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Biostatistics Advance Access published online on December 20, 2005
Biostatistics, doi:10.1093/biostatistics/kxj014
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© The Author 2005. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org The online version of this article has been published under an open access model. Users are entitled to use, reproduce, disseminate, or display the open access version of this article for non-commercial purposes provided that: the original authorship is properly and fully attributed; the Journal and Oxford University Press are attributed as the original place of publication with the correct citation details given; if an article is subsequently reproduced or disseminated not in its entirety but only in part or as a derivative work this must be clearly indicated. For commercial re-use, please contact journals.permissions@oxfordjournals.org.
Received July 27, 2005
Revised December 9, 2005
Accepted December 16, 2005

Article

Multivariate Survival Analysis for Case-Control Family Data

Li Hsu 1 * and Malka Gorfine 2

1 Program in Biostatistics and Biomathematics, Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue N., M2-B500, Seattle, WA 98109, USA
2 Department of Mathematics Bar Ilan University, Ramat-Gan 52900, Israel Faculty of Industrial Engineering and Management Technion - Israel Institute of Technology, Technion City, Haifa 32000, Israel

* To whom correspondence should be addressed.
Li Hsu, E-mail: lih{at}fhcrc.org


  Abstract

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 pseudo-likelihood 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 (Shih and Chatterjee, 2002). Simulation studies and an analysis of case-control family data of breast cancer illustrate the methodology's practical utility.

Keywords: case-control family study; frailty model; Cox proportional hazards model; innovation theorem; familial aggregation.
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