of surgeries and do notfit the context of this study. Second, following our surgeon collaborator’ssuggestions, we focus on shifts with at least three surgeries, as they containenough variation in the shift composition. The remaining departments arelisted in Table 3.1. Third, apart from elective surgeries, emergent add-oncases may occur during the shift. Sometimes, add-on cases will be performedin different ORs, disrupting the original schedules. On urgent occasions, thesurgeon may leave the focal surgery (with the surgical team taking over) andattend to the inserted emergent add-on case. To eliminate the interference ofadd-on cases, we exclude all emergent add-on cases and the subsequent im-pacted cases, accounting for 3.6% of the total cases. Similarly, to eliminatethe interference of cancellations, we exclude surgeries following cancellationsin shifts (4.7% of all). To test the robustness of our findings, we conductedadditional analyses in the second appendix, excluding entire shifts contain-ing at least one add-on case and entire shifts with at least one cancellation.The results obtained from these robustness tests are consistent with our es-513.4. Clinical Setting and Datatimates. Finally, to avoid potential extra training or interruptions of shifts,we exclude shifts that do not start during the normal period (i.e., before 9am) and surgeries occurring outside typical shift times (before 7 am or after7 pm), which account for 4.8%.For the turnover stage, it is worth noting that when the next patient is notpresent or not ready yet, the subsequent surgery must be postponed, leadingto an artificially longer recorded turnover duration (as turnover is the periodfrom the prior end to the next start). To reduce this possibility, we onlyinclude turnover samples in which the second surgery’s patient arrives atleast 30 minutes earlier than the recorded start time of the surgery (ensuringthat the patient should be ready for surgery as soon as the turnover finishes).Additionally, the turnover duration following the final surgery in each shiftis not included in our study.The final sample consists of 7,868 surgery cases across various departmentsfrom April 2018 to October 2019. For the turnover stage, we obtain 6,210final observations. The sample includes 1,928 shifts, with the number ofsurgeries ranging from three to eight for each shift. There are 111 differentprocedure codes across all departments. The sample features 69 surgeonswith an average of 18 years of experience, and 75% of them have more thannine years of experience. Overall, 65.3% of the surgeries in the sample ex-perience delayed starts compared to schedules. Table 3.1 summarizes thevariables. Most surgeries take approximately 45 to 99 minutes, as shownby the 25% and 75% quartiles and the average procedure duration is 78.53minutes. As measures of the relative speed of surgical teams, the averageRPD and RTD in the samples are -1.048 minutes and 1.432 minutes, re-spectively, which are much smaller than the average realized procedure andturnover durations. This demonstrates that the scheduled procedure andturnover durations are almost unbiased estimators of the actual durations.Sequence shuffling occurs in 3.7% of total cases. We control for it by creat-ing a dummy variable to label those cases. Since the turnover stage connectstwo surgeries, we also include a dummy indicating whether the two surgeriesare of the same procedure type. Different procedure combinations accountfor 53.4% of the turnover sample.For patient demographics, the average age of patients is 7.6 years in thesample. Elective cases constitute most of the sample, with only 0.1% of thesample representing emergent cases. As for post-surgical risk measures, theaverage probability for 30-day readmission is 0.034, and 0.029 for reopera-tion.523.4. Clinical Setting and DataTable 3.1: Summary StatisticsPanel A: Continuous VariablesVariables Mean Median Std 25% Q. 75% Q.Surgery part:Real procedure duration⋆ 78.53 67 50.47 45 99RPD⋆ -1.048 -3 25.62 -14 10DSS⋆ 7.746 7 32.02 -9 20Delayed start (DSS+)⋆ 15.55 7 23.03 0 20Early start (DSS−)⋆ 7.803 0 15.88 0 9Age 7.561 6.571 5.197 3.014 11.81N 7,868Turnover part:Real turnover duration⋆ 27.33 25 11.49 21 31RTD⋆ 1.432 -1 11.49 -5 5DSE⋆ 7.779 6 38.26 -15 27Delayed exit (DSE+)⋆ 18.29 6 26.87 0 27Early exit (DSE−)⋆ 10.51 0 18.89 0 15N 6,210Post-surgical risk part:30-day readmission 0.034 0.18230-day reoperation 0.029 0.168Notes: Variables with ⋆ are measured in minutes. Relative procedure duration (RPD);Deviation from scheduled start (DSS); Relative turnover duration (RTD); Deviation fromscheduled exit (DSE)533.5. Empirical Methods for Clinical Teams’ Responsive BehaviourIn Panel B of Table 3.1, we report the distribution of departments and pa-tient types. Most cases are surgical daycare (SDC) patients who rarely needto stay in the hospital overnight. Admitted cases (ADP) account for 13.27%and require post-surgical observation. From the patient severity distribu-tion, we observe that most patients belong to the moderate categories: levelIII, IV, and V, while severe cases (I, II a, and II b) account for about 10% ofall cases. Regarding department distribution, dental, urology, gastrointesti-nal, ophthalmology, general, and otolaryngology are the major departments,each constituting more than 10% of all cases.3.5 Empirical Methods for Clinical Teams’Responsive BehaviourThe surgery data set consists of multiple shifts, each consisting of surgeriesperformed by the same surgical team in the shift. We use i = 1P . . . P Nto index the shifts, with the total number of shifts being N = 1P 928. Ineach shift, the sequence of surgical cases is indexed by t = 1P . . . P ii bytheir actual start time, with ii denoting the number of surgeries in shifti. Different shifts may have different numbers of surgeries. As a result ofour exclusion criteria, ii ≥ 3, while the maximum value of ii is 8 in oursample. Since ii varies across shifts, we obtain an unbalanced panel. Byslightly abusing notation, we use RPDi( to denote the difference betweenthe actual and planned start time of the first case in shift i. Let Sit denotethe deviation from the scheduled finish time of case t in shift i includingturnover stage, or equivalently, the deviation from the scheduled start time(DSS) of case t+ 1, which has the following expressionSit = RPDi( +t∑k5)(RPDik + RTDik) t = 1P . . . P ii. (3.1)As shown in the above expression, Sit is the cumulative deviation from theschedule, beginning with the deviation (if any) of the start time of the firstsurgery RPDi( and including all relative procedure and turnover durationsthrough the first t cases.To estimate the impact of a positive DSS (delayed start) or a negative DSS(earlier start) on the RPD, we formulate the following specification:RPDit = γn ·(Si,t−))−+γp ·(Si,t−))++x⊤itβ+δt+αi+uitP t = 1P . . . P ii (3.2)543.5. Empirical Methods for Clinical Teams’ Responsive Behaviourwhere the negative and positive parts of Si,t−) are included. The coefficientsγn and γp represent how surgical teams respond when getting ahead andfalling behind, respectively. The unobserved fixed (case-independent) effectfor shift i is represented by αi, and δt denotes the unobserved case-specificeffect that varies with t. β stands for the coefficient vector of the regressorsxit, which includes patient demographics and case type information. uitdenotes the model’s error term.Since Sit is a linear function of RPDi(PRPDi)P . . . PRPDi,t−) as given inEquation (3.1), multiple lagged response variables RPDikP k = 1P . . . P t − 1appear on the right-hand-side (RHS) of the regression Equation (3.2). Ifwe use the OLS method to estimate the coefficients, the errors in differentregression equations will be correlated, which violates the basic assumptionof OLS [95]. Thus, we reformulate the problem as an auto-regressive speci-fication using a linear transformation. To that end, Equation (3.1) rendersthe following relation between RPDit and Sit,RPDit = Sit − Si,t−) − RTDitP t = 1P 2P . . . P ii (3.3)Plugging the above expression of RPDit into the left-hand-side of Equa-tion (3.2) with a simple transformation, we haveSit−RTDit = (γn−1)·(Si,t−))−+(γp+1)·(Si,t−))++x⊤itβ+δt+αi+uit (3.4)We thus obtain an auto-regressive model where the coefficients of interest,γn, and γp, are absorbed into the coefficient of the positive and negativepart of the auto-regressive term Si,t−). Such an auto-regressive formulationis often employed in dynamic panels, in which the regressors include oneor more lagged dependent variables, allowing for the modeling of dynamicbehavior across time series [119].For the relative turnover duration (RTD), with a slight abuse of notation,we have the following similar specification:RTDit =,n · (DSEi,t−))− + ,p · (DSEi,t−))+ + x⊤itβ)+ n⊤itβ2 (3.5)+ δ˜t + α˜i + u˜itP t = 1P . . . P iiwhere DSE stands for deviation from the scheduled exit time, which is ex-actly the scheduled start time of the turnover stage. Apart from the same re-gressors xit as in Equation (3.2), we also include nit for RTD that comprises1) indicator of whether case t and case t + 1 belong to the same type and2) the patient type of case i+1. This is because the turnover stage consists553.6. Estimation Results and Interpretationsof both cleaning and preparation steps for two consecutive operations. LikeDSS, a positive DSE means that the focal surgery finishes late (thus the sub-sequent turnover stage starts late) and vice versa. The coefficients of interestare ,n and ,p for the negative and positive parts, respectively. The relation-ship between DSE and RTD is DSEi,t = DSEi,t−)+RTDi,t+RPDi,t+). Af-ter similar transformation processes, we obtain the following auto-regressivemodel for RTD:DSEi,t − RPDi,t+) =(,n − 1) · (DSEi,t−))− + (,p + 1) · (DSEi,t−))+ (3.6)+ x⊤itβ) + n⊤itβ2 + δ˜t + α˜i + u˜itP t = 1P . . . P iiTo obtain unbiased estimates of γnP γp in Equation (3.4) and ,nP ,p in Equa-tion (3.6), we employ the Arellano-Bond (A-B) generalized method of mo-ments (GMM) for dynamic panel data [96]. Essentially, the A-B methodutilizes higher-order lagged regressors as instrumental variables (IVs) thatinduce a series of moment conditions for GMM estimation. It is importantto note that the directly obtained estimates are γˆn − 1 and γˆp + 1 for RPD(,ˆn−1 and ,ˆp+1 for RTD), while we report γˆnP γˆpP ,ˆnP ,ˆp after adding (sub-tracting) one. The details of the estimation process can be found in thesecond appendix.3.6 Estimation Results and Interpretations3.6.1 Main ResultsTable 3.2 displays the GMM estimation results. Note again that the directlyobtained estimates are γˆn−1 and γˆp+1 for RPD (,ˆn−1 and ,ˆp+1 for RTD)and we report γˆnP γˆpP ,ˆnP ,ˆp after adding (subtracting) one. We control forother regressors that vary with case sequence t in the same shift, such aspatient type, patient severity, procedure type, and the sequence fixed effectt itself, which will not be eliminated after first-difference (FD) or forward-orthogonal deviation (FOD) transformations in the GMM estimation process(see Appendix B.1).From Table 3.2 columns (1) and (2), we see that in the surgical stage, bothFD and FOD GMM estimates are significant for both early and delayed startwhere γ̂n by FOD-GMM is 0.444 (0.617 by FD-GMM) and γˆp equals -0.164(-0.219 by FD-GMM). To gain a general understanding of these estimates,we consider a scenario where a surgical team faces an early start by onestandard deviation (SD) of the focal case (15.88 minutes). From FOD-GMM estimates, we know that the surgical team would slow down the focal563.6. Estimation Results and InterpretationsTable 3.2: GMM Estimation ResultsSurgery TurnoverVariables (1) FD (2) FOD (3) FD (4) FODEarly Start 0.617*** 0.444*** 0.190*** 0.292***(0.159) (0.126) (0.051) (0.047)Delayed Start -0.219* -0.164* -0.121** -0.096*(0.106) (0.081) (0.045) (0.045)Elective case 13.78 -25.54 4.505 -20.74(60.37) (58.13) (2.843) (19.96)Sequence shuffling -1.557 5.274 -7.235*** -9.074***(5.549) (5.274) (1.864) (2.284)Age 0.280 0.277* 0.361* 0.025(0.148) (0.138) (0.163) (0.172)Different procedure 0.976 1.748**(0.588) (0.543)Next case type Included IncludedPatient type Included Included Included IncludedPatient severity Included Included Included IncludedProcedure type Included Included Included IncludedTime fixed effect Included Included Included IncludedNumber of instruments 253 253 258 253Number of observations 7,868 7,868 6,210 6,210Notes: Both GMM models are estimated using the Arellano-Bond method. In column(1) and (2), we report γˆn and γˆp for RPD. In column (3) and (4), we report νˆn and νˆpfor RTD. Time fixed effect t stands for the sequence of cases in shift i while the shiftfixed effect is zeroed out in the FD (FOD) processes. Robust standard errors clusteredby shift i with the [120] correction are shown in parentheses (* p < 0.05, ** p < 0.01, ***p < 0.001).surgery by 0.444 × 15.88 = 7.05 minutes (10.5% of the median procedureduration) compared to the scheduled duration, ceteris paribus. Conversely,for one SD delayed start of a case (23.03 minutes), the surgical team wouldexpedite the focal surgery by 0.164 × 23.03 = 3.78 minutes (5.6% of themedian procedure duration).We observe the behavior of cleaning teams during the turnover stage fromcolumns (3) and (4). We find that both FD and FOD yield significant573.6. Estimation Results and Interpretationsestimates for both early and delayed start, where ,ˆn by FOD is 0.292 (0.190by FD) and ,ˆp by FOD is -0.096 (-0.121 by FD). If there is a one SD earlyexit of the preceding surgery (18.89 minutes), then the following turnoverwill be extended by 5.52 minutes (22.1% of the median turnover duration)than planned. On the other hand, if the exit is delayed by one SD (26.87minutes), the turnover will be shortened by 2.58 minutes (10.3%). Theseresults illustrate how cleaning teams adaptively manage the turnover stageto minimize the deviation from schedules in both directions. We also findthat the scale of response in turnover is greater compared to that of surgicalteams in surgeries.In summary, we find that surgical and cleaning teams exhibit both speedupand slowdown behavior, supporting Hypothesis 1A and 1B, which reflectsthe presence of balancing feedback behavior for both teams. We illustratethe estimates visually in Figure 3.4, where the slopes of the four lines repre-sent the coefficients in Table 3.2. Although the coefficients for the surgerystage are larger than those for the turnover stage, the responses in termsof percentage scale are more pronounced in the turnover stage. For bothsurgical and cleaning teams, the magnitude of slowing down behavior isgreater than speedup. Based on our discussions with surgeon collabora-tors, we understand that it is more feasible for surgical teams to slow downrather than speed up, as the latter poses potential safety concerns. Addi-tionally, surgical teams have incentives to slow down because when theyare ahead of schedule, the OR administrator is more likely to assign extraadd-on cases to their shift with little to no extra financial compensation dueto the fixed salary scheme. During the turnover stage, cleaning teams facefewer concerns regarding clinical quality and thus have more flexibility toaccommodate responses in both directions.In Table B.1, we also report the FE-OLS estimation results of Equation (3.2)and Equation (3.5). We find that the estimates differ in scale from the GMMestimates due to Nickel bias [95], as mentioned in Section 3.5, although thesigns of the estimates are consistent.3.6.2 Heterogeneity Across Surgeon SeniorityIn this section, we explore the responsive behavior across different surgeonseniority groups and we focus on the RPD. As the leader of the surgicalteam during an operation, a surgeon’s experience is crucial for guiding otherteam members. There is extensive literature on the relationship between ex-perience and performance, particularly in healthcare settings [9, 105, 121].583.6. Estimation Results and InterpretationsFigure 3.4: Surgical and Cleaning Teams’ Responsive BehaviorSenior surgeons, with more experience, are better acquainted with proce-dures and are therefore aware of both the challenging and more manageableaspects of a procedure.To investigate how surgical teams’ behavior varies by surgeon seniority, weperform a subsample study for junior and senior surgeon groups. Basedon discussions with our surgeon collaborators, we choose 20 years after ob-taining the Doctor of Medicine (M.D.) degree as the threshold for surgeonseniority. In our setting, the junior (< 20) and senior (≥ 20) groups comprise3,793 and 4,075 surgical cases, respectively.Table 3.3 reveals that the senior surgeons’ group yields significant estimatesfor both early and delayed starts. To understand the scale of such adaptivebehavior, we again consider one SD delayed (early) start as an example. Onaverage, senior surgeons speed up by 0.319× 23.03 = 7.35 minutes (10.97%of median procedure duration) or slow down by 0.505×15.88 = 8.02 minutes(11.97% of median procedure duration) in the focal case. Surgical teams ledby senior surgeons tend to expedite when facing delays and slow down whenahead of schedule at a similar pace, that is, the balancing feedback. Incontrast, junior surgeons do not consistently exhibit speedup or slowdownbehavior. As our surgeon collaborators explain, one reason for such discrep-ancies between their responsive patterns could be that, compared to juniorsurgeons, senior surgeons may have trainees in the OR. Senior surgeons593.6. Estimation Results and InterpretationsTable 3.3: Heterogeneity of Responses in Surgery Stage between SurgeonSeniority GroupsSenior JuniorVariables (1) FD (2) FOD (3) FD (4) FODEarly Start 0.679*** 0.505*** 0.368 0.404(0.150) (0.141) (0.265) (0.210)Delayed Start -0.359* -0.319** -0.313* -0.234(0.155) (0.113) (0.154) (0.136)Elective case 59.10* 42.09 15.79 -13.77(23.89) ( 37.86) (65.03) (48.12)Sequence shuffling -5.889 -4.485 0.166 -3.363(7.337) (5.698) (10.28) (8.709)Age -0.255 -0.129 0.324 0.410(0.273) (0.189) (0.247) (0.224)Patient type Included Included Included IncludedPatient severity Included Included Included IncludedProcedure type Included Included Included IncludedTime fixed effect Included Included Included IncludedNumber of instruments 244 244 227 227Number of observations 3,793 3,793 4,075 4,075Notes: Robust standard errors clustered by shift i with the [120] correction are shown inparentheses. (* p < 0.05, ** p < 0.01, *** p < 0.001).603.7. Exploration on Surgical Qualitywould be faster and more likely to allow trainees to participate in proce-dures for better practice. When running late, the senior surgeon may takeover from the trainee to steer the schedule back on track. Junior surgeons,on the other hand, might perform the work themselves without substantiallyinvolving the trainees.3.7 Exploration on Surgical Quality3.7.1 Empirical Methods on QualityIn this section, we investigate the impact of procedure duration speedupand slowdown on patients’ post-surgical risks (refer to Hypotheses 2A and2B in Section 3.3). This analysis allows us to examine the second-ordereffects of surgical teams’ responses to delayed and early starts. We considertwo indicators: post-surgical 30-day readmissions and 30-day reoperations.These indicators are widely used to measure patient risk and clinical quality[122, 123].To ensure the accuracy of our analysis, we exclude all dental (DDS) and gas-trointestinal (GAST) surgeries based on our surgeon collaborator’s recom-mendations. These two service types typically do not involve readmissions orreoperations due to the nature of the procedures (0.61% and 1.17%). Afterremoving these two types of surgeries, we are left with 5,204 observations.We first consider a probit model to analyze the relationship between thereadmission/reoperation binary variable and the RPD of a case:r∗it = / · RPDit + ζ · RTDi,t−) + s⊤itβ) + F⊤i β2 + ϵit (3.7)P (rit = 1) = P (r∗it S 0) = Φ(/ · RPDit + ζ · RTDi,t−) + s⊤itβ) + F⊤i β2)(3.8)P (rit = 0) = P (r∗it ≤ 0) = 1− Φ(/ · RPDit + ζ · RTDi,t−) + s⊤itβ) + F⊤i β2)(3.9)where rit denotes a binary indicator for the post-surgical risk event for caset in shift i, which could be either 30-day readmission or reoperation; r∗itstands for the associated latent variable; and / is the coefficient of interest,(i.e., how the RPD of the surgery influences the probability of a patient’spost-surgical readmission). We also control for the RTD of the precedingsurgery (i.e., RTDi,t−)) in the model to explore whether the change in theturnover duration before the focal case starts influences post-surgical risks613.7. Exploration on Surgical Qualityand ζ stands for the associated coefficient. We include other explanatoryvariables sit and fixed effects Fi such as day-of-week and surgeon. β) andβ2 denote the coefficients for sit and Fi respectively. ϵit is the error termthat follows a standard normal distribution, and Φ(·) denotes the cumulativestandard normal distribution function.The above probit model, however, may yield biased estimates for /. Vari-ous factors influence a patient’s post-surgical readmission/reoperation likeli-hood. Although we have controlled for patient demographics, surgeon fixedeffects, and time fixed effects, other unobservables could still be included inthe error term ϵit and correlate with the critical explanatory variable, RPD.For example, the surgical team may encounter unexpected complicationsduring surgery, which may take longer to complete and result in a largerRPD. Meanwhile, unexpected complications during the surgery are associ-ated with a higher risk of developing post-surgical complications. Thus, evenwhen RPD and post-surgical complication rates are positively correlated, itdoes not imply causality since unobservables, such as complications duringthe procedure, can trigger both. In other words, a direct estimate of / mayhave overlooked the existence of confounders and lead to an upward bias.We search for an appropriate IV to address the endogeneity in Equation (3.7)to obtain unbiased estimates. Based on the previous section’s analyses ofsurgical teams’ adaptive behavior, we utilize DSS as our IV here. First,DSS satisfies the relevance condition, as it leads to a change in the RPDof the focal case. Second, regarding the exogeneity condition, DSS reflectsthe cumulative deviations from the schedule based on earlier cases in thesame shift (see Equation (3.1) in Section 3.5) and should be uncorrelatedwith the post-surgical complication rate of the current surgery. We haveperformed robustness tests to rule out other potential aspects by which thefocal surgery might be influenced by DSS, such as fatigue (see AppendixB.2). Therefore, the exogeneity condition is also satisfied, lending supportthat our IVs are valid for the estimation of /. Here, we adopt the IV-probitmodel for identification. The structural equations are as follows:RPDit = γ ·DSSit + x⊤itω) + F⊤i ω2 + ξitrit = 1{/ · RPDit + ζ · RTDi,t−) + s⊤itβ) + F⊤i β2 + ϵit S 0}P(3.10)where the first equation stands for the relation between endogenous RPDand instruments. xit represents exogenous variables. ω) and ω2 representthe associated coefficients of the control variables. ξit denotes the error term623.7. Exploration on Surgical Qualitywhere ξit and ϵit follow multivariate normal distribution. We utilize the con-ditional maximum likelihood (CMLE) method to obtain the estimates fromthe joint equations mentioned above. The CMLE estimator is unbiased andoffers two advantages compared to the traditional two-step control function(CF) approach: (1) it is more efficient, and (2) it simplifies the computationof partial effects [124]. The estimated correlation between the two errorterms in Equation (3.10) is used to examine the existence of endogeneity.We employ 30-day readmission/reoperation as proxy measures for surgicalquality. We do not have detailed data on the readmissions, so we can-not distinguish those related to the surgery, which would otherwise providegreater accuracy. Despite the limitation of using readmissions and reopera-tions as proxies for service quality, our analysis offers an IV-based approachto identify the potential impact of service speed on service quality, which ischallenging due to various potential confounding factors [125].3.7.2 Estimation ResultsIn Table 3.4, we present the estimation results from IV-probit and plainprobit models based on 30-day readmissions and reoperations, respectively.From columns (3) and (4), we find that for 30-day readmission and reoper-ation, the RPD of focal surgery is positively significant as /ˆnonIVrdms+( = 0.0043and /ˆnonIVrwop+( = 0.0052. The RTD of the preceding surgery (connects theprevious and focal surgery) is not significant under the plain probit model.The non-IV probit model seems to imply that speedup in surgeries (negativeRPD) decreases the patient’s 30-day readmission and reoperation probabil-ity. This suggests that longer procedure duration is correlated with increased30-day readmission and reoperation rates, which is consistent with the cor-relative findings in the literature [91]. As we mentioned earlier, however, theobserved positive correlation does not necessarily imply causality. Instead,it is likely driven by confounders that are positively correlated with both theRPD and the readmission/reoperation probability. This speculation is fur-ther supported by the second-to-last row in the table, where all IV-probitmodels yield positively significant-from-zero correlations of the two errors(ξit and ϵit as shown in Equation (3.10)).The IV-probit model yields estimates /ˆIVrdms+( = −0.0316 for readmissionsand /ˆIVrwop+( = −0.0332 for reoperations. All of them are negatively signifi-cant. Comparing estimates from the IV-Probit and plain probit models, itis clear that the estimates become negative when the upward bias is elimi-633.7. Exploration on Surgical QualityTable 3.4: Impact of Relative Procedure and Turnover Duration on Post-surgical RisksPanel A: IV-Probit Panel B: NonIV-ProbitVariables (1) 30-Read (2) 30-Reop (3) 30-Read (4) 30-ReopRPD -0.0316*** -0.0332*** 0.0043** 0.0052**(0.0066) (0.0051) (0.0014) (0.0018)Previous RTD 0.0007 0.0016 0.0020 0.0050(0.0025) (0.0022) (0.0053) (0.0050)Seqchange Included Included Included IncludedAge Included Included Included IncludedPatient type Included Included Included IncludedPatient severity Included Included Included IncludedProcedure type Included Included Included IncludedTime Fe Included Included Included IncludedDay-of-week FE Included Included Included IncludedSurgeon FE Included Included Included IncludedCorr of errors 0.8842*** 0.9292***N 5,204 5,204 5,204 5,204Notes: Estimated by the maximum likelihood method. Dependent variables: 30-dayreadmission, 30-day reoperation indicators. We report the correlation of the errors of thetwo equations in the IV-probit models in the final part. Robust standard errors are shownin parentheses (* p < 0.05, ** p < 0.01, *** p < 0.001).643.8. Counterfactual Studynated. Thus, speedup (slowdown) in the surgery procedure leads to an in-crease (decrease) in both 30-day readmission and reoperation probabilities,supporting Hypothesis 2B and rejecting Hypothesis 2A. However, under theIV-probit model, the RTD of the preceding surgery remains insignificant foreither risk measure.The coefficients in Table 3.4 do not directly quantify the impact on read-missions and reoperations due to the nonlinear probit function. To betterunderstand the scale of the RPD’s impact on post-surgical risks, we com-pute how marginal changes in the RPD lead to different readmission andreoperation probabilities. We perturb the RPD in each observation of thesample by plus or minus one minute and compute the associated readmissionand reoperation probabilities based on the fitted structural model eq. (3.10),holding other variables constant. We then take the average of all samples’fitted values. We find that expediting the relative speed of surgeries byone minute increases the average 30-day readmission probability by 3.973×10−+ (and increases the average 30-day reoperation probability by 3.994×10−+), while prolonging the RPD of surgeries by one minute decreases theaverage readmission probability by 3.629 ×10−+ (and decreases the averagereoperation probability by 3.587 ×10−+).3.8 Counterfactual StudyThe results in the previous section reveal the trade-off between surgical speedand quality in operating rooms (ORs). We find that faster-than-scheduledoperations lead to increased post-surgical readmission/reoperation risks andvice versa. This section presents a counterfactual study to quantitativelymeasure the trade-offs between efficiency and quality, providing managerialinsights to surgeons and hospital managers. Specifically, the counterfactualstudy aims to demonstrate the relationship between the disparity betweenthe actual and planned end-of-shift times (EOS) and post-surgical readmis-sions and reoperations. Surgical teams are likely concerned about minimiz-ing the difference between the actual and scheduled EOS, which refers tothe finishing time of the last surgery in a shift. If the shift ends later, itmeans that the surgical team has to work overtime, whereas if the shift endssignificantly earlier than scheduled, another add-on surgery may be assignedto the team.Using the actual timestamps of surgeries, we construct six counterfactualscenarios where each operation is prolonged or shortened by 5, 10, and 15653.8. Counterfactual StudyFigure 3.5: Surgical Quality and End-of-Shift Timeminutes, respectively. We then obtain the average fitted probabilities of 30-day readmissions and 30-day reoperations based on the updated RPD valuesthrough the structural model Equation (3.10). In addition to the readmis-sion and reoperation rates as quality metrics, we compute the counterfactualEOS time based on the counterfactual RPD of cases in the same shift. Wethen obtain the average difference between each shift’s counterfactual EOSand planned EOS.The analysis is based on the quality exploration sample we adopt, wheredental and gastrointestinal surgeries are not included since these depart-ments have scarce readmissions and reoperations. To analyze the effects onthe EOS, we select 1,584 unabridged shifts to conduct counterfactual anal-ysis (we exclude those cases after an urgent add-on case or a cancellation,as explained in Section 3.4). The final case sample size is 4,429.Figure 3.5 and Table 3.5 summarize the relationship between surgical qual-ity and the differences between the actual and planned EOS under six sce-narios. The x-axis represents the change in EOS compared to the currentscenario, which serves as a baseline, depicted using a dashed vertical line.The y-axis represents quality measures, the average fitted 30-day readmis-sion/reoperation probabilities. Overall, their relationship presents a convex663.9. Conclusions and Future Researchshape. In the sample, the average difference to the planned EOS is approx-imately 10 minutes (i.e., on average, a shift ends later than planned), witha 0.0327 average 30-day readmission probability and 0.0275 average reop-eration probability. If we extend each operation by 5 minutes, we obtainreduced average readmission and reoperation probabilities equal to 0.0188and 0.0144, and the difference to the planned EOS increases to 33.51 min-utes. On the other hand, when each surgery is expedited by 5 minutes,we obtain a reduced difference to the planned EOS (-10.2 minutes) andincreased 30-day readmission/reoperation probabilities (0.0571 and 0.0530).Overall, this relationship provides guidance for hospital managers to achievedesired quality goals when creating OR schedules.Table 3.5: Results of the Counterfactual AnalysisScenario Readmission Reoperation Diff EOS-15 min 0.1385 0.1455 -53.92-10 min 0.0915 0.0911 -32.06-5 min 0.0571 0.0530 -10.20Original 0.0327 0.0275 10.03+5 min 0.0188 0.0144 33.51+10 min 0.0099 0.0068 55.37+15 min 0.0049 0.0030 77.23Observations 4,429 4,429 1,584Notes: Readmission and reoperation columns present the fitted average rates based onchanging RPD (plus or minus 5, 10, 15 minutes) for each case using the estimated Equa-tion (3.10). The Diff EOS column present the averaged difference to planned EOS timewhen RPD is changed.3.9 Conclusions and Future ResearchOperating rooms exemplify service sites where deviations from prescribedschedules frequently occur, often leading to physical and financial reper-cussions. Although abundant literature exists on this topic, two questionsremain open. First, while many researchers have studied surgical team re-sponses to schedule deviations, they primarily rely on surveys to exploreresponse mechanisms instead of using real-time and scheduled surgery data.Second, concerning the relationship between surgical speed and quality,many researchers conduct correlative analyses, which may be biased dueto various confounders in surgical procedures. In this paper, we address673.9. Conclusions and Future Researchboth questions by investigating surgical teams’ immediate responses to earlyand late starts of surgeries, cleaning teams’ responses in the turnover stage,and exploring how such responses further influence post-surgical complica-tion risks. We apply econometric identification techniques to a unique andcomprehensive surgical dataset to achieve this goal.To answer the first question, we employ a series of empirical strategies. Theprimary challenge is that the ordinary least squares (OLS) estimator is bi-ased since the general deviation from the scheduled start (DSS) is correlatedwith the relative procedure duration (RPD) of prior cases. We propose anauto-regressive model to address the serial correlation of procedure dura-tions within the same shift. We then utilize the dynamic panel model andthe associated GMM estimators to identify the parameters. We find thatsurgical and cleaning teams speed up when they fall behind schedule andslow down when they get ahead of schedule, with the slowdown exhibitinga stronger effect. That is, they exhibit the balancing feedback behavior.Quantitatively, surgical teams expedite the next surgery by an average of5.6% when facing a one standard deviation (SD) delay in the planned startfor that surgery, whereas they take on average 10.5% longer when they areone SD ahead of schedule. In the turnover times, cleaning teams accelerateby 10.3% (slow down by 22.1%) on average when they are one SD aheadof (behind) schedule. This insight is valuable for OR managers, as under-standing the responsive behavior of clinical teams can further improve ORscheduling practices and potentially enhance patient satisfaction. Our find-ings are particularly relevant to ORs in a socialized healthcare system. Theidentified phenomenon likely results from the lack of incentives in the social-ized healthcare system, which may motivate the redesign of incentives forsurgical teams within such a system. Additionally, we explore the hetero-geneity of behavior among different surgeon seniority groups for the surgerystage, finding that the speedup/slowdown phenomenon occurs only in thesenior group.On the second question, we explore how the speedup/slowdown of an op-eration influences a patient’s post-surgical risks, measured by 30-day post-surgical readmissions and reoperations. Estimating the impact of servicespeed on service quality is challenging due to endogeneity issues. To ad-dress this, we propose an instrumental variable (IV) based on our observa-tion that the early/late start (DSS) of a case may impact surgical qualityonly through the procedure duration. After correcting the upward bias, wefind that speeding up procedures increases 30-day readmission and reop-eration probabilities, contrary to the correlative findings of existing liter-683.9. Conclusions and Future Researchature. Through a counterfactual analysis, we reveal a convex relationshipbetween the readmission/reoperation rate and the difference between realand planned end-of-shift (EOS) times. This curve relates to the fundamentaltopic of efficiency-quality trade-offs in service operations. Surgical teams canadjust their paces to reduce the difference in scheduled EOS time; however,this may lead to increases in 30-day post-surgical readmission and reoper-ation risks, as captured in Figure 3.5. This finding has important implica-tions for healthcare providers, particularly surgeons and hospital managers.Methodologically, we propose an IV to address endogeneity issues in esti-mation, which is shown to work effectively. This method can be extendedto analyses in other service sectors, such as appointment scheduling andproject management.We conclude our paper by suggesting some directions for future research.Our paper focuses on how clinical teams respond to schedule deviations andthe subsequent impacts on post-surgical risks. Future studies can considerprescriptive data-driven models that incorporate such behavior to optimizedaily surgical schedules. We also note that Canada’s socialized healthcaresystem differs significantly from the diversified health insurance systems inthe U.S. Therefore, another interesting angle relates to the incentive schemedesign of healthcare systems and how surgical teams behave under differentpayment modes. For example, the OR manager may provide appropriateincentives for clinical teams to work overtime. Researchers can also inves-tigate similar mechanisms in project management, transportation, and anyservice areas where time schedules for tasks are made in advance.69Chapter 4ConclusionIn this chapter, we summarize the two essays and discuss their limitationsand potential future research directions.In the first essay, we collaborate with frontline ED physicians to empiricallyexplore how task-switching among ED physicians impacts ED operationsin terms of efficiency, quality, and patient selection behavior, and then wepropose operational solutions. We find that, on average, when task switchingis more frequent, the physician’s service speed decreases. Quantitativelya 10% increase in switching freq leads to about 8-11% decrease in speed,which indicates a switch cost. On quality, we find that it has little impacton quality measured by 7 and 30 day revisit-and-admission probabilities. Inthe identification process, there are two major challenges. One is to capturethe time the physician spends on each patient and second is the selectionbias as a result of physicians’ choices. We manage to find a clean periodin which the service time on patients can be identified to address the firstchallenge. To tackle the second challenge, we propose an instrument variablecalled switching likelihood to address the endogeneity issue led by selectionbias.With these empirical results, we further propose to optimize ED operations.Directly changing or intervening physicians’ patient sequencing is not fea-sible as physicians follow medical acuity guidelines. Therefore, we proposeto cluster patients into two queues, in which we minimize the intra-queueswitch cost and maximize the inter-queue switch cost. We find that solvingsuch an optimization problem is equivalent with solving a max-bisection ofa graph. This two-queue design can be promisingly implemented as there isan acute/fast track system based on acuity in the studied ED and we canincorporate the patient type information into that system. Through a sim-ulation, we find, if implemented in the ED, the proposed two-queue designcan reduce average waiting time by about 38%.There are several potential directions for further exploration in this project.70Chapter 4. ConclusionFirst, we can investigate the impact of task switching on other outcomessuch as patient satisfaction, physician burnout, and other work-related psy-chological outcomes. Additionally, it is important to learn the long-termeffects of task switching on operational efficiency and healthcare qualityover time for EDs.Another interesting point is to conduct comparative studies across differenthealthcare service settings (e.g., hospitals, urgent care, primary care) toexplore whether the effects of task switching are consistent across variousmedical environments. Also, it is important to examine the effectiveness ofdifferent types of technological aids (e.g., electronic health records systems,AI-based patient sorting algorithms) in mitigating the negative effects oftask switching. For example, integrating large-language-models (LLM) withthe triage notes and physician charting may mitigate the switch costs andimprove the productivity.In the second essay, we focus on operating rooms. Schedules and disruptionsare everywhere in various sectors, such as healthcare, transportation, andproject management. The operating room is a typical healthcare site thatfunctions with detailed schedules.We study how surgical and cleaning teams adaptively adjust the servicespeed in response to real-time deviations from the planned OR schedulesand the further impact on surgical quality of these responses, using a uniquesurgery data set. Here we use a transformed dynamic panel model to capturethe serial correlation between consecutive surgeries in the same shift.We unveil that surgical and cleaning teams speed up when they fall behindschedule and slow down when they get ahead of schedule, with the slow-down exhibiting a stronger effect. Quantitatively, surgical teams expeditethe next surgery by an average of 5.6% when facing one standard deviation(SD) delay in the planned start for that surgery, whereas they take on av-erage 10.5% longer when they are one SD ahead of schedule. We furtherexamine the subsequent impact on surgical quality, measured by 30-dayreadmission and reoperation probabilities. The adaptive service behaviorgenerates an instrumental variable for us to address endogeneity issues inestimating the relation between surgical speed on surgical quality, that is,the deviation from scheduled start time of a surgery case. After employingthis IV, we find that a faster-than-scheduled procedure duration hurts surgi-cal quality by increasing 30-day readmission and reoperation probabilities.Through a counterfactual analysis, we quantify and obtain a convex re-lationship between readmissions/reoperations and end-of-shift (EOS) time,71Chapter 4. Conclusionwhich can assist hospital managers in scheduling surgeries to achieve desiredefficiency-quality trade-offs.Currently we only consider the short-term outcomes of the negative feedbackbehavior. However, we can further investigate the psychological and long-term career impacts on surgical staff due to frequent schedule deviations.This could include stress levels, job satisfaction, and turnover rates amongclinical personnel. It’s also of vital importance to study and quantify theeconomic impacts of adaptive server behaviors, such as the cost implicationsrelated to changes in surgical speeds, including resource utilization and op-erational efficiencies. 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We find that the distribution is similar to that of the entiresample as reflected in Figure A.4. There is a slight difference in the triagedistribution, as physicians tend to pick more acute patients during the firsthours. However, since our patient type is defined based on CCS, the dis-tribution among the patients picked in the clean period is almost identicalto that of the entire patient population. Consequently, the patients used inour study are representative of ED operations.To check the representativeness of our refined sample for ED operations, weexamine the distribution of patient demographics, including triage, CCS,gender, and age, in both the refined sample and the entire sample. Wepresent their distribution histograms in Figure A.4. Our analysis revealsthat the distribution of patient demographics is similar between the twosamples. There is a slight difference in the triage distribution, as physicianstend to select more acute patients during the first hours. However, sinceour patient type is now defined based on CCS, the distribution among thepatients picked during the clean period is almost identical to that of theentire patient population. As a result, the patients used in our study arerepresentative of ED operations.87A.1. Additional Tables and FiguresTable A.1: Effect of Task Switching on PPH: OLS EstimatesED A ED BSwitching frequency -0.162 0.073(0.102) (0.056)Average queue length 0.088*** 0.032***(0.015) (0.011)Average ED load 0.013* 0.026***(0.007) (0.004)Average age -0.002 -0.002(0.001) (0.001)Average triage 0.435*** 0.096**(0.063) (0.041)Female proportion 0.028 -0.021(0.060) (0.043)Homeless proportion 0.216 -0.020(0.290) (0.118)Ambulance arrival proportion -0.032 -0.013(0.088) (0.052)Waiting time 15-30 min 0.583*** 0.661***(0.082) (0.044)Waiting time 30-60 min 0.844*** 0.972***(0.117) (0.063)Waiting time 60-120 min 0.846*** 1.114***(0.165) (0.083)Waiting time S 120 min 0.859** 1.216***(0.323) (0.167)Fixed effects:Clock hour Included IncludedPhysician Included IncludedDay-of-week Included IncludedObservations 7,845 10,521R2 0.196 0.142Notes: Estimated by OLS. All estimates control for physician fixed effects, day-of-the-week fixedeffects, clock-hour fixed effects. We also control for the share of patients in each CCS which isomitted from the table due to size constraint. Robust standard errors clustered by physicians inparentheses (* p N (.), ** p N (.(5, *** p N (.()).88A.1. Additional Tables and FiguresFigure A.1: Distribution of Patient Triage in the Refined Sample vs. EntireSampleNext, we examine the robustness of the switch cost to alternative definitionsof patient types and an integrated sample period format (instead of 30-minblocks). The results are presented in Table A.2.In the preferred specification, patient types are defined based on their CCS.Alternatively, we define patient types as (i) both distinct CCSs and triagelevels, and (ii) distinct chief complaint categories (CCC). Both definitionsare more granular, as there are 15 unique CC systems, 68 unique CCS-triage combinations, and 163 unique CC categories. With more granularclassification, the switching frequency and switch likelihood of physicianservice also increases. In panel A and panel B of Table 2.3, we find that theLIML estimates of the switch cost δ remain negatively significant. The effect89A.1. Additional Tables and FiguresFigure A.2: Distribution of Patient Sex in the Refined Sample vs. EntireSamplemagnitudes are very similar to those from the main model. The results showthe robustness of the switch cost under different patient type definitions.In addition, we calculate PPH for each physician-shift over the entire cleanperiod, i.e., from the beginning of the shift until when the first lab test comesout. As before, we construct the switch likelihood at the beginning of theshift. The sample size is then reduced to 2,754 for ED A and 4,141 for EDB. In Table A.2, panel C, we find that switching frequency is still negativeand significant. The results support our strategy of restricting the sampleperiod using the earliest lab result time.90A.1. Additional Tables and FiguresFigure A.3: Distribution of Patient Age in the Refined Sample vs. EntireSampleA.1.3 Switch Cost in the Fast TrackFor ED B operating both regular and fast tracks, we also explore the effect oftask switching in the fast track using the same empirical strategy. As before,we focus on the clean period obtained by the same process of each fast-track shift and exclude potential idle periods. Consistent with the previousfindings, the estimated switch cost at the fast track remains negative andsignificant. The results are presented in Table A.3.91A.1. Additional Tables and FiguresFigure A.4: Distribution of Patient CCS in the Refined Sample vs. EntireSample92A.1. Additional Tables and FiguresTable A.2: Alternative Patient Type Definition and Sampling MethodVariables ED A ED BPanel A. Patient type by CCS × triageSwitching frequency -3.050*** -2.443***(0.841) (0.670)Observation 7,845 10,521Kleibergen-Paap rk Wald F statistic 145.5 83.06Panel B. Patient type by CC categorySwitching frequency -3.387*** -3.814***(0.922) (0.785)Observation 7,845 10,521Kleibergen-Paap rk Wald F statistic 174.4 102.6Panel C. Integrated sample periodSwitching frequency -3.074*** -7.442***(0.819) (2.127)Observation 2,754 4,141Kleibergen-Paap rk Wald F statistic 121.4 20.07Fixed effects:Clock hour Included IncludedPhysician Included IncludedDay-of-week Included IncludedNotes: Estimated by LIML. All estimates control for explanatory variables xit and zit and fixedeffects Fi and Dt. Other regressors are omitted from the table due to size constraints. Robuststandard errors clustered by physician in parentheses (* p N (.), ** p N (.(5, *** p N (.()).93A.1. Additional Tables and FiguresTable A.3: Effect of Task Switching on PPH in Fast-track of ED BVariable EstimatesSwitching frequency -10.15***(1.691)Average queue length 0.083***(0.014)Average ED load -0.009(0.020)Average age -0.003(0.003)Average triage 0.313***(0.094)Female proportion 0.034(0.133)Homeless proportion -0.309(0.293)Ambulance arrival proportion 0.114(0.214)Waiting time 15-30 min 0.344(0.283)Waiting time 30-60 min 0.413(0.272)Waiting time 60-120 min 0.178(0.281)Waiting time S 120 min 0.252(0.371)Fixed effects:Clock hour IncludedPhysician IncludedDay-of-week IncludedObservations 5,604Kleibergen-Paap rk Wald F statistic 46.84Notes: Estimated by LIML. All estimates control for physician fixed effects, day-of-the-week fixedeffects and clock-hour fixed effects. The results for the share of patients in each CCS are omittedfrom the table due to size constraint. Robust standard errors clustered by physicians in parentheses(* p N (.), ** p N (.(5, *** p N (.()).94A.1. Additional Tables and FiguresA.1.4 Effect Heterogeneity across PhysiciansIn this appendix, we investigate the switch cost heterogeneity across individ-ual physicians. To obtain physician-specific estimates of the switch cost δ,we split the sample by physician ID and estimate Equation (2.2) separatelyon each subsample. We focus on top 10 physicians at each ED to ensurethere are enough observations to identify the regression parameters.Figure A.5 plots the resulting estimates at both EDs, with physicians rankedby the number treated of patients. Almost all physicians’ productivity isnegatively impacted by task switching, and the effect magnitudes differ sig-nificantly across physicians.Figure A.5: Switch Cost Coefficients Across Top Five ED Physicians95A.1. Additional Tables and FiguresA.1.5 Effect Heterogeneity across CCS PairsAs discussed in Section 2.5.3, we estimate the coefficients δm,n in Equa-tion (2.5) to explore the heterogeneity among 156 different switch pairs.Based on these estimates we further compute eq. (2.7) and obtain ω(iP j) asthe weight of edges. Here we present the significant (at 5% level) estimates.Table A.4: Significant CCS Pairs Estimates in ED APair δ Pair δ Pair δgas - neu -0.657** gen - gnr -0.893* gnr - neu -0.591**gas - car -0.637** ent - gas -0.849*** ort - ent 0.672*ent - car -0.924** gas - res -0.528* neu - res -1.056***res - car -0.592** oth - gas 1.051* gen - oth -1.785***gas - men -1.291** gen - men 1.908* men - neu -1.1**oph - ski -0.841* oph - gnr -1.261*** oph - ort -1.077**oph - car -1.038* oph - res -1.475** gas - obg -1.167**obg - gas 1.542** obg - neu -1.294* res - obg -1.557***obg - oth -1.354** men - obg -2.355** oph - obg -3.94***Notes: ED A sample comprises 7,845 observations and d2 is equal to 0.375 (* p N (.(5, **p N (.(), *** p N (.(()).Table A.5: Significant CCS Pairs Estimates in ED BPair δ Pair δ Pair δneu - gnr -0.576* gas - gnr -0.379** gas - ent -1.022**ent - gnr -1.538** car - ent -1.109*** neu - ort -0.889**ort - neu 1.691* gas - ort -0.479* gnr - ort -0.987***car - ort -0.551* ent - ort -1.576* oth - neu -0.775*gnr - oth -0.946** oth - gnr -0.724* gas - ski -0.715*gnr - ski -1.636*** ski - gnr -1.158** car - ski -0.92***ent - ski -0.965*** ort - ski -0.901* -ski - ort -2.036***neu - men -0.488** men - gnr -0.659** car - men -0.299*men - ort -0.948** men - oth -0.717** sub - oth -1.189***car - res -0.385** res - ort -0.659* oth - res -0.816**res - ski -0.812* obg - car -0.579* oth - obg -0.916*obg - res -1.162*** gas - gen -0.512* gen - ort -1.261**oth - gen -0.797* gen - ski -1.995*** sub - gen -0.941**Notes: ED B sample comprises 10,521 observations and d2 is equal to 0.398. Robust standarderrors clustered by physicians in parentheses (* p N (.(5, ** p N (.(), *** p N (.(()).96A.1. Additional Tables and FiguresA.1.6 Proof of Proposition 1Proof. Suppose all patient visits have been partitioned into two queues Sand SC , with |S| = |SC |. If two patients i and j are in the same queue,then they will be picked consecutively by the same doctor with probabilityC. This probability C does not depend on i and j by our assumption thateach sequence is uniformly sampled from the population. Thus, the totalintra-queue switch cost is given byC ·∑i ̸5j, i,j∈eω(iP j) + C ·∑i ̸5j, i,j∈eCω(iP j)which equalsC ·∑i ̸5j,i,j∈Vω(iP j)− C ·∑i∈e,j∈eCω(iP j).Since C ·∑i ̸5j,i,j∈V ω(iP j) is a constant, minimizing the above difference isequivalent to maximizing the second termC ·∑i∈e,j∈eCω(iP j)which is equivalent tomax(i,j)∈ eE12∑(1− yiyj)ω(iP j)by letting yi = 1 if i ∈ S and yi = −1 if i ∈ SC .The additional constraint ∑iNj yiyj ≤ −nR2 is equivalent to ∑m ym = 0,which requires the sought-for partition to be a bisection. Q.E.D.97A.2. Computation Steps in SimulationA.2 Computation Steps in SimulationIn the simulation study, we simulate each patient visit to the ED and re-construct the activity path accordingly. Specifically, we compute the wait-ing time and pick-to-pick (P2P) duration of each patient under the simu-lated scenario. Moreover, we need to consider the impact of switch cost onphysician productivity under the new patient clustering and physician shiftscheme. To achieve this, we consider the following approximation proceduresregarding the translation between PPH and P2P.Consider the picking moment of a patient i in a physician j’s shift. Wewant to obtain the associated modified P2P duration until the next avail-able time to select another patient. As a heuristic, we consider the timeperiod starting from 40 minutes prior to the selection of patient i to theselection moment of the next patient after i by the focal physician as thePPH “surrounding” patient i. For the first 30-minute interval of a physi-cian’s shift, we compute the PPH and switching frequency associated witheach CCS pair in Table A.4. We then use these values for all patients pickedin the interval.Now we take into account the switch cost impact using the estimates δ̂lfrom Table A.4. In the simulation, we may obtain different patient selectionresults, which result in modified task switching frequency in this period oftime. Compared with the switching frequency in the real data, we obtainthe difference between the switching frequency denoted by di and we obtainthe modified PPH denoted by]PPHi as:]PPHi = PPHi + δ̂⊤diwhere PPHi represents the original PPH level in the data. We then obtainthe proportional relation as]PPHiPPHi= 1 +δ̂⊤diPPHiTo translate the impact into P2P duration, we need the reciprocal of that.Therefore, the modified average P2P duration P˜2Pi for each patient i in thesimulated paths is:P˜2Pi =P2Pi1 +bδ⊤diPPHiwhere both P2Pi and PPHi are known based on original data. The aboveequations show that, as the switching frequency decreases, PPH should in-crease and the average P2P duration will decrease and vice versa.98Appendix BAppendix for Chapter 3B.1 GMM EstimationFor dynamic panel data, the classic fixed-effect ordinary-least-square (FE-OLS) estimator yields biased estimators, especially when the panel datahas large cross-sectional units N and short time periods i (in our case,N = 1P 928 and i ∈ [3P 8]). This bias is known as the Nickell bias [95].The bias arises because the lagged response variable is one of the explana-tory variables. Therefore after the demeaning process (a step of the FEestimator), there will be a correlation between the autoregressive regressorand the error term. Thus, to achieve unbiased estimates of γn and γp fromEquation (3.4), we adopt the Arellano-Bond (A-B) method [96] of dynamicpanel models. The A-B approach utilizes higher-order lagged regressors asinstrumental variables (IV) that induce a series of moment conditions forGMM estimation. The IV selection criterion depends on the properties ofthe explanatory variables. We now take the model of RPD as an example toelaborate the GMM estimation process. For RTD, the estimation process islargely the same. First, we transform the original model Equation (3.4) viafirst-difference (FD) or forward-orthogonal deviation (FOD). We try bothapproaches to reach a robust estimate. FD is a simple and direct methodby taking the first order difference between two consecutive cases, which isalso applied to regular static panel models [96, 126].[127] proposed FOD method for dynamic panel data and the estimator iscalled the FOD-GMM estimator. The FOD transformation operator is asfollows∆˜tuit =√i − t+ 1i − t(uit − 1i − t+ 1T−t∑s5(ui,t+s)Under the assumption that uit is serially uncorrelated, we obtain thatCorr(∆˜tuitP ∆˜tui,t−))= 099B.1. GMM EstimationThe advantage that the FOD-GMM estimator has compared with diff-GMMis the higher data utilization rate for unbalanced panel data sets. Note thatwe set Si,(, the DSS of the first case in a shift as the difference between thereal start time and scheduled start time so that more data can be utilized.After transformation, we obtain the following two equations for them, re-spectively,FD : ∆(Sit − RTDit) = (γn − 1)∆(Si,t−))− + (γp + 1)∆(Si,t−))++∆x⊤itβ +∆δt +∆uitFOD : ∆˜t(Sit − RTDit) = (γn − 1)∆˜t(Si,t−))− + (γp + 1)∆˜t(Si,t−))++ ∆˜tx⊤itβ + ∆˜tδt + ∆˜tuitP(B.1)where ∆ and ∆˜t stand for the FD and FOD transformation operators, re-spectively. Both FD and FOD transformations eliminate all time-invariantfixed effects such as αi in Equation (3.2). We control for other variablesthat vary with case index (time) t in the same shift, such as patient type,case type, and case index, by including them in xit, which remain in theregression equations after the FD or FOD transformation.Second, we need to determine the appropriate lag order of all explanatoryvariables on the RHS of Equation (B.1), which leads to the moment condi-tions that are indispensable for GMM estimation in the A-B method. Gener-ally speaking, the right-hand-side regressors yi,t−) and xit can be categorizedinto four types further for which the moment conditions are different. (i).Lagged dependent variable:Z [yi,t−s∆uit] = 0P s = 2P 3P . . . P t;(ii). Strictly exogenous regressors:Z [xi,t−s∆uit] = 0P t− s = 1P . . . P i ;(iii). Predetermined regressors:Z [xi,t−s∆uit] = 0P s = 1P 2P . . . P t;(iv). Endogenous regressors:Z [xi,t−s∆uit] = 0P s = 2P 3P . . . P t.100B.1. GMM EstimationThe criterion that determines the category of a regressor is condition inde-pendence where strictly exogenous regressors satisfyZ [uit | xi(Pxi)P . . . PxiT ] = 0, that is, all of them are conditionally independent of the current error termat t. Predetermined regressors should satisfy Z [uit | xi(Pxi)P . . . Pxit] = 0and endogenous ones satisfy Z [uit | xi(Pxi)P . . . Pxi,t−)] = 0.Here we consider higher lags of the auto-regressive term, namely (Si,t−2)−,(Si,t−+)− and (Si,t−2)+P (Si,t−+)+ , as instruments for ∆(Si,t−))−P∆(Si,t−))+in Equation (B.1). The associated moment conditions are formulated inEquation (B.2). Regressors in xit include exogenous variables of case t suchas the patient age, surgery procedure, and case types, which are uncorre-lated with uit. We select these explanatory variables and first-order laggedterms as instruments and formulate their moment conditions. The momentconditions for the FD transformed model are presented in Equation (B.2)below:Z[(Si,t−s)−∆uit]= 0P Z[(Si,t−s)+∆uit]= 0P s = 2P 3Z [xi,t−s∆uit] = 0P s = 1P 2(B.2)In the FOD model, by subtracting forward means from the current levels,we can utilize the first-order lagged terms as instruments, and the associatedmoment conditions are as follows:Z[(Si,t−s)−∆˜tuit]= 0P Z[(Si,t−s)+∆˜tuit]= 0P s = 1P 2Z[xi,t−s∆˜tuit]= 0P s = 0P 1(B.3)In fact, we can adopt further lagged terms as instruments. Nevertheless,too many instruments may lead to over-identification issues in estimation.Thus, for endogenous variables, we only use their lags of the second andthird order for the FD-GMM model, and we use lags of the first and secondorder for the FOD-GMM model. While for exogenous variables, we alwaysuse themselves and first-order lagged terms as instruments. We conducta series of specification tests to validate the choice of lagged terms (seeAppendix B.2).We then conduct GMM estimation based on the above moment conditions.After stacking the moment conditions, we obtain the vector-form momentconditions for GMM estimation:Z [mi(θ)] = 0P θ = (γPβ)101B.2. Robustness Checkswhere θ is the vector of all estimands in Equation (B.1),mi(·)P i = 1P 2P . . . P NPN = 7P 868denotes the left-hand-side of the moment conditions (B.2) applied to a casei in the FD-GMM model (or Equation (B.3) in the FOD-GMM model). TheGMM estimators are obtained through the following two-step minimization:θˆ = argminb(1NN∑i5)mi(b))⊤W((1NN∑i5)mi(b))θˆstwp2 = argminb(1NN∑i5)mi(b))⊤W(θˆ)(1NN∑i5)mi(b))PW(θˆ) =(1NN∑i5)mi(θˆ)mi(θˆ)⊤)−).In the first step of the GMM, we utilize an initial (suboptimal) weightingmatrix W(, and the purpose is to obtain a GMM estimate of θ. We thenobtain the consistent estimate of the inverse of the asymptotic covariancematrix of m(θˆ), as shown in the second set of equations. We finally up-date W( by W(θˆ) and obtain the two-step GMM estimator. More detailsregarding GMM computation can be found in[96, 120, 127, 128].B.2 Robustness ChecksWe present the normal FE-OLS estimation results of Equation (3.2) andEquation (3.5) in Table B.1 as a reference.B.2.1 Dynamic Panel Model Specification TestsSerial Correlation Test. Recall that we utilize higher-order lagged regressorsas instruments in Equation (B.2) for GMM estimation of the dynamic panelmodel. Under such an IV configuration, for these lagged explanatory vari-ables to be valid instruments, the absence of higher-order serial correlationbetween error terms ∆uit and ∆ui,t−sP (s = 2P 3) is indispensable. Here theformal null hypothesis isH( : Corr (∆uitP∆ui,t−j) = 0P j = 2P 3. (B.4)102B.2. Robustness ChecksTable B.1: FE-OLS Estimation ResultsVariables Surgery TurnoverEarly start 0.430*** 0.283***(0.035) (0.018)Delayed start -0.533*** -0.059***(0.023) (0.013)Elective case 13.49 6.419*(10.25) (2.948)Sequence shuffling -2.353 -5.208**(2.217) (1.589)Age 0.348*** 0.060(0.091) (0.046)Different procedure 1.175**(0.435)Next case type IncludedPatient type Included IncludedPatient severity Included IncludedProcedure type Included IncludedShift fixed effect Included IncludedSequence fixed effect Included IncludedR2 0.496 0.531N 7,787 6,120Notes: The linear model Equation (3.2) and Equation (3.5) are estimated by OLS. Esti-mated by FE-OLS. Robust standard errors clustered by shift are shown in parentheses (*p < 0.05, ** p < 0.01, *** p < 0.001).103B.2. Robustness ChecksWe thus adopt the Arellano-Bond specification test, also known as the AR(p)test, to examine the above validity requirements, where p stands for thelagged order. To be specific, we perform AR(1) to AR(3) tests for bothModels (1) and (2) to identify the starting level of the lag structure of theinstruments. From the p values in the last part of Table B.2 we find that theAR(1) test is rejected, since applying FD transformation to Equation (3.2)naturally brings first order serial correlation between ∆uit and ∆ui,t−). Wecannot reject the null hypotheses of AR(2) and AR(3), which means thereis no higher order serial correlation in Equation (B.1). Therefore, our nullhypothesis Equation (B.4) is supported and the IV configuration we chooseis valid for identification. For moment equations of the FOD-GMM modelwe also conduct similar tests and the results also cannot reject the nullhypothesis.We also conduct the Hansen J-test [129] of model over-identification, as thenumber of instruments is relatively large. The null hypothesis isH( : Over-identifying restrictions are valid.We see that both the FD-GMM and FOD-GMMmodels yield non-significantχ2 values. Thus they pass the Hansen test and the IV configurations foridentification are supported.Apart from the main model of Table B.2, we also conduct AR(p) serialcorrelation tests and Hansen J-tests for the seniority exploration. As shownin the third part of Table B.3, both regressions pass the serial correlationtests and Hansen J-tests, which validate the estimation results.B.2.2 Sample Inclusion CriterionRemove all shifts with add-on cases. We remove the shifts that includeadd-on cases from our sample, which yields 7,484 cases (5,827 for RTD) inall. The results are shown in Table B.4. We find that the estimates forboth surgery stage (RPD) and turnover stage (RTD) are consistent withTable 3.2 and significant. Both surgical and cleaning teams respond to bothdirections.Remove all shifts affected by cancellations. We remove all shifts that areaffected by cancellations, which yields 7,777 cases in the refined sample(6,122 for RTD). The GMM estimation results are shown in Table B.5. Wefind that the estimates are still consistent. These results support our findingsof the adaptive behavior by surgical and cleaning teams.104B.2. Robustness ChecksTable B.2: Specification Tests for Main ModelSurgery TurnoverVariables (1) FD (2) FOD (3) FD (4) FODEarly Start 0.617*** 0.444*** 0.190*** 0.292***(0.159) (0.126) (0.051) (0.047)Delayed Start -0.219* -0.164* -0.121** -0.096*(0.106) (0.081) (0.045) (0.045)Elective case 13.78 -25.54 4.505 -20.74(60.37) (58.13) (2.843) (19.96)Sequence shuffling -1.557 5.274 -7.235*** -9.074***(5.549) (5.274) (1.864) (2.284)Age 0.280 0.277* 0.361* 0.025(0.148) (0.138) (0.163) (0.172)Different procedure 0.976 1.748**(0.588) (0.543)Next case type Included IncludedPatient type Included Included Included IncludedPatient severity Included Included Included IncludedProcedure type Included Included Included IncludedTime fixed effect Included Included Included IncludedSpecification tests:Arellano–Bond AR(1) p 0.000 0.000 0.000 0.000Arellano–Bond AR(2) p 0.593 0.299 0.205 0.589Arellano–Bond AR(3) p 0.950 0.868 0.951 0.436Hansen J-test χ2 129.2 124.6 135.2 108.6Hansen J-test p value 0.287 0.392 0.163 0.649Number of instruments 253 253 258 253Number of observations 7,868 7,868 6,210 6,210Notes: Both of the GMM models are estimated using the Arellano-Bond method. Se-quence fixed effect is exactly the time effect t in shift i. We control for other fixed effectsthat vary with case index in the same shift, such as patient type, case type and caseindex. Robust standard errors clustered by shift i with the [120] correction are shown inparentheses (* p < 0.05, ** p < 0.01, *** p < 0.001).105B.2. Robustness ChecksTable B.3: Estimates for Different Surgeon Seniority GroupSenior JuniorVariables (1) FD (2) FOD (3) FD (4) FODEarly Start 0.679*** 0.505*** 0.368 0.404(0.150) (0.141) (0.265) (0.210)Delayed Start -0.359* -0.319** -0.313* -0.234(0.155) (0.113) (0.154) (0.136)Elective case 59.10* 42.09 15.79 -13.77(23.89) ( 37.86) (65.03) (48.12)Sequence shuffling -5.889 -4.485 0.166 -3.363(7.337) (5.698) (10.28) (8.709)Age -0.255 -0.129 0.324 0.410(0.273) (0.189) (0.247) (0.224)Patient type Included Included Included IncludedPatient severity Included Included Included IncludedProcedure type Included Included Included IncludedTime fixed effect Included Included Included IncludedSpecification tests:Arellano–Bond AR(1) p 0.000 0.000 0.000 0.000Arellano–Bond AR(2) p 0.355 0.078 0.279 0.496Arellano–Bond AR(3) p 0.978 0.353 0.477 0.990Hansen J-test χ2 105.3 112.4 109.6 108.0Hansen J-test p value 0.731 0.550 0.309 0.350Number of instruments 244 244 227 227Number of observations 3,793 3,793 4,075 4,075Notes: Robust standard errors clustered by shift i with the [120] correction are shown inparentheses. We omit other regressors in xit. (* p < 0.05, ** p < 0.01, *** p < 0.001).106B.2. Robustness ChecksTable B.4: Robustness with Add-on Cases Estimation ResultsSurgery TurnoverVariables (1) FD (2) FOD (3) FD (4) FODEarly Start 0.590*** 0.424** 0.250*** 0.306***(0.166) (0.134) (0.057) (0.057)Delayed Start -0.242* -0.167* -0.120* -0.088†(0.110) (0.082) (0.048) (0.050)Next case type Included IncludedElective case Included Included Included IncludedSequence shuffling Included Included Included IncludedAge Included Included Included IncludedPatient type Included Included Included IncludedPatient severity Included Included Included IncludedProcedure type Included Included Included IncludedTime fixed effect Included Included Included IncludedSpecification tests:Arellano–Bond AR(1) p 0.000 0.000 0.000 0.000Arellano–Bond AR(2) p 0.627 0.367 0.430 0.514Arellano–Bond AR(3) p 0.812 0.610 0.858 0.488Hansen J-test χ2 129.3 121.0 123.5 119.9Hansen J-test p value 0.286 0.482 0.394 0.435Number of instruments 253 253 256 252Number of observations 7,484 7,484 5,827 5,827Notes: Both of the two GMM models are estimated using Arellano-Bond method. Thetime fixed effect is t in shift i. Robust standard errors clustered by shift i with the [120]correction are shown in parentheses (†p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001).B.2.3 IV Specification TestsThe validity of using DSS as an IV relies on the underlying assumptionthat they will impact readmission/reoperation risk only through impactingthe RPD. One may argue that DSS is correlated with the fatigue level ofthe surgical team, which further impacts the readmission/reoperation risk.To address this concern, we control for the hour-of-shift (HOS) of eachcase, where HOS n stands for the n-th hour after the focal shift starts.The HOS well captures the surgical team’s cumulative working hours since107B.2. Robustness ChecksTable B.5: Robustness with Cancellations Estimation ResultsSurgery TurnoverVariables (1) FD (2) FOD (3) FD (4) FODEarly Start 0.614*** 0.499*** 0.203*** 0.291***(0.159) (0.131) (0.048) (0.045)Delayed Start -0.212* -0.170* -0.098* -0.081†(0.105) (0.084) (0.043) (0.043)Next case type Included IncludedElective case Included Included Included IncludedSequence shuffling Included Included Included IncludedAge Included Included Included IncludedPatient type Included Included Included IncludedPatient severity Included Included Included IncludedProcedure type Included Included Included IncludedTime fixed effect Included Included Included IncludedSpecification tests:Arellano–Bond AR(1) p 0.000 0.000 0.000 0.000Arellano–Bond AR(2) p 0.630 0.551 0.194 0.581Arellano–Bond AR(3) p 0.977 0.608 0.806 0.519Hansen J-test χ2 128.2 120.3 133.8 108.5Hansen J-test p value 0.311 0.500 0.184 0.653Number of instruments 253 253 258 253Number of observations 7,777 7,777 6,122 6,122Notes: Both of the GMM models are estimated using Arellano-Bond method. The timefixed effect is t in shift i. Robust standard errors clustered by shift i with the [120]correction are shown in parentheses (†p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001).the start of shift, and hence provides a proxy for the fatigue level. Theregression results with HOS as an extra control are presented in Table B.6.We find that the IV-Probit estimates of the focal RPD still remain negativelysignificant for both 30-day readmissions and reoperations. That is, a faster-than-scheduled surgery leads to increased post-surgical risks. We also findthat HOS indicators are mostly insignificant across the four models, whichmanifests that post-surgical readmission and reoperations are not influencedby the fatigue level.To further verify that DSS is not correlated with the unobserved errors108B.2. Robustness ChecksTable B.6: Effects of RPD on Read/Reop with HOSPanel A: IV-Probit Panel B: NonIV-ProbitVariables (1) 30-Read (2) 30-Reop (3) 30-Read (4) 30-ReopRPD -0.0316*** -0.0332*** 0.0043** 0.0052**(0.0066) (0.0051) (0.0014) (0.0018)Previous RTD 0.0007 0.0016 0.0020 0.0050(0.0025) (0.0022) (0.0053) (0.0050)HOS: 2 -0.0917 -0.1480 -0.2150 -0.4366*(0.0971) (0.1100) (0.2620) (0.2050)HOS: 3 -0.0970 -0.1744 -0.1983 -0.4851*(0.1070) (0.1118) (0.2826) (0.2226)HOS: 4 -0.2333 -0.2371 -0.5403 -0.6356*(0.1264) (0.1436) (0.3121) (0.3013)HOS: 5 -0.1996 -0.1669 -0.3980 -0.3576(0.1127) (0.1186) (0.2600) (0.2829)HOS: 6 -0.1616 -0.2093 -0.2629 -0.4316(0.1184) (0.1298) (0.3183) (0.3212)HOS: 7 -0.2037* -0.2190 -0.3084 -0.3846(0.1014) (0.1198) (0.2505) (0.2490)Seqchange Included Included Included IncludedAge Included Included Included IncludedPatient type Included Included Included IncludedPatient severity Included Included Included IncludedProcedure Included Included Included IncludedTime FE Included Included Included IncludedDay-of-week FE Included Included Included IncludedSurgeon FE Included Included Included IncludedCor Errors 0.8842*** 0.9292***N 5,204 5,204 5,204 5,204Notes: Estimated by the maximum likelihood method. Dependent variables: 30-dayreadmission, 30-day reoperation indicators. We report the correlation of the errors of thetwo equations in the IV-probit models in the final part. Robust standard errors are shownin parentheses (* p < 0.05, ** p < 0.01, *** p < 0.001).109B.2. Robustness Checks(so they are valid), we run a regression by controlling them and RPD in aplain probit model for 30-day readmission and reoperation. The results, assummarized in Table B.7, show that the estimates of DSS are not significant.This means that DSS is only correlated with the RPD but not with otherunobserved variables. Thus, it is valid to serve as an IV.Table B.7: Effect of RPD on Readmissions and Reoperations with DSS30-Read 30-ReopRPD of the focal surgery 0.0044*** 0.0053***(0.0013) (0.0015)DSS 0.0018 0.0023(0.0011) (0.0013)RTD of the preceding surgery 0.0015 0.0042(0.0043) (0.0046)Sequence shuffling Included IncludedAge Included IncludedPatient type Included IncludedPatient severity Included IncludedProcedure type Included IncludedTime fixed effect Included IncludedDay-of-week fixed effect Included IncludedSurgeon fixed effect Included IncludedNumber of observations 5,204 5,204Notes: Estimated by the maximum likelihood method. Dependent variables: 30-dayreadmission and reoperation indicators. Robust standard errors are shown in parentheses(* p < 0.05, ** p < 0.01, *** p < 0.001).110
Thesis/Dissertation
eng
Business Administration - Management Science
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Nagarajan, Mahesh
Ding, Yichuan
Essays on healthcare delivery analytics
Text