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Modelling survival rates in bilateral breast cancer Dunn, Lindsay Allison 1986

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M O D E L L I N G SURVIVAL R A T E S IN B I L A T E R A L B R E A S T C A N C E R by LINDSAY A L L I S O N D U N N B.A. , The University of British Columbia, 1982 A THESIS S U B M I T T E D IN PARTIAL F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E in T H E F A C U L T Y O F G R A D U A T E STUDIES Department of Statistics We accept this thesis as conforming to the required standard T H E UNIVERSITY O F BRITISH C O L U M B I A May 1986 ©Lindsay Allison Dunn, 1986 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department o r by h i s o r her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department o f S t a t i s t i c s The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date A p r i I 28 , 1986 Abstract This study involves modelling hazard rates for failure from two related causes, unilateral and bilateral breast cancer in women. Of interest is the incorporation of information from cases who survived the first cause of death into the hazard for the second cause of death. Proportional hazards regression models and survival plots are used to investigate this question for breast cancer patients seen by the A. Maxwell Evans Clinic in Vancouver; a large data set was provided by the Cancer Control Agency of B .C. It is discovered that controls and cases differ in covariates impor-tant to the first cause of death. As a result, hazard functions for the two causes of death are not directly comparable. A multistate model using hazards specific to particular transitions towards death is recommended for further analysis of the survival relationships. ii T A B L E O F C O N T E N T S Abstract i t List of Tables iv List of Figures v Acknowledgement vi Chapter 1. Introduction 1 1.1 Background 1 1.2 Data Used for this Study 2 1.3 Focus of this Study 10 1.4 Methods 11 Chapter 2. Survival from Time of First Tumour 16 2.1 Modelling Matched Controls from First Tumour Date to Death 16 2.2 Modelling Cases from First Tumour Date to Death . 20 2.3 Modelling the 5% Sample 22 2.4 Discussion of Recurrence 31 Chapter 3. Survival from Time of Second Tumour 35 3.1 Introduction 35 3.2 Modelling Cases and Controls from Second Tumour Date to Death 37 3.3 Survivor Function Estimates 42 Chapter 4. Discussion of Alternate Methods 48 4.1 Transition-Specific Hazards 48 4.2 Multiplicative Effect of Second Tumour . . . . 51 4.3 Methods Used on Stanford Heart Transplant Data 51 4.4 Bivariate Analysis 53 4.5 Cause-Specific Hazards 53 4.6 Paired Failure Times . 54 Chapter 5. Summary and Conclusions . 5 5 References 57 Appendix 59 iii List of Tables Table I. Variable names and descriptions 6 Table II. Summary of patient information 8 Table DX Matched controls from first tumour date, stepwise results 17 Table IV. Cases from first tumour date, stepwise results for first tumour variables . . . . 21 Table V . Cases from first tumour date, stepwise results for first and second tumour variables . . . 21 Table VI. Survival from first tumour date, stratified on recurrence 26 Table VII. 5% sample, stepwise results 29 Table VHJ. Stepwise results, from second tumour date to death, stratified on recurrence 38 Table DC. Results for cases from second tumour date, stratified on recurrence, grouped on time between first and second primary tumours . . . 41 Table X. Relevant groups for transition-specific hazards . . 50 iv List of Figures Figure 1. Survival from first tumour date; cases, matched controls and 5% sample 12 Figure 2. Log{—logSoifci)} versus time t for controls, stratified on recurrence 19 Figure 3. Log{—logS0i(t;i)} versus time t for cases, stratified on recurrence 23 Figure 4. Log{—logSQi(t\i)} versus time t for cases, stratified on size of first tumour 24 Figure 5. Log{—logS0i{t;i)} versus time t for cases, stratified on description of first tumour 25 Figure 6. Residual plot for cases with recurrence 27 Figure 7. Residual plot for controls . 27 Figure 8. Survival of 5% sample, stratified on recurrence . . . . 30 Figure 9. Survival of cases from date of recurrence .33 Figure 10. Survival of controls from date of recurrence 33 Figure 11. Survival of matched controls versus cases from date of second tumour 36 Figure 12. Survival of cases from second tumour date, stratified on time between first and second tumours . . 39 Figure 13. Survival of controls based on different covariates, for stratified model 43 Figure 14. Survival of controls based on mean covariate values, for unstratified model 44 Figure 15. Survival of cases based on different covariates, stratified model 45 Figure 16. Survival of cases based on mean covariate values, unstratified model 46 Figure 17. Transitions of interest 49 v Acknowledgements I would like to express my appreciation to Dr. Nancy Reid for her guidance in the preparation of this thesis, and for her support and time, always generously given. I also benefitted from discussions with Dr. John Petkau, and I thank him for his helpful suggestions. I am indebted to Andrew Coldman for suggesting the interesting topic of this thesis; to the Cancer Control Agency of British Columbia for providing the data; and to Dr. T . G . Hislop for advice on the medical aspects of this study. The support of the U B C Department of Statistics is also gratefully acknowledged. vi C H A P T E R 1 I N T R O D U C T I O N 1.1 Background The Cancer Control Agency of British Columbia ( C C A B C ) helps improve the health of British Columbians with its comprehensive, coordinated province-wide cancer programme, which includes providing quality clinical care and education, and researching improvements in methods for the prevention, detection and treatment of all forms of cancer. The C C A B C is highly regarded in the medical world, and has had many accomplishments over the past ten years. The A. Maxwell Evans Clinic, the agency's special purpose hospital, is the major cancer referral centre for B.C. Each year, the clinic sees approximately 5500 new patients for consultation, diagnosis, treatment and follow-up; approximately 100,000 outpatient visits are made to the clinic annually. The agency's registry records information on all types of cancer patients. Incidence of breast cancer in women is high (93.9 per 100,000 per year) compared to other types such as lung cancer in women (34.7 per 100,000 per year) or lung cancer in men (73.0 per 100,000 per year). Breast cancer accounts for approximately 30% of new cases of cancer in females aged 15 and over, and approximately 20% of this group's annual cancer deaths ( C C A B C Annual Report, 1985). Records show that while most of these women had cancer in one breast only, a small percentage (approximately 3%) developed additional cancer in the second breast. The C C A B C ' s division of Epidemiology, Biometry and Occupational Oncology was interested in knowing the relationship between the two related causes of death, unilateral and bilateral breast cancer in women. Unilateral cancer refers to a first primary tumour in one breast only, and bilateral cancer here refers to a second 1 primary tumour in the contralateral (opposite) breast. Disease recurrence and metastasis (transmission from the original site to one or more other sites) may occur in either situation. Although specialists do not agree that all cases allow certain differentiation be-tween primary and metastatic disease, there is some consensus in general terms. A second primary tumour may be identified by clinical evidence as well as micro-scopic tissue structure differentiation from the first primary. Distinction of a second primary tumour from metastatic disease may be difficult when the carcinomas are not in situ, and especially when there is a combination of invasive (i.e., invading and attacking new cells) cancer in one breast, and in situ and infiltrating (i.e., ac-cumulating gradually in tissues) cancer in the other; in this case, indication of a second primary may be by either obvious histologic (i.e., tissue structure) difference or a long interval between development of the first and second tumours. Various other criteria for problematic cases are listed in the medical literature; see for exam-ple Leis (1980) or Robbins &; Berg (1964). The Cancer Control Agency identified women with bilateral disease after examining information from clinic physician Dr. Ellison, the pathology chart, the clinician's opinion and the pathology review. This data set contains a variable called "likelihood of second primary" which is used to identify questionable cases. 1.2 D a t a U s e d for this S t u d y The population considered for this thesis is British Columbian women with a diagnosis of cancer in either one or both breasts. Information on three groups of women was extracted from data collected on over 9,000 breast cancer patients referred to the A . Maxwell Evans Clinic in Vancouver between 1946 and 1976; follow-up was recorded up to 1985. 2 One data set contains information on the 375 patients identified as having de-veloped a second primary tumour in the contralateral breast; these are the "cases" or "bilaterals". The second data set provides information on 375 "matched con-trols"; these are women from the remaining unilateral patients, each selected as a "match" for a bilateral case. Matching criteria were age at diagnosis ( ± 2 yrs), year of diagnosis of the first primary tumour ( ± 1 year), and survival time. A "control" does not necessarily live longer than her "matched case", but is required to live at least as long as it took for that case to develop a second primary. The third data set contains information for a random sample of 5% (434) of the unilateral patients. The cases and two comparison groups were used in Hislop et aJ (1984) in a study of incidence and risk factors for bilateral breast cancer. The data set contains 158 variables recording patient information on personal and family history; non-malignant breast disease and other types of cancer; use of drugs; diagnosis of disease; clincial, surgical and pathologic examinations of the first and second tumours; treatment, recurrence and outcome. Outcome refers to a patient's status at last contact: either dead from disease, dead from other causes, alive with or without disease, or lost to follow-up. A sample coding sheet is included in the Appendix. Before the variables themselves could be examined, a certain amount of clean-up and correction was necessary in the three data sets. Patient records which appeared more than once within a data set were discovered and deleted, and problems with duplicate matching and matching errors had to be resolved. Adjustments were made to shifted data columns, and information where none was expected was inves-tigated. The Cancer Control Agency kindly researched patient records for missing values of important variables such as outcome. Variables which were thought to 3 be irrelevant to survival of breast cancer patients (e.g., use of non-treatment drugs, mammograms, position of tumour) were identified by A. Coldman and G . Hislop of the C C A B C , and removed from the data files, leaving 63 variables to be examined. For each of these remaining variables, a decision was required on interpreting its values. The coding sheet (Appendix) had inconsistencies so careful examination was necessary, and some recoding was required before analysis could begin. For example, "blank" was not always a missing value; it sometimes meant "no" (as for the metastasis variable), or was a required code dependent on another variable (e.g., if the number of excised lymph nodes was zero then the number of positive nodes had to be "blank"). The use of several missing value codes (e.g., blank, 99, 0) and binary codes (e.g., 0/1, 1/2) was initially confusing. Values not listed as coding options (such as 4 or 5 for "hormonal therapy") had to be checked and recoded when appropriate. Ambiguities in coding were resolved, for the purposes of this study, with the help of A. Coldman. Although there were no major problems in the data set, resolving all the minor difficulties took a considerable amount of time. It might be worthwhile to recode the current data file and revise the coding form if substantial further use of this data is planned. The corrected data set and a list of recommendations for recoding are available. For this particular study, further adjustments in coding were suggested by G . Hislop to allow a more direct interpretation. For example, the pathologic description of a tumour was reduced from two variables with twelve possible values to one binary 0/1 variable representing descriptions "ductal" or "other"; the five categories of "surgery" were reduced to simply "yes" or "no". Of the remaining variables, 23 were rejected. Some were uninformative due to a high proportion (more than 10%) of missing values. There was no obvious pattern in the distribution of missing 4 values, so rejection was necessary here in order to retain as many complete patient records as possible. For some variables, the response lacked diversity (for example, "multiple tumours" was 4% "yes", 96% "no"), while for others, the response was difficult to interpret (for example, "weight" was recorded within six months of diagnosis, so could have been affected by treatment or disease). The remaining 38 variables to be included in the preliminary analysis are listed in Table I. (They are also identified on the sample coding sheet in the Appendix.) Although the matched pairs and the 5% sample were examined separately, the initial data clean-up resulted in the same first tumour variables, plus xrtl for the 5% sample. From the records for the matched pairs, nine controls and seven cases were eliminated during data clean-up because of duplicate records, matching errors, or missing date of biopsy, leaving 366 matched controls and 368 cases. (The two extra cases were left in, for the analysis does not involve matching in the usual sense.) From the 5% random sample of unilateral patients, 5 duplicate records were eliminated, leaving 429 controls. Descriptive statistics for the three groups of patients are presented in Table II. Time on study ranged from 1 month to 34 years. The mean time on study was approximately 6 years for the 5% sample, and almost 10 years for cases and for matched controls. Observed failures (deaths from disease) occurred from 1 month to 32 years after diagnosis of the first tumour; mean failure times were, approximately, 3.5 years for the 5% sample, 5 years for the matched controls and 7 years for the cases. Approximately 48% of the 5% sample died from disease, compared to 34% of the cases and 26% of the matched controls. Only 34% of the women in the 5% sample were alive at last contact, compared to 47% of the cases and 58% of the 5 Table I. Variable names and descriptions idlidS status age race kids frstsymp molsymp yrlsymp main yrin moseen yrseen sizel clinstgl growthl descripl lymphl posnodel zrtl ooph morecur yrrecur scndsymp moSsymp yrSsymp mobiop yrbiop growths descrip2 insitu intrdnct posnode2 patient identification number (6 digits) whether the patient was a control (code 1, unilateral disease) or a case (code 2, bilateral disease) age of patient at diagnosis of first primary tumour actually records place of birth rather than race number of liveborn children first symptom of first tumour (9 categories, e.g. painless lump, enlarged nodes) month and year of first symptom month and year of diagnosis (from biopsy) of first primary tumour month and year first seen at the Cancer Control Agency diameter (cm) of first primary tumour assessment (according to standard guidelines) of clinical stage of first tumour (5 categories) pathologic assessment of the type of growth of the first primary tumour (carcinoma may be in situ, infiltrating, or both) pathologic description, which together with pathologic type, indicates whether the carcinoma is "ductal" or "other" clincial identification of lymph node involvement at time of first primary tumour (yes/no) of the lymph nodes excised for the first tumour, the number that were positive (carcinogenic) whether the patient had x-ray treatment (yes/no) whether the patient had an oophorectomy (removal of the ovaries) as treatment for first breast cancer (yes/no) month and year of first recurrence of first carcinoma first symptom of second primary tumour (same categories as for frstsymp) month and year of first symptom of second tumour month and year of diagnosis (from biopsy) of second primary tumour pathologic assessment of the type of growth of the second primary tumour (carcinoma may be in situ, infiltrating, or both) pathologic description indicating whether the carcinoma is "ductal" or "other" whether or not carcinoma was in situ (yes/no) whether or not carcinoma was intraductal (yes/no). [insitu and intrduct are used to help differentiate second primary tumour from recurrence] of the lymph nodes excised for the second tumour, the number that were positive 6 Table I. (cont'd) surgS xrtS outcome molaat yrlast matchid whether or not the patient had surgery as treatment of second primary tumour (yes/no) whether or not the patient had x-ray therapy as treatment of second primary tumour (yes/no) status of patient at last contact, either dead from disease or one of seven censored choices (e.g. dead, other malignancy; alive, no disease) month and year of death or last follow-up identification number of matched patient Additional variables calculated for each patient were the following: recur whether or not the patient had recurrence of disease (yes/no) rectime time in months between the diagnosis of the first primary tumour and recurrence of disease lstto2nd time in months between the first and second primary tumours 7 Table II. Summary of patient information Matched Variable Cases Controls 5% Sam total number 368 366 429 age mean years (se) 53(.62) 53(.61) 57(.60) range 25-83 28-81 28-90 race % Canada 2 1 3 Great Britain 72 70 68 Europe 25 26 26 other 1 3 3 kids mean number (se) 2.0(.08) 2.1(.09) 2.2(.09) median number 2.0 2.0 2.0 % in [0,4] 96 89 88 yrin % 1946-55 14 13 14 56-65 33 33 29 66-75 41 41 51 76-82 12 13 6 clinstgl % 1 66 64 52 2 22 20 22 3 9 9 11 4 3 7 15 sizel mean cm (se) 3.3(.10) 3.3(.ll) 3.9(.13) median cm 3.0 3.0 3.0 range 1-12 1-15 1-15 frstsymp 74.1 76.5 75.1 2-8 25.9 23.5 24.9 growthl % in situ 5 3 2 infiltrating 76 86 78 both 19 11 20 descripl % ductal 42.8 41.5 49 other 57.2 58.5 51 lymphl % yes 30 32 43 posnodel mean number (se) 1.37(.19) 1.35(.14) 1.62(.19) range 0-28 0-19 0-36 % with none 63 61 62.5 ooph % yes 16.6 18.6 15.4 growths % in situ infiltrating both 13 65 22 descrip2 % ductal other 39.6 60.4 posnode 2 mean number(se) range % with none 0.84(.16) 0-41 79 8 Table II. (cont'd) recur % yes 28.8 32.2 59.2 continuous recurrence % yes 1.6 2 15 rectime mean months (se) 54.2(4.9) 43.9(4.4) 39.1(3.3) median months 38 28 22 range 1-230 1-309 1-309 lstto2nd mean months (se) 55.3(3.3) median months 30.0 range 0-320 time on study mean months (se) 113(4.5) 115.7(4.5) 76.7(3.3) median months 88.5 92 59 range 5-410 2-397 1-397 % dead from disease 33.7 26.2 48.2 failure time mean months (se) 83.6(6.7) 62(5.5) 42.7(2.9) median months 56.5 50 30 range 5-380 3-311 1-311 % alive, no disease at last contact 46.7 58 33.6 9 matched controls. Only one patient, a control, was lost to follow-up. There are welcome similarities in summary values for variables such as race, kids and frstsymp, lending homogeneity across groups: the three groups of women have similar distributions by race (place of birth, in fact); each group had approximately the same mean number of children, and almost the same proportion of each group had a painless lump as the first symptom of the first primary tumour. On the other hand, values for the variables age, clinstgl and recur reveal some interesting differences: for instance, the mean age for cases and matched controls (equal to each other by design) is lower than the mean age of the 5% sample; also of note is the much higher percentage in the 5% sample of patients with disease recurrence. These similarities and differences will be discussed in the following chapters. 1.3 Focus of this S t u d y Most studies of bilateral breast cancer have investigated the incidence of second primary tumours, and risk factors for this are reasonably well established (Hislop et ai, 1984; Robbins & Berg, 1964; Alderson, Hamlin & Staunton, 1971). The main risk factors for incidence of second primary tumours are lobular carcinoma, level of axillary node involvement, and family history of breast cancer. In this study the main goal was the description of survival experience for patients with a second primary tumour, and the comparison of their survival to that of patients with unilateral breast cancer in the matched control group and in the 5% sample. For this study, death from disease (outcome code 1) was the endpoint of interest. Deaths from other causes were treated as censored observations. The question posed was whether or not the hazard function for survival from the second primary tumour could be systematically related to the hazard function for survival from the first primary tumour. For instance, perhaps the bilateral 10 hazard rate is two or three times the unilateral hazard rate; or perhaps there is a residual effect, possibly a function of time, from the first primary tumour which may be added to the hazard rate for the second primary tumour. Comparison is not straightforward because of the fact that women with bilateral disease lived long enough to get a second primary tumour, this length of time being different for every case, and that selection of matched controls was based, in part, on this length of time. On the other hand, the 5% controls allow no way to accommodate this waiting time. Kaplan-Meier curves indicate that matched controls have longer survival times than bilateral cases, as expected. But 5% controls have poorer survival than cases, at least for the first twenty years from diagnosis of first primary. (Refer to Figure 1.) This was surprising at first, but see the discussion in the following chapters. The difficulty lies in adjusting for the time during which a case remained healthy enough to survive the first tumour, yet was unhealthy enough to allow development of a second primary tumour. The survival experience was different for the three groups, and the goal was to characterize these differences while accommodating explanatory variables. 1.4 M e t h o d s The statistical literature presents no clear approach to this problem, although there is some relevant material in, for example, Kalbfleisch & Prentice (1980, Ch.7 & 8), Kay (1984) and Cox & Oakes (1984). Ideas suggested by various authors are briefly discussed below, in Chapter 4. The plan for this study was to first derive models for the hazards of interest, then try to relate them to each other in an empirical way. However, the analyses presented some surprises and problems, and at this stage allow for descriptive, problem-specific discussion rather than general 11 Figure 1 Survival from first tumour date 0.2 H — i 1 1 1 1 1 1 1 1 1 0 40 80 120 160 200 240 280 320 560 400 Time (months) Legend A controls X casss • SX «ompk 12 results. Further work on this problem could be very interesting and useful, for both practical and theoretical results. As a preliminary step, Kaplan-Meier survival curves were constructed for the three basic groups of patients: matched controls, 5% controls, and cases. Figure 1 shows survival from first tumour date, with the number of deaths and the group size in parentheses. Bearing in mind that a control is constrained to live at least as long as her matched case, the plot indicates overall better survival for matched controls when measured from first tumour date. The 5% sample, however, does poorly compared to cases (and therefore matched controls), indicating the strong positive influence of living long enough to develop a second primary (and, as discovered later and discussed below, the negative influence of recurrence); many women with unilateral cancer died before they had a chance to develop a second primary. This interpretation is supported by the following summary statistics: 5% matched sample controls % dead (from disease) 48.2 26.2 failure time (mean mos.) 42.7 62.0 (median mos.) 30.0 50.0 time on study (mean mos.) 76.7 115.7 (median mos.) 59.0 92.0 As noted by Hislop et al (1984) for this same data set, the women in the 5% sample tended to be older and have more advanced disease (clinical stage 4 is the highest) than those in the matched control group (see Table II); this could also contribute to the higher death rate. The implication is that matched controls are different from the 5% group; it is necessary to recognize this difference while trying to establish the relationship of the hazard for unilateral patients to the hazard for bilateral patients. Further evidence that there is a difference to be examined between cases and controls is provided by a Kaplan-Meier plot for survival from second tumour date. See Chapter 3. (For 13 a control, "second tumour date" is that of her matched case.) Such a graphical comparison is not possible for the 5% sample since there is no extractable second tumour date equivalent. Covariate effects were incorporated into the hazard function as described below. We wish to interpret results for S(t; z) , the survival function at time t for a person with covariate vector z, but it is the hazard function, or "instantaneous failure rate", defined as A « , , ) = U m P < r e " - ' + f " r ^ ; , > ' e—0 t which may be more easily modelled. /S^fjz) and A(*;z) are related by S(t;z) = exp[— I A(u;z)duJ . Jo Cox (1972) proposed the proportional hazards model for modelling failure time depending on explanatory variables: A(*;«) = A 0 ( 0 « P ( ^ » ) , where A ( £ ; z ) is the hazard rate at time t for an individual with covariate values z, Ao(<) is an unspecified underlying hazard function, and exp(/3'z) is the proportion-ality factor corresponding to z . Hazards for any two individuals are proportional, and their proportionality factor is independent of time provided the model contains no time-dependent covariates z(t). Estimation of the vector is obtained by the method of partial likelihood proposed by Cox (1972, 1975). The proportional hazards model was fit separately for cases, matched controls and the 5% sample. The results from the fittings are discussed in Chapters 2 and 3. Cases and matched controls were analyzed both from date of first primary to death and date of second primary to death in order to inspect differences based on comparable starting times. The 5% sample was of course analyzed from date of 14 first primary tumour only. Because of the large number of initial variables, stepwise regression for Cox's model was done to identify a smaller set of important covariates. (Testing all possible subsets of the 38 variables was rejected as being too costly.) The selection of variables is discussed in Chapters 2 and 3. The stepwise pro-cedure on first tumour variables selected different subsets of variables for the three groups of women so it was decided to force certain less important variables into the various models to make them comparable. Important second tumour variables were added to the covariate set for bilateral cases. Problems to be accounted for included non-proportionality, interaction and difficulty of interpretation. Complica-tions which arose during modelling are discussed in Sections 2.4 and 3.2. Once hav-ing obtained "reasonable" models, comparisons were possible for "typical" patients, but not for overall hazard functions. This was because second tumour variables were decidedly important, so could not be ignored. 15 C H A P T E R 2 SURVIVAL F R O M T I M E O F FIRST T U M O U R 2.1 M o d e l l i n g M a t c h e d Controls f rom First Tumour Date to Death Using stepwise selection in the proportional hazards regression model, with ini-tial variables age, kids, frstsymp, yrin, sizel, clinstgl, growihl, descripl, lymphl, posnodel and ooph, the variables clinstgl, posnodel and ooph were identified as sig-nificantly associated with survival and thus useful in a predictive model. Disease recurrence is believed to be related to survival, so is possibly relevant for a descrip-tive model. The date of recurrence was examined first since it was available directly from the data set. When the variable yrrecur was added to the set of initial vari-ables, it alone was significant, but difficult to interpret since "no recurrence* was coded as "00". To further investigate, then, the variable recur (yes/no) was created, yrrecur was removed and recur was added to the initial variable set; it was highly significant, as was clinstgl. As a further check on time of recurrence (since yrrecur had been important), the variable rectime was created. Selection from the initial variables plus recur and rectime resulted in a completely different set of variables being identified as important covariates. Investigation of this revealed dependence between recur and each variable selected from the initial set, indicating that they were substitutions for recur in the regression and became less important once recur was included in the regression. Table HI summarizes the stepwise results for the different starting sets of variables. The final model for controls contained the covariate set { frstsymp, sizel, de-scripl, recur, rectime }; the estimated coefficients are given in Table HI, part (iv). This agrees to some extent with current literature, although comparison is awkward 16 Table III. Matched controls from first tumour date, stepwise results (djn is number of deaths/number of patients) (i) Initial variable set (68/268) Variable /? se fijse clinstgl .2829 .0808 3.5009 posnodel .0644 .0318 2.0224 ooph .6910 .2655 2.6026 (ii) Initial variable set plus yrrecur (45/224) Variable /9 se fl/se yrrecur .0598 .0085 7.0471 (iii) Initial variable set plus recur (68/273) Variable $ ee 0/se clinstgl .2125 .0872 2.4371 recur 2.9599 .3361 8.8079 (iv) Initial variable set plus recur and rectime (56/259) Variable se fl/se frstsymp -.1573 .0844 -1.8627 sizel -.2784 .0686 -4.0585 descripl -.7204 .3178 -2.2668 recur 8.0952 1.1126 7.2763 rectime -.0324 .0058 -5.5799 17 since much of the medical literature deals with how survival is affected by treatment factors alone, rather than by both disease variables and treatment choices. Some re-cent studies in the latter category indicate that factors thought to influence survival time of breast cancer patients include age, stage and histologic grade (Hislop et al, 1984); lymph node involvement, stage and tumour size (Skipper, 1979); stage and recurrence (Kay, 1984); size, pathologic description, axillary node involvement, and stage (Fracchia et al, 1984); nodal involvement, size and fixation level (Gore, Pocock & Kerr, 1984). Important explanatory variables, once identified, must still satisfy the assumptions of the proportional hazards model. To check the proportionality assumption, Kalbfleisch & Prentice (1980, p.91) suggest plotting log{-logSi(t;i)} against t, where Si(t;i) is the estimated survival function, corresponding to the mean covariate vector z, for the t-th stratum of the variable in question. A plot for two or more strata should reveal constant difference (in vertical distance) for proportional hazards, since All variables except recur did not show substantial departure from proportional hazards. From Figure 2 it is clear that further measures are required if recur is to be included in the model. An approach suggested in Kalbfleisch &; Prentice (1980, p.87) and in Kay (1977) is to stratify on recur, that is to allow the baseline hazards to differ for the two levels, with one set of regression coefficients ft for both strata: and, if Aoi = &A02 , then A,(*;z) = A0,(*)exp(/3'z), * = 1,2 . 18 Figure 2. Logj-fog S(t;z)J vs time, for controls, stratified on recurrence 2T Legend A recurrence X no recurrence Time (months) 19 The baseline hazards X0i(t) may be arbitrary and unrelated; they could be esti-mated by, for example, the Kaplan-Meier estimators for the two separate groups of recurrence and recurrence-free patients. Estimates of coefficients obtained via strat-ification on recur are reported later in this chapter (Table IV) because of subsequent considerations for the "final" covariate set. 2.2 M o d e l l i n g Cases f r o m Firs t Tumour Date to Death For cases, modelling from first tumour date to death revealed similar depen-dence on recur. For the first stepwise regression, second tumour variables were not considered as eligible covariates. Those selected from first tumour variables were clinstgl, growthl, ooph, recur and rectime: see Table IV. Although recur and rec-time are important for both cases and controls, the significant first tumour variables are different, indicating that information from first tumour variables is not adequate for modelling survival of potential bilateral patients. Inclusion of second tumour variables for cases led to yet another covariate set: selected from all first and sec-ond tumour variables for cases were sizel, ooph, growths, surg2, recur, rectime and IsttoSnd; the only variables common to the selection from first tumour variables are ooph, recur and rectime (see Table V) , confirming the inadequacy of first tumour variables alone for prediction. This also suggests that getting a second tumour is not like getting another first tumour. Tables III(*v) and V identify the variables associated with survival of controls and of cases. Since interest lies in comparison of hazards for cases and controls, it seemed desirable to have models which incorporate information common to both. For this reason, the variable ooph was added to the model for controls, even though it was not significant. Two first tumour variables were added to the model for 20 Table IV. Cases from first tumour date, stepwise results for first tumour variables (84/269) Variable 0 se 0/se clinstgl .3737 .1039 3.5963 growthl .7625 .3155 2.4165 ooph .5389 .2476 2.1764 recur 3.6449 .3992 9.1310 rectime -.0262 .0050 -5.2317 Table V. Cases from first tumour date, stepwise results for first and second tumour variables (78/244) Variable se P/se sizel .1383 .0676 2.0456 ooph .5330 .2664 2.0008 growths .7321 .2431 3.0115 surgS -.6901 .2825 -2.4427 recur 3.1838 .4654 6.8405 rectime -.0232 .0070 -3.3232 IsttoSnd -.0140 .0034 -4.1120 21 cases: frstsymp and descripl. Model assumptions are investigated before results are presented. Proportionality checks for cases again suggest stratification on recurrence; see Figure 3. Log{—logSoi(t; a)} plots for sizel and descripl are shown for comparison in Figures 4 and 5. See also Kay (1977) or Kalbfleisch & Prentice (1980, p.92-95). We now have recur contributing via the baseline hazard for its two strata, and the other covariates forming the regression vector. Coefficient estimates for controls and cases are shown in Table VI . Note that the presence or absence of recurrence is incorporated into the overall hazard for cases in two ways. Separate baseline haz-ards are fitted for the recurrence and recurrence-free groups and a proportionality constant is added for the time to recurrence. Residuals for a proportional hazards model are constructed as e, = Ao(*f5 •«•) = Ao(*«) e i P(0 ' B «) i where A.0(t) = —logS0(t) = f* X0(u)du and ti is the time of death of the i-th individual. A survival curve based on these residuals (that is, the residuals become the "survival times") should yield an approximately straight line with slope —1 when plotted on a log scale against the residuals (Kalbfleisch & Prentice, 1980, p.96). Residual plots for each model were constructed and were satisfactory. Examples are shown in Figures 6 and 7. 2.3 M o d e l l i n g the 5% Sample The 5% sample was expected to be rather like the controls except for the in-fluence of the waiting time required for a control to match its case. This however was not the case, and when survival for the 5% sample was modelled, covariates important for survival were quite different from those for controls. 22 Figure 3. LogJ-log S(t;z)} vs time, tor cases, stratified on recurrence 4n -7-t Legend X neraeurrane* ~i— 40 80 120 — I 1 1 1 1 1 1 WO 200 240 280 320 360 400 Time (months) 23 Figure 4. Logj-log S(t;z)} vs time, tor cases, stratified on size of first tumour s-4-3-2-1-1r? o-•*> S -1-1 3 - 2 - if - 3 -i - 4 -- 3 -- 6 -Legend A < 1 cm X 1—5 cm • > 5 c m —7" 0 40 80 120 KO 200 240 280 320 360 400 Time (months) 24 Figure 5. Logj-log S(t;z])j vs time, tor cases, stratified on description of first tumour S-j 4-» _ 2-1-If? o-</> Q - 2 - / / - 3 -- 4 --8^ - 8 - I Legend A ductal - 7 - 1 1 1 1 1 1 1 1 1 1 X other 0 40 80 1 2 0 1 6 0 2 0 0 2 4 0 280 3 2 0 3 6 0 4 0 0 Time (months) t 25 Table VI. Survival from first tumour date, stratified on recurrence Controls (75/313) Variable frstsymp sizel descripl ooph rectime Cases (106/304) Variable frstsymp sizel descripl ooph growths surgS rectime IsttoSnd P -.1320 -.1809 -.7267 .5295 -.0244 se .0632 .0555 .2748 .2672 .0044 p/se -2.0872 -3.2601 -2.6445 1.9814 -5.5320 h -.1195 -.0300 .0277 1.1510 .1986 -.7013 -.0186 -.0134 se .0566 .0541 .2167 .3575 .2043 .2596 .0047 .0028 P/se -2.1111 -.5553 .1280 3.2197 .9721 -2.7009 -3.9884 -4.8374 26 Fipjure & Resldud plot for oases wffh recurrence -a--n- 1 1 i 1 I r — — i 1 i i I U t U f M ! U 4 4 A * SMducl* Flours 7. Residue! plot for controls -* -it-Si "*4--«• -4V 27 For the 5% sample, stepwise selection identified age, clinstgl, lymphl, xril, recur and rectime as important explanatory variables; see Table VII for coefficient estimates. As noted in section 1 of this chapter, the medical literature attaches importance to the variables age, stage, histologic grade, node involvement, tumour size and recurrence. The 5% sample's xrtl is of questionable importance; this variable was not so lacking in diversity to be excluded from the regression, as it was for the other patient groups (85% "yes" in the 5% sample, 90% "yes" in the others), however its effects may be confounded with surgery or recurrence. The effect of recurrence is noticeable in the Kaplan-Meier curves (Figure 8): there is only one death in the recurrence-free group compared to 207 deaths for those with recurrence, and this is possibly the cause of the difference in variable selection for matched controls and the 5% sample of controls. (Compare Tables HI and VII.) A possible explanation is that matched controls, by being required to live a certain length of time, were precluded from having recurrence at as high a rate as the population represented by the 5% sample, and so variables associated with recurrence were more important for the 5% sample, but were not significant for controls. Analysis of the 5% sample using recurrence date as the endpoint revealed im-portant explanatory variables sizel, clinstgl, posnodel, and surgl. The coefficient for clinstgl changes sign, to 0.1437 (ae = 0.0579), which reverses its effect on the hazard. With recurrence as the endpoint, a higher clinical stage is associated with a negative influence on "survival". Lymphl was marginally significant, and xrtl is associated with the now significant surgl, so there may be some support for the 28 Table VII. 5% Sample, stepwise results (208/433) Variable age -.0164 clinstgl -.2677 lymphl -.4584 ZTtl -1.0777 recur 7.2592 rectime -.0277 se Pfse .0088 -1.8588 .1112 -2.4075 .2640 -1.7366 .3593 -2.9996 1.1185 6.4900 .0040 -7.0050 29 Figure 8. Survival of 5% sample, stratified on recurrence 0.8-i \ \ \ \ \ I I \ J 0.8 c o X. © a. \ \ \ \ \ V V ^ - - ^ Legend X r t c u r r a i c * — i 1 1 1 1 1 1 1 40 80 1 2 0 1 6 0 2 0 0 2 4 0 280 320 Time (months) SO above explanation. The only variable from this set which was important for controls is sizel. 2.4 Discussion of Recurrence The summary statistics and Kaplan-Meier curves support the strong influence of recurrence on the different survival experience of the three groups: 59% of the 5% sample had a recurrence of disease, compared to only 32% and 29% for con-trols and cases, and a much higher proportion of the 5% sample had "continuous recurrence" (meaning the first disease never really went away) - 15% versus ap-proximately 2%. The time between the first primary and the recurrence (excluding "continuous recurrence" patients) was shorter for the 5% sample than for controls or cases (respectively 39, 44, 54 months on average, with medians 22, 28, 38 months), as were both time on study and time to failure (i.e. death from disease), the latter times being 43, 62 and 84 mean months, and 30, 50 and 57 median months. The proportion of patients alive with no disease at the time of last follow-up was con-siderably smaller for the 5% sample: 34% versus 58% and 47%. (See Table II.) These differences suggest that for this data set comparison of the 5% sample with controls or cases would not be meaningful without separating the groups according to recurrence status. It may be helpful to examine recurrence and recurrence-free survival for a ran-dom sample of unilateral versus a group of bilaterals, but it was not possible to do so with this data set because of the lack of failures among the recurrence-free patients. (See Figure 8.) Whatever the explanation for the differences, these re-sults combined with the importance of second tumour variables discourage the use of information from the 5% sample for modelling bilateral cases. 31 Recurrence and time to recurrence present a number of difficulties for analysis of the three patient groups, cases, matched controls and the 5% sample. Recurrences are relatively common (Pater, Mores & Loeb, 1981; Gilliland, Barton & Copeland, 1982; Fracchia et al, 1984; this study), and it seems generally believed that patients with recurrent cancer have a poor chance of survival. Although there are few explicit studies of this in the literature, it seems implicit in many reports such as Gilliland et al (1982), Tough (1966) and Ytredal et al (1977). Concurrence is provided by the data used in this study: Kaplan-Meier curves for survival from date of recurrence for cases and for matched controls (Figures 9 and 10) show that approximately 65% of cases and 75% of matched controls die within 5 years of recurrence date, and almost 90% die within 10 years of this date. (The Kaplan- Meier curve for the 5% sample of controls was virtually indistinguishable from that for the matched controls, and is not included here.) In addition, regression analysis indicates that recurrence is significantly associated with survival. (Refer to Tables HI, IV, IV, VI, VII.) Stratification on recur clarifies the situation to some degree, but necessitates separate discussion of disease-free versus recurrence-plagued survival. Also, for those patients with recurrence, the time to recurrence is confounded with survival time so the significance of rectime is not clear. Patients with recurrence seem to die soon after recurrence date although cases show somewhat better survival from this point than do controls. (See Figures 9 and 10.) Developing a second primary appears to be "better" than having recurrence. In the 5% random sample, among 177 unilateral patients with no recurrence only one died from disease, but there were 207 deaths (81%) among the 256 patients with recurrence; in the group of bilateral cases, 63 of the 93 patients with recurrence died (68%) compared to 42 of the 210 patients without recurrence (20%). 32 Figure 9. Survival of oases from date of Figure 10. Survival of controls from date of recurrence * I i i i i i > • m m m m mo m 33 Although it is reasonably common in the cancer literature to stratify on recur-rence when using the proportional hazards model, this data set suggests that it is probably of more relevance to model time to recurrence and time from recurrence to death separately in a multistate analysis. Note that the 5% sample does not permit analysis of recurrence-free survival. This is somewhat surprising in light of similar studies referred to in Skipper (1979) showing a higher proportion of deaths among recurrence-free patients. 34 C H A P T E R 3 SURVIVAL F R O M T I M E O F S E C O N D T U M O U R 3.1 Introduction The analysis of survival from first tumour date was intended to be preliminary to a study of the hazard rates for bilaterals, from the time of second tumour, and to a characterization of the difference in hazards between the unilateral and bilaterals. It was felt that the 5% sample could not be used for this, so analysis centres on cases versus matched controls. A model for survival of bilaterals from second tumour date, when compared to the model for controls from first tumour date, may reveal obvious parallels. For instance, perhaps the important second tumour variables for bilaterals correspond to the important first tumour variables for unilaterals. If so, this may suggest that having a second tumour is like having a first tumour all over again, in terms of survival experience. Unfortunately, such a comparison is not possible for this data set because the variables available for analysis from the date of the second tumour are not all counterparts of those available for analysis from the date of the first tumour. (For example sizel is available but sizeS had too many missing values to be useful.) The approach used was to look at cases and controls from the time of second tumour to death, as a way of making use of the matching. For a control, "second tumour date" is that of her matched case. The Kaplan- Meier curves (Figure 11) show the advantage in survival of controls over cases, adjusted for the time between the first and second tumours. (The time between tumours is subtracted from survival time.) The questions of interest are, if one lives long enough to get a 35 Figure 1t Survival of cases and controls from date of second tumour 0.2 H Legend A oontrota X eo*t — I 1 1 1 1 1 1 1 40 80 120 160 200 240 280 320 Time (months) 36 second tumour, how much worse is this than living at least as long but not getting a second primary, and what are the important explanatory variables? 3.2 M o d e l l i n g Cases a n d Controls f rom Second Tumonr Date to Death It was thought that different waiting times might necessitate different answers to this question; initial examination showed that for cases the variable IsttoSnd was highly significant for survival from first tumour date. However, this time is con-founded with survival time, and once the starting time is redefined as second tumour date, the time between tumours is no longer significant (/3 = .0013, se = .0024) in the model containing the variables from Tables ni(iv) and V . Proportional haz-ards regression for cases from second tumour date identifies the following impor-tant explanatory variables: ooph, frstsymp, surg2, recur and rectime; once again stratification on recurrence is appropriate to adjust for non-proportionality. Table VIII displays coefficient estimates in the stratified version for comparison with the model using survival time from first tumour (Table VI.) Also shown are estimates for the corresponding model for controls. Note that lstto2nd remains significant for controls. Kay (1984) in his discussion of "transition-specific hazards" suggests that in this situation, adequate description is provided by the analysis involving the adjustment for time between tumours and that death given that a second tumour occurs depends on time from second tumour rather than on time from first tumour. Much of the medical literature on bilateral breast cancer deals with patients grouped on the interval between tumours (Hislop et al, 1984; Fracchia et al, 1984) and this led to checking results for various intervals, even though the above analysis suggests that the interval between tumours is not important for cases. Kaplan-Meier curves for three different intervals (Figure 12) hint at better survival for an 37 Table VIII. Stepwise results, from second tumour date to death, stratified on recurrence Cases (105/303: 63/93 w/recur, 42/210 w/no recur) Variable se fi/se frstsymp -.1460 .0545 -2.6784 sizel .0071 .0521 .1369 descripl -.0558 .2088 -.2670 ooph .6061 .2389 2.5372 growth2 .3623 .2040 1.7763 surg2 -.7052 .2690 -2.6217 rectime -.0101 .0036 -2.7838 lstto2nd .0006 .0024 .2512 Controls (73/309: 72/106 w/recur, 1/203 w/no recur) Variable se P/ee frstsymp -.0886 .0658 -1.3471 sizel -.1918 .0604 -3.1748 descripl -.4280 .2682 -1.5959 ooph .5263 .2684 1.9606 rectime -.0156 .0038 -4.1065 lstto2nd .0073 .0030 2.4591 38 Figure 12. Survival of cases from 2nd tumour date, stratified on time between 1st and 2nd tumours 0.2 H Legend A C l y r X 1-5 yr» • > 5 y r « 40 -1 1 1 1 1 1 1 80 120 180 200 240 280 320 Time (months) 39 interval of more than five years to second tumour date, and analysis of patients grouped on the three intervals indicates some influence when l8tto2nd is less than or equal to 1 year [P/se = 2.014) or greater than 5 years (P/se = 2.1126), but not for between 1 and 5 years (P/se = 1.3034). See Table DC. The nominal p-values associated with these estimates should be interpreted with caution in light of the large number of estimates being computed. Note that for the coefficients of some variables (e.g. surgS ) sign as well as significance changes across groups. A change in sign from one group to another could result in the same value of the variable having the opposite effect on survival within the different groups. (A positive value of pi increases the hazard, and a negative value of Pi decreases the hazard.) There is also a noticeable difference in values for these coefficients and those for the ungrouped cases (refer to Table VIII). For example, the variable surg2, when taking the value 1 for "yes", has a positive influence on survival based on the entire set of cases; for the separate groups however, surg2 has a negative influence in the B< 1 yr" group (although P is not significant here), and a greater positive influence for both the "1-5 yrs" and "> A 5 yrs" groups. (Although the /?'s are greater in this case, they are less significant than for all cases taken together.) The reason for the reversals is not clear. The cases have been stratified on recurrence to accommodate the non-proportionality, but this just allows a different (unrelated) baseline hazard A0y(<) for the j'-th stratum; the estimates of /? are the same for all strata in the model Ay(f;s) = X0j(t)exp(Pz). Table VTJI shows the A A /?'s for all cases, stratified on recurrence. Table IX shows the P*s for subsets of A cases, stratified on recurrence, thus giving a different /9, for each subset in the model A,-y(i;s) = Ao,y(£)ezp(/9,B) , where » indicates the subset based on lstto2nd 40 Table IX. Stepwise results for cases from second tumour date, stratified on recurrence and grouped on lstto2nd Variable < 1 yr 1-5 yrs >5 yrs $ . (se) h (»e) $ ( « ) frstsymp -.0770 (.0699) -.1310 (.1308) -.2318 (.1890) sizel .1460 (.0867) .1210 (.1610) -.0218 (.1201) descripl -.2490 (.4041) .1811 (.4389) -.4404 (.4526) ooph .7967 (.4495) 1.1442 (.4824) 1.2607 (.6764) growths 1.0433 (.4022) 1.0514 (.4696) -.6444 (.4039) surgS .3916 (.4432) -.9806 (.5432) -.9363 (.5831) rectime -.1425 (.0343) -.0678 (.0203) -.0207 (.0085) IsttoSnd .0876 (.0435) .0232 (.0178) .0093 (.0044) 41 grouping, and j indicates the stratum based on recur status. Time to recurrence (rectime) is significant for the three separate groups and for the combined group, suggesting that recurrence, the stratification variable, may be influencing the effects of the other variables within a group. It is not clear that stratification on recurrence is satisfactory. It seems to have such a strong influence on survival that it is questionable whether the other co-variates even matter in the presence of recurrence. This apparent strong influence of recur led to separate examination of recurrence and recurrence-free patients in the unilateral and bilateral groups; the results, however, were difficult to interpret, partly because of the lack of deaths (only 12 out of 219) in the no-recurrence group of controls, so are not included here. A data set containing a higher number of deaths among recurrence-free controls might provide more useful information for comparing unilateral and bilateral survival based on recurrence experience. Such a data set may not be obtainable, since both the 5% sample and the matched control group indicate that recurrence-free unilateral generally do not die from disease. 3.3 Survivor Function Estimates As a description of the relative survival experience for cases and controls, sur-vivor function estimates are displayed in Figures 13,14,15 and 16 for some "typical" patients. Figures 13 and 14 display survival experience for some controls with different co-variate values. For controls stratified on recurrence (Figure 13), there is a dramatic difference in survival of recurrence and recurrence-free patients: curve A repre-sents all recurrence-free controls; it is horizontal since only one death occurs in this group. Curve B, representing a typical control with a long time between first and second primaries (55 months) has much better survival than either the "average" 42 Figure 13. Survival of controls based on covariates, for stratified model Legend B typted control wHh late recurrence D typical control wHh tarty recurrence 80 120 WO 200 Time (months) i = (fretsymp, sizel, deeerlpl, ooph, rectime, 1stto2nd) 1 death) ,,.,1,0.44,88} IS, 3.2, 0.4, 0.1,15.5. 54.6) L i . 1.1, 28, 30) 43 Figure 14. Survival of controls based on mean covariate values, for unstratified model 0.8 h OA H o^H I — 40 I 80 I — 120 Time (months) — i — wo — i 200 44 Figure 15. Survival of cases based on different rovariates, for stratified model Legend rncurr«nc« fr«« ccntj, rrxon covortahi vctuw typical fcurrrto-fr— co—  c o m wWh r»curr«nc«, moon covorlati yqlu— _ typfcd coo with rocurwnco, lot* 2nd tumour 1— 160 -1— 200 120 Time (months) — i — 240 260 —I 320 i (frattymp, dial, oaiorlpl, ooph, growth2, sura2, raetlm*. 1*tto2nc0 230, 59.6) ,65.6) 45 46 control (curve C) with the mean covariate vector, or the typical control represented by curve D with a short time to recurrence (28 months) and a short time between first and second primaries (30 months). The survival of patients represented by curves B, C and D may be related by the exponents 0.514, 1 and 1.442 respectively. (These are the conversion factors for converting the survival probability for the mean covariate vector to that for a particular covariate vector.) In comparing Figure 14 (unstratified controls) to Figure 13, it is clear that recurrence has a heavy influence on survival: without stratification on this variable, survival appears to be much better (Figure 14) than should be expected (Figure 13) even for the same mean covariate values. Survival for cases with particular covariate values is displayed in Figures 15 and 16. Those cases without recurrence have much better survival than those with recurrence in the stratified version of the model (Figure 15). There is little difference between the mean A and a typical case B. The three different cases with recurrence (curves C, D and E) have practically the same survival even though their times to recurrence and times between first and second primaries are quite different. As with controls, recurrence-free cases have better survival than those with recurrence. It seems that cases without recurrence have approximately the same survival experience whether they have long or short times between first and second primaries; similarly for cases with recurrence; thus the difference in survival may be attributed to the influence of the underlying hazard for the two recurrence strata. Survival of a case with the mean covariate values in the unstratified model is shown in Figure 16 for comparison. Again, the unstratified version seems an inadequate representation of survival experience. 47 CHAPTER 4 DISCUSSION OF ALTERNATE METHODS The process of analyzing this data set and devising suitable models involved investigation of methods proposed by various authors, to decide if other ideas might be applicable to this study. Discussion of some of these ideas, and why they were thought to be inappropriate, follows. 4.1 Transition-Specific Hazards Kay (1984) discusses breast cancer with and without recurrence using "transition-specific hazards" and an extended proportional hazards model, and he models haz-ards by choosing transition-specific cases. Figure 17 shows the possible transitions for this study and Table X summarizes the groups that would be used for estimating each of the hazards. Note that all covariates relating to the second tumour would need to be time-dependent. Note as well that estimation of incidence of second primary should really use the entire population, not just the matched controls. This approach was considered beyond the scope of this study. Fitting the pro-portional hazards model with many time dependent covariates is very costly, and the coefficient estimates are difficult to interpret. As well, a number of dummy covariates would have to be added to the model to distinguish controls and cases on second tumour variables. For example, surgS would no longer be adequate as a 0/1 variable: a value of 0 could mean either no surgery was performed because there was no second primary, or no surgery was performed even though there was a second primary. 48 Figure 17. Transitions of interest 0 occurrence of first primary 1 recurrence of first primary 2 occurrence of second primary 3 recurrence of second primary 4 death Possible hazards of interest: Aoi A14 (A04) (A02) (^ia) ^31* ^34 ^23* [ ( ) not of interest in this study; * probably cannot be assessed with this data, i .e . A24 includes A234 and A214 ] 49 Table X . Relevant groups for translation-specific hazards Hazard Aoi AH *02 A24 Aj4 At Risk all (ignore 2nd primary covariates) all with recurrence (ignore 2nd primary covariates) all (ignore 2nd primary covariates) all with recurrence (ignore 2nd primary covariates) cases cases cases with recurrence Censored -any controls who died before recurrence -any cases who got 2nd primary before recurrence of first -any controls still alive without recurrence -any controls who died of other causes without recurrence -any cases who got 2nd primary before death -controls with recurrence still alive -controls with recurrence who died of other causes -controls -cases with recurrence before 2nd primary -controls -cases dead before recurrence -cases still alive without recurrence -cases with recurrence before death -cases still alive -cases dead from other causes -cases still alive -cases dead from other causes Failures -controls or cases who had recurrence before 2nd primary date -controls who died -cases without recurrence at time of second primary -cases -cases with recurrence of 2nd primary -cases who died before recurrence of 2nd primary -cases who died after recurrence of second primary Covariates associated with the second primary take the value 0 until occurrence of second primary, then take the actual value after that. Covariates associated with the first primary are available at time 0. Recurrence is no longer a covariate. 50 4.2 Mult ipl icat ive Effect of Second Tumour Crowley's (1978) discussion of changing group membership suggests estimating the hazards for unilateral patients and assuming a multiplicative effect of the second tumour, so that the overall hazard would be Ai(t)ezp(/?'z) + 1*(t) , where Q would be obtained from the model A(<;z) = Ai(i)ezp(/8'z) for a unilateral patient with covariate vector z , and 7 would be estimated as the coefficient of time-dependent z(t), where (4\ _ J °> i f ' <lstto2nd ; ZW ~ \ 1, if t > lstto2nd . A Important second tumour variables could be included by setting the B's for second tumour variables equal to zero for controls. (This is also discussed in Kalbfleisch & Prentice, 1980, p. 134.) This however would require that the coefficients for first tumour variables be equal for controls and cases, which is not a reasonable condition for this data set, as shown in the preceding chapters. It seems that if covariates are to be included in a model, they should reflect reasonable assumptions. If recurrence rather than a second primary tumour were the event of interest, this approach would make sense since, except for recurrence status, the values of the explanatory variables would not change for a particular individual; it seems plausible that the effect of recurrence is multiplicative, as in Crowley's model. 4.3 M e t h o d s Used on Stanford Heart Transplant D a t a The Stanford heart transplant data is treated in two ways by Kalbfleisch & Prentice (1980, Ch.5), the first of which is similar to the above description for a multiplicative effect. A time-dependent covariate representing change in transplant status is included to determine the effect of a treatment (transplant) on survival. This could correspond to the effect of our second tumour on survival. 51 The second analysis involves comparing the two hazard functions A(0 = A o(t)e^ l B , and X(t\w) = Xo(t\w)e^9Z , t > w = waiting time . This model is non-parametric with hazard affected by transplantation but no further role played by the waiting time. Since the time between first and second tumours was an important covariate, it did not seem appropriate to ignore it; to include the waiting time w requires separate estimation oi X(t\w) at each value of w. As well, the Stanford heart patients differ from our breast cancer patients in important ways. The heart transplant patients are comparable in the sense that they each require a new heart and must simply wait for a donor. The non-transplanted heart patients are assumed to eventually get a transplant, but we do not assume that our unilateral patients will eventually become bilaterals. Bilateral breast cancer patients in this study differ from the unilateral patients in more ways than "status": summary statistics differ for the two groups (refer to Table II) and, as shown in Chapter 2, second tumour variables are more important than first tumour variables for survival of bilaterals. We hesitate to use a model based just on the change in status for another reason: the Stanford heart transplant starting group represents those patients eligible for heart transplant; our matched controls, whom we use to equate waiting times, are not really representative of the population of unilaterals. Table II shows that the 5% sample is older {age), with more advanced disease (clinstgl, lympkl), a higher recurrence rate (recur), and a higher percentage of failures (% dead from disease) occurring within a shorter time (failure time). Tables HI and VII display the different covariates found to be important for survival of the matched controls and the 5% sample. 52 4.4 Bivariate Analysis A bivariate survival distribution would involve modelling the vector (W, T), where failures are second tumour date and death, with T > W since a patient would continue past the second tumour date to death. The difficulties are as noted above: cases are different from controls in important covariates. It was not clear how to make a comparison of cases to controls even if a plausible bivariate model could be determined. 4.5 Canse-Specific Hazards Failure in this data set could result from either first or second primary disease, and a model based on competing causes of death could be informative. Analysis of competing risks and cause-specific failures leads to an overall hazard function which is the sum of the cause-specific hazard functions, as in Prentice et al (1978) and Kalbfleisch & Prentice (1980, p.172). For controls known to die from the first tumour, let A l ( ( ; i ) = I i m £ i l e l M ± ^ I M l i , and for cases dying from either the first or second tumour, let A*(f;z) = A?(t ;«) + A;(*;z) , where Ai(f;z) = Aoi(O e i P(r^i z ) a n c « Kit>z) = ^oi(O e zP(/^!B) a r e the cause-specific hazards. We could estimate AJ and A^ for cases if the causes of death were known, and use them for comparison with A i , the hazard for controls. Unfortunately this type of analysis is not possible for this data set because it is not known except in a few special cases whether an uncensored patient died from the first or second tumour. Unless the histologies of the tumours were clearly 53 distinguishable, it is difficult to determine the exact cause of death for patients who have had cancer in both breasts. Analysis for groups whose cause of death is known to be one or the other might lead to meaningful comparison of hazards, as described. 4.6 Paired Failure T i m e s Analysis of failure times of our matched pairs according to Holt & Prentice (1974) or Kalbfleisch & Prentice (1980, Ch.8) involves A,(<;z) = Xoi(t)exp(d'z), which requires a stratum i for each pair of patients and a commmon 3. Including a stratum for each of our 366 pairs would seem rather unwieldy, and a common 8 does not seem appropriate for this problem because of the difference in importance of covariates between controls and cases. 54 C H A P T E R 5 CONCLUSIONS The 5% random sample of women with unilateral breast cancer is quite different from the group of matched controls and from the cases. Women in the 5% sample are older, have more advanced disease, a higher rate of recurrence and a shorter time to failure than either of the other two groups. The matched controls and cases were more alike with respect to the non-matching variables. The important covariates for predicting survival from first tumour are, for the 5% sample: age, clinical stage, lymphadenopathy status, x-ray therapy, recurrence and time to recurrence; for the matched controls stratified on recurrence: oophorec-tomy, first tumour symptom, size of first tumour, pathologic description of first tumour, and time to recurrence; for the cases stratified on recurrence: oophorec-tomy, first tumour symptom, surgery on second tumour, time to recurrence and time between first and second tumours. The important covariates for predicting survival from second tumour date are, for the matched controls: oophorectomy, size of first tumour, time to recurrence, and time between first and second tumours; for the cases: oophorectomy, first tumour symptom, surgery on second tumour, and time to recurrence. Recurrence is relatively common and has great influence on survival. It may be worthwhile to include recurrence status and time to recurrence as criteria for matching cases and controls. Once recurrence time is controlled for in this way, procedures for comparing covariates important to survival of cases and controls could follow those used in this study. Another suggestion is to look at bilateral patients who had post-second tumour recurrence and compare them to unilateral patients with recurrence. This would 55 provide a set of women who lived long enough without recurrence to get a second primary tumour, but later got recurrence and thus became more like the group of unilateral with recurrence. In the data set used for this study, there are 80 such patients with 50 deaths. Recurrence is defined to be recurrence prior to second primary, however the recurrence date recorded for some patients was later than the date of second primary disease. It is not clear whether recurrence refers to the first or the second primary disease; those cases with recurrence of the first primary disease would be more comparable to the controls experiencing recurrence. It might also be of interest to compare cases to recurrence-free controls to see if getting a second primary tumour was better than suffering recurrence of the first. Almost no information is available on recurrence-free survival. This suggests that time to recurrence, and time from recurrence to death, could be modelled separately. Introducing second primary tumour occurrence into these models would present several other transitions of interest. A full multistate model would be interesting, but complex. 56 References Alderson, M.R. , Hamlin, I., and Staunton, M . D . (1971). The relative significance of prognostic factors in breast carcionoma. Br. J. Cancer, 26, 646-655. Cancer Control Agency of British Columbia, Annual Report for 1984-85. Cox, D.R. (1972). Regression models and life tables (with discussion). J. R. Stat. Soc. B, 34, 187-220. Cox, D.R. (1975). Partial likelihood. Biometrika, 62, 269-276. Cox, D.R. and Oakes, D. (1984). Analysis of Survival Data. Chapman and Hall, London. Crowley, J . (1978). Some extensions of the log rank test. In Clinical trials in 'early' breast cancer, Lecture Notes in Medical Informatics, (eds. H.R. Scheurlen, G . Weckesser, I. Armbruster), Springer-Verlag, New York. Fracchia, A . A . , Robinson, D. , Legaspi, A. , Greenall, M.J . , Kinne, D . W . , and Groshen, S. (1985). Survival in bilateral breast cancer. Cancer, 55, 1414-1421. Gilliland, M . D . , Barton, R . M . and Copeland, E . M . (1983]. The implications of local recurrence of breast cancer as the first site of therapeutic failure. Ann. Surg., 197(3), 284-287. Gore, S .M. , Pocock, S.J. and Kerr, G.R. (1984). Regression models and non-propor-tional hazards in the analysis of breast cancer survival. J. R. Stat. Soc. C, 33, 176-195. Hislop, T . G . , Elwood, J . M . , Coldman, A.J . , Spinelli, J.J., Worth, A . J . and Ellison, L . G . (1984). Second primary cancers of the breast: incidence and risk factors. Br. J. Cancer, 49, 79-85. Holt, J .D. and Prentice, R.L. (1974). Survival analyses in twin studies and matched pair experiments, Biometrika, 61, 17-30. Kalbfleisch, J .D. and Prentice, R.L. (1980). The Statistical Analysis of Failure Time Data. Wiley, New York. Kay, R. (1977). Proportional hazard regression models and the analysis of censored survival data. J. R. Stat. Soc. C, 26, 227-237. Kay, R. (1984). Multistate survival analysis: an application in breast cancer. Meth-ods of Information in Medicine, 23(3), 157-162. Leis, H.P. (1980). Managing the remaining breast. Cancer, 46, 1026-1030. Pater, J .L . and Loeb, M . (1983). Improvement in survival after recurrence of carci-noma of the breast. Clin. Invest. Med., 6(4), 281-285. Pater, J.L., Mores, D. and Loeb, M . (1981). Survival after recurrence of breast cancer. Can. Med. Assoc. J., 124, 1591-1595. Prentice, R.L. ; Kalbfleisch, J .D. ; Peterson, A.V.,Jr . ; Flournoy, N. ; Farewell, V . T . and Breslow, N.E . (1978). The analysis of failure times in the presence of competing risks. Biometrics, 34, 541-554. Robbins, G . F . and Berg, S.W. (1964). Bilateral primary breast cancers. Cancer, 17, 1501-1527. 57 Skipper, H . (1979). Repopulation rates of breast cancer cells after mastectomy (judged from breakpoints in remission-duration curves), Booklet XII, Southern Re-search Institute. Tough, I.C.K. (1966). The significance of recurrence in breast cancer. Brit. J. Surg., 53(10), 897-900. Ytredal, D .O. , Zeigler, M . G . , Hagen, R .O. and Bradfield, J.S. (1977). Recurrence patterns and survival after combined radical mastectomy and postoperative irradi-ation: a retrospective analysis. Southern Medical Journal, 70(6), 698-701. 58 APPENDIX: PATIENT INFORMATION FORMS USED BY THE CCABC Forms EP3A Feb/81 (70536) EP3D Feb/81 (60536) EP3E Feb/81 (60536) For further information, contact the Cancer Control Agency of B . C . , 600 West 10th, Vancouver, B . C . , V5Z ^E6. Leaves 59-65 not filmed; quality of copy too poor. 58a A P P E N D I X : CJO NO. P A T I E N T I N F O R M A T I O N F O R M S U S E D B Y T H E C C A B C ( A s s i g n e d v a r i a b l e n a m e s a r e s h o w n o n t h e r i g h t . ) IKIT1AI-5 (Surr.aae tizsz) c.c.K.i.c. NO STATUS: 1 -ACE AT DIACSOSIS: bilateral , 2 - bilateral • .1 I I 2-7 ID1ID2 • 8 S T A T U S L I 1 9-1C A G E •tidal Origin: Ksrital Status: 1 - carried 2 - sever married 3 - widowed It - divorced/separated I 1 I I ' - i R A C E • " i s Hurler o f Liveborn Children: 8 -8+ 9 • unknown Kii=b»r of• Stillbirths and Abortions: 8 -3+ 9 - unknown Age at First 3irth: 99 - unknown • .24-• » 27 K I D S >inarcbe Age: 99 — unknown Type of Menopause: 0 • s t i l l tteostniacin^ 1 - natural 2 - art if icial 9 - "iknowa _ _ _ . _ q ifcmopause Age: 00 - s d . l l menstruating 99 - unknown First Recorded Weight: (kg) • Eiight (cn): C D • Faaily Hlstorv: Breast Cancer: "^Mother: Age at onset, 99 - rge unknown %, Ja. Crandoocher: 1 - caternal, 2 - paternal, 3 - both, ».3« oh is 9 - ycu, bot not specified • -•4 <"< •+ -*-*<} oS \S ^ i S C e r « : Age at c.set (youngest), 99 - age unknown • © - 5 ^ OW VW Ovary or endo m n cr aonctrlal cancer Large bowel cancer 0:hcr enneer C I O thcr, 2 - ulster, 3 - both 29-30 31 m 32-33 n r n 34-36 T 37-39 40-41 " 43-44 45 46 47 J! / £?3A Feb/Sl (70536) 59 /~\ j J | J O I I VJ I A \ V - U I I I VJ / 1 1 1 • 1 1 ! • 1 1 1 • 1 I 1 • Cose Tear • • • • m 4 8 - J 54-5 60-6 66-7 Type Code: 1 - Clinical Diajnosis only (if followed by, biopsy, record only biopsy) 2 - Pibrocvscis, cystic hyperplasia ^•s'aAitr'ku^ccoVa**^ 3 - Fibrocystic, some ductal atypla 4 - Fibrocystic, narked ductal atypia 5 - Careinc7J in situ 6 - Fibroadenoma 7 - Other biopsied benign tumour, speclty: InVoi^ cA fa^ .\\g^vC .V.yor*4_/  8 - Other-bicp*ied lesions, specify: 9 - Fibrocystic, O . O . S . ep<Wy.r*>MS -.drrevl rrv*\A^)-!5CVrtX~r*<A*'C*<-11 - Fibrocystic or fibroadenoma 1 > breast Code:! - Ipsilateral 2 — Contralateral 3 - Soto. Xime Code: 1 - Before 1st" prissry 2 - Simultaneous with 1st primary 3 ~ Between .1st .prinary_and.second primary, or equivalent dett 4 ." Simultaneous or after second primary or equivalent.date 9 Time unknown DIAGNOSIS Or: Dlcbetes Mellitus Rheumatoid Arthritis Osteoarthritis ' Arthritis N.O.S. Hypertension Callbl* Jder Disease Hypot! .jidlsa Hyperthyroidism iXV^ro^o,:,M^, , * > H C <^>>VCC -,&«ue& Aiv Thyroid Disease N.O.S. 72 73 74 75 76 77 78 79 80 riss. code: 0 - no 1 - yes, before 1st primary 2 - yes, simultaneous with 1st pri=ary 3 - yes, between 1st end 2nd primary or equivalent dace 4 - yes, after or simultaneous with 2nd primary or equivalent date 9 • yes, time unknown CATJ) HO: C C A . B . C . HO. CD DtACSOSIS OF: CANCER I: CKiCtK II: Disease Code *Time Code Ovarian " - 1 Endometrium - 2 Large bowel - 3 Salivary glr.nd -Polycytfcc-ia (Specify) . • • • • Year m c n 8-11 12-15 Sas* as nea-r. 60 Appendix (cont'd) V$Z 0~ Sr.'JCS Cexiluilng use la :r*i:s<r.:s) : U«c of Korr.;r.es : Kccorcctf by parier.:: 1 - »ei, 2 • no, S - oo recori By £ . P . ' * letter: 1 • yes, 2 » no. no record • » o » 4>.0ral Contraceptives £ Estrogens (Preeiarin) Diethylscilboestrol 4, Other Horcones Beserpiae Thyroid snpplenents Ti=e Code Length of Use before 1st diagnosis, 8 - 8+, 9 ~ unknown Trs. Length of Use between 1st & 2nd diagnosis,' 8 - 8+, 9 - unknown 18-21-24-: 27-: 30-: 33-: Tine Code: 1 — before first diagnosis only 2 — between first & second diagnosis or equivalent di-e. 3 - both Bilateral oophorectomy prior to 1st tunour: 0 " D O 2 • yes, no replacenent 1 « yes, vich replacepenr 3 - yes, unknown Tear of oophorectomy: MAMMOCRAMS: • 36 37-2 Result ?irst Pri&ary: Nearest to. Diagnosis. Contralateral: - Fron diagnosis backyard In tine. i I I I I ' • • 7IRST TPMOOR: First Synpton: 1 - painless lump 2 - painful luap 3 ~.pain, no lu=p 4 " enlarged nodes 5 - nipple discharge 6 - n i p p l e i n v e r s i o n tt*nc*«or^ ajcii.<>A<or\ 7 - asy=pto=aticC«A <^i^^^^%'JrVn\Q°r 8 - other \c -^a^.r^i 9 " u n k n o w n \ • Bate of First Symptom: OOOO - P\.&>-vv*pTc»-i<«\.c~. n Method.of Finding Tuoour: 1 - noticed by patient, casually 2 - noticed by patient during BSE 3 " noticed by husband or other 4 - noticed by own physician, etc. on physical exas. 5 - noticed by CCABC physician (2nd tumour only)>cNner Cx. ^p>c^ ,s>\e^K.c*-«-\ 6 - nassography 8 - other 9 - unknown w_ v -Date o f Diastasis (Biopsy): caCO - rxc Vi-.-v--^ I t 39-4 44-4 49r5 54^ 5 59-6 6A 65-6 69 C<:« f irst C.C.A.S.C. 61 A p p e n d i x ( c o n t ' d ) ctsc i.e. c . c . A . s . c . » ; c . Location of tu=s Position of tucour: I I ! 1 - l e f t b r e a s t righ: breast 1 - 0.0.Q. 5 - vhole breast 2 - L.O.Q. ' 6 - nipple area 3 - L.I.Q. 7 - lover H 4 - U.I.Q. 8 - upper 4 9 - unknown • 3 i ixe : Kax. dlaaeter, ca. Multiple Tumours - 1 Clinical Stage: 9-— Pathological Stage: 9- - ..ik:io«.-a 99 » no record 17 •• J - r -i ' JL. 1 ' 3 a 10-1 2 • • » • M PATHOLOGY: Differentiation: Growth: 1 2 3 f9 veil moderately or fairly veil poorly B O record • 1 5 Type Description: - ductal - other • 1 2 3 f 1 • 2 3 4 5 • 6 • insitu (intraductal) infiltrating A. <J.. ductal ductular lobular • 16 • » medullary tubular papillary colloid or mucoid comedo carcinoma adenocystic "1* SoirrV\o<j*> 1 - scirrhous carcinoma, adenocarcinoma, scirrhous adenocarcinoma C^ve H.O \ i^cat ^ e s * ) 2 - carcint ., carcinoma simplex 3 ~ maligru .^t cystosarcooa phyllodes ' 4 - carcino sarcoma 5 - Paeat'j ticcaos. • Axillary Node Status: Clinical lyzphadenopachy: ." 1 - yes, 2 - no. ( \Ati-ooe?b Pp*-tf»toc£. V W L £ d u t ^ s " ) . Excision lycph nodes: State no. 99 - no. not stated n • IS IS 20 Ho. of nodes positive: Estrogen Receptor Status: State no. 99 - no. not stated^ 0 - not done 1 -. high 2 --low 3 - indeterminate level 9 - specimen unsatisfactory. m 21-2: H I 23-2. S I Z E I C L I N S T G I G R O W T H I D E S C R I P l L Y M P H I P O S N O D E I • Date of " lrst Treatment: 25 62 A p p e n d i x ( c o n t ' d ) S-rgery: XRTs Scmnnil Therapy: Adjuvant Chemotherapy: Oophorectomy: 0 - DO. 0 - no surgery 1 " simple mastectomy 2 - modified radical mastectomy 3 • radical castectory 4 m lumpectomy ,e>-_*i.c-«* 0 - none 1 - XRT • 2 - Caesium 3 " XRT and Caesium 1 " estrogens 2 • androgens 3 - other \t*-r.r+ •. S * tobtnX 4 tS 1 - melphalas 2 - C.M.F. 3 - other 5"- Mer*w<u=ji. ( .XAeA- -l«*> 1 - surgical, 2 - radiation. C o . RECURRENCE: (pfUCR^ Xo a * 0 e>oucw!rc's) Date of f irst recurrence: 00 - no recurrence code 99 « unknown • • • • a • 30 3 1 X R T l 2Xi_ 32 33 34 35 36-2 OOPH MORECUR YRRECUR CARD NO. CiC-A.B.C NO. n 2-7 6o SECOND TUMOUR "irst Symptom (see codes for 1st tumour) Date cf First Symptom : . Method of Finding Tumour (see codes for 1st tumour) Date o f Biopsy: Position of Tumour (see codes for 1st tumour): Size, max. diameter, cm. .99 - no record. Multiple tumours - 1 Clinical Stage: 9 - unknown Pathological Stage: 9 - unknown • BO* 0 2' SCNDSYMP M 0 2 S Y M P Y R 2 S Y M P 30-3 34 M i l l 35-2 M 0 B I 0 P YRBIOP • m • • 39 ' 40-4 42 43 44 r : : . u . / E?3E rsfc/3i (60536") 63 Appendix (cont'd) J l i G R 0 W T H 2 Description: - ductal - other • B Kention of: 2a situ carcinoma 1 - yes Likelihood of 2nd primary 1 - yes X'-r*c*»i**\ i e iMw » « a > ( 4 • OCTiwfUf(jot ^«u«oefcvHi<*C|(,c«»*"(,>fT6*_^ Intraductal carcinoma Axillary node status: yes Clinical lymphadenopathy: 1 - yes, 2 » no, 3 - previously involved 1 » —• --< -,—' Excision lyaph socles: State no. 99 - no. not stated Kc. of nodes positive: State no. 99 - no. not stated Fstrogen receptor status (see codes for 1st tumour) Local spread across" chest vail from 1st site: 1 ~ yes Other metastases present: 1 - yes, 2 « suspected • m • • • 48 49 50 51 52 53 54-56-58 59 60 D E S C R I P 2 I N S I T U I N T R D U C T P 0 S N 0 D E 2 Surgery: (see codes for 1st tumour) (see codes for 1st tumour) Eormonal therapy: (see codes for 1st tumour) Adjuvant chemotherapy: (see codes for 1st tumour) Outcome: 1 ~ dead, from disease 2 - dead, ocher causes, disease present 3 ™ dead, unknown i f disease present 4 - dead, other malignancy 5 - dead, other causes, no disease present 6 ~ al ive , no disease 7 - a l ive , with disease 8 - lose, to follow-up. Date of Death cr last Follow-uo: Dr. El l ison: 1 - 2nd primary 3 — undecided 2- - metastatic 9 » no opinion * Pathology (chart): Clinician's Opinion: ?a:r:Icr,y ( r e v i e w ) : 1 3 2nd primary undecided 1 - 2nd prir.ary 3 - undecided 1 - 2.-.d priory 3 - uniec'.ii-2 - metastatic 9 - no opinion 2 - cetascaclc 9 * no opinion I - • : : a f : i ; : c • • • • • -XT.: S U R G 2 X R T 2 61 62 63 64 65 O U T C O M E I j ) ] I £ r c M O L A S T 1 ( { 1 ' " - 6 S Y R L A S T • • • j i 70 71 72 64 A p p e n d i x ( c o n t ' d ) :A7J NO. . C . A . B . C . NO. 2-7 PRIMARY RADIOTHERAPY TREATXDJT Type of treatnent: Method of treatment: 1 » no treatment 2 - kilovoltage 3 - cobalt 4 - radium implant 5 - other: specify on separate l i s t 9 • unknown 1 - no treatment 2 - not tangents 3 - tangents. 9 " unknown fc » hnwVV. M e w txtevwi^*.f ere* f^f i l o o u c Dose to I-M.F. Rads (enter no.) / a»*c^js»url 0000 - no treatment v ' ' / 9999 • treated, dose unknown 8688 - unknown if treated Dose to tangenxs: (-foHofO o«»e.^ As above RECURRENCE I ^P^oe^. t o 2J*° PSJ^AWO-^ . Date of f irst local recurrence.: Date of f i rs t ' loca l axillary nodes:^+/_ Date of f i rs t metastases: • I | B O . I m o . • V T T . io- r 14-17 18-21 22-25 26-29 mo. y r . 65 A p p e n d i x ( c o n t ' d ) Total IMF Dose (Given) 3 0 - 3 3 Supra Clavicular Total (Given) 34-37 Axilla Total (Given) {Posterior} 38-41 Tangential Dose (Tumour) 42-45 Medial Tangential Dose (Given) 46-49 Lateral Tangential Dose (Given) 50-53 Direct Tumour Dose (Given) 54-57 66 

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