1. SCT 2010 1 The analysis of case cohort design in the presence of competing risks Melania Pintilie, Yan Bai, Lingsong Yun and David C. Hodgson Ontario Cancer Institute, University of Toronto, ICES, Princess Margaret Hospital

2. SCT 2010 2 Hodgkin’s disease Hodgkin’s disease is a type of cancer which affects the young adults (median age=37). 5 year survival 84% in USA Treatment: Radiation and/or chemotherapy Treatment may be cardiotoxic. Aim: Study the incidence of cardiac events

3. SCT 2010 3 HD cohort In Ontario over 16 year period (1988-2003) ~3000 HD ~300 cardiac events ~ 600 die without a cardiac event Time to event analysis the number of events determines the power of the study To study the cardiac events a large amount of information is needed to be collected –Treatment –Cardiac history –Risk factors The presence of competing risks

4. SCT 2010 4 Outline Case-cohort definition and analysis Competing risks PsL for case-cohort with competing risks Prediction for a case-cohort study Simulations and results

5. SCT 2010 5 Case-cohort Select randomly a subcohort from the source cohort. This set contains some cases –1/3 of the 3000. Subcohort=1108, 105 cardiac events Add to this all the rest of the cases –204 cardiac events Take advantage of all 309 cardiac events, but collect detail information only on 1108+204=1312 instead of ~3000.

6. SCT 2010 6 Analysis of case-cohort, pseudolikelihood Prentice RL. A Case-Cohort Design for Epidemiologic Cohort Studies and Disease Prevention Trials. Biometrika 73: 1-11, 1986. The cases which are not part of the subcohort participate in the PsL only at the time of the event.

7. SCT 2010 7 Presence of competing risks Among the 1108 in the subcohort 198 patients died before having a cardiac event. These are competing risks. Fine JP and Gray RJ. A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association 94: 496-509, 1999.

8. SCT 2010 8 Fine and Gray - modelling the hazard of the subdistribution time J=1J=3 J=2 J=6J=4 J=5 R1R1 R3R3 R4R4 R6R6 w 32 w 42 w 62 w 65 w 32 >w 42 >w62

9. SCT 2010 9 The analysis of case-cohort in the presence of competing risks Jackknife variance

10. SCT 2010 10 Prediction, where Using the subcohort only

11. SCT 2010 11 Simulations To verify that –The estimated coefficient is correct –The predicted probabilities are correct –The type I error is correct

12. SCT 2010 12 Description of the simulations The parameters The covariate The distribution of time The censor time

13. SCT 2010 13 Description of simulations Source cohort N=1200 Subcohort = 1/3 of the source cohort, n=400 Case-cohort: 400+the rest of cases Obtain: –Coefficients –Predicted probabilities at 1,2,3,4,5 years Repeated 2000 times

14. SCT 2010 14 Coefficients

15. SCT 2010 15 Predicted probabilities

16. SCT 2010 16 To verify the type I error Source cohort N=120 Subcohort = 1/3 of the source cohort, n=40 Case-cohort: 40+the rest of cases Repeated 2000 times Type I error = 0.0375, close to 0.05

17. SCT 2010 17 Thank you

18. SCT 2010 18 References 1.Prentice RL. A Case-Cohort Design for Epidemiologic Cohort Studies and Disease Prevention Trials. Biometrika 73: 1-11, 1986. 2.Fine JP and Gray RJ. A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association 94: 496-509, 1999. 3.Barlow WE, Ichikawa L, Rosner D, and Izumi S. Analysis of case- cohort designs. Journal of Clinical Epidemiology 52: 1165-1172, 1999. 4.Borgan O, Goldstein L, and Langholz B. Methods for the analysis of sampled cohort data in the Cox proportional hazards model. Annals of Statistics 23: 1749-1778, 1995. 5.Barlow WE. Robust Variance-Estimation for the Case-Cohort Design. Biometrics 50: 1064-1072, 1994. 6.Self SG and Prentice RL. Asymptotic-Distribution Theory and Efficiency Results for Case Cohort Studies. Annals of Statistics 16: 64-81, 1988.

19. SCT 2010 19 7. Therneau TM and Li HZ. Computing the Cox model for case cohort designs. Lifetime Data Analysis 5: 99-112, 1999. 8.Sorensen P and Andersen PK. Competing risks analysis of the case- cohort design. Biometrika 87: 49-59, 2000. 9.Crowder MJ. Classical competing risks. London: Chapman and Hall/CRC Press, 2001. 10.Tibshirani RJ and Efron B. An Introduction to the Bootstrap. New York: Chapman & Hall, 1993. 11.Lag R, Melbert D, Krapcho M, Stinchcomb DG, Howlader N, Horner MJ, Mariotto A, Miller BA, Feuer EJ, Altekruse SF, Lewis DR, Clegg L, Eisner MP, Reichman M, and Edwards BK. SEER Cancer Statistics Review, 1975-2005. Bethesda, MD: National Cancer Institute. 12.Myrehaug S, Pintilie M, Tsang R, Mackenzie R, Crump M, Chen ZL, Sun A, and Hodgson DC. Cardiac morbidity following modern treatment for Hodgkin lymphoma: Supra-additive cardiotoxicity of doxorubicin and radiation therapy. Leukemia & Lymphoma 49: 1486- 1493, 2008.

20. SCT 2010 20

21. SCT 2010 21