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Biostatistics Advance Access originally published online on December 20, 2005
Biostatistics 2006 7(3):387-398; doi:10.1093/biostatistics/kxj014
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Multivariate survival analysis for case–control family data

Li Hsu*

Program in Biostatistics and Biomathematics, Public Health Sciences Division, Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue North, M2-B500, PO Box 19024, Seattle, WA 98109-1024, USA lih{at}fhcrc.org

Malka Gorfine

Department of Mathematics, Bar Ilan University, Ramat-Gan 52900, Israel and Faculty of Industrial Engineering and Management, Technion—Israel Institute of Technology, Technion City, Haifa 32000, Israel

* To whom correspondence should be addressed.

Multivariate survival data arise from case–control family studies in which the ages at disease onset for family members may be correlated. In this paper, we consider a multivariate survival model with the marginal hazard function following the proportional hazards model. We use a frailty-based approach in the spirit of Glidden and Self (1999) to account for the correlation of ages at onset among family members. Specifically, we first estimate the baseline hazard function nonparametrically by the innovation theorem, and then obtain maximum pseudolikelihood estimators for the regression and correlation parameters plugging in the baseline hazard function estimator. We establish a connection with a previously proposed generalized estimating equation-based approach. Simulation studies and an analysis of case–control family data of breast cancer illustrate the methodology's practical utility.

Keywords: Case–control family study; Cox proportional hazards model; Familial aggregation; Frailty model; Innovation theorem


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