Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Survey

Document related concepts

Cardiac contractility modulation wikipedia, lookup

Saturated fat and cardiovascular disease wikipedia, lookup

Arrhythmogenic right ventricular dysplasia wikipedia, lookup

Myocardial infarction wikipedia, lookup

Coronary artery disease wikipedia, lookup

Transcript

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 1 SCT 2010 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 2 SCT 2010 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 3 SCT 2010 Outline • • • • • Case-cohort definition and analysis Competing risks PsL for case-cohort with competing risks Prediction for a case-cohort study Simulations and results 4 SCT 2010 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. 5 SCT 2010 Analysis of case-cohort, pseudolikelihood j The cases which are n not part of the exp x j PsL subcohort participate I exp x j 1 rj r rR j in the PsL only at the 1 if event was observed at t j time of the event. j 0 if event was not observed at t j 1 observation r is in subcohort or I rj r is a case not in the subcohort and tr t j 0 r is a case not in the subcohort and tr t j Prentice RL. A Case-Cohort Design for Epidemiologic Cohort Studies and Disease Prevention Trials. Biometrika 73: 1-11, 1986. 6 SCT 2010 Presence of competing risks • Among the 1108 in the subcohort 198 patients died before having a cardiac event. These are competing risks. 1 if the event of ineterest was observed at time t j 1 C j 1 C j 2 if the competing risk event was observed at time t j j 0 C j 0 or C j 2 0 no event was observed at time t j n exp x j PL j 1 wrj exp xr rR~ j dj wrj Gˆ t j Gˆ min(t j , tr ) R j r ; tr t j or Cr 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. 7 SCT 2010 Fine and Gray - modelling the hazard of the subdistribution j r exp x j PL( ) w exp x j 1 ji i iR j w42 J=1 w32 R4 w65 w62 J=3 J=2 w32>w42>w62 R6 J=4 J=5 J=6 time R3 R1 8 SCT 2010 The analysis of case-cohort in the presence of competing risks exp x j PsL j 1 I rj wrj exp xr rR~ j dj n 1 if the event of ineterest was observed at time t j C j 2 if the competing risk event was observed at time t j 0 no event was observed at time t j 1 I rj 0 1 C j 1 j 0 C j 0 or C j 2 observation r is in subcohort or Gˆ t j r is a case not in the subcohort and tr t j w rj ˆ min(t , t ) G j r r is a case not in the subcohort and tr t j R j r ; tr t j or Cr 2 Jackknife variance 9 SCT 2010 Prediction Fˆ t | x 1 e Hˆ t|x Hˆ t | x hˆ ti | x ti t , where ˆ x ˆ ˆ h t | x h0 t e dj h0 t j Using the ˆx subcohort only w exp rj r ~ rR j 10 SCT 2010 Simulations • To verify that – The estimated coefficient is correct – The predicted probabilities are correct – The type I error is correct 11 SCT 2010 Description of the simulations The parameters • The covariate 0 x 1 • The distribution of time Tev , x 0 ~ Expev 0 0.03 Tev , x 1 ~ Expev1 0.07 Tcr , x 0 /1 ~ Expcr 0.05 Tobs min Tev , Tcr • The censor time Tc ~ U 2,10 12 SCT 2010 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 13 SCT 2010 Coefficient obtained using the case-cohort dataset Coefficients 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.2 0.4 0.6 0.8 1.0 Coefficient obtained using the source cohort SCT 2010 1.2 1.4 14 Predicted probabilities Probability of event of interest 0.4 0.3 0.2 0.1 0.0 at 1 years at 3 years x=0 SCT 2010 at 5 years at 2 years at 4 years x=1 15 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 16 SCT 2010 Thank you 17 SCT 2010 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 casecohort 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. 18 SCT 2010 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 casecohort 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: 14861493, 2008. 19 SCT 2010 Women, 45 years old, no risk factors Probability for cardiac hospitalization 0.20 D+RT RT D 0.15 0.10 0.05 0.00 0 5 10 Time to cardiac hospitalization SCT 2010 15 20 Men, 45 years old, no risk factors Probability for cardiac hospitalization 0.20 D+RT RT D 0.15 0.10 0.05 0.00 0 5 10 Time to cardiac hospitalization SCT 2010 15 21