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Biometrika Advance Access published online on April 27, 2009
Biometrika, doi:10.1093/biomet/asp008
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© 2009 Biometrika Trust

Article

Gamma frailty transformation models for multivariate survival times

Donglin Zeng

Department of Biostatistics, University of North Carolina, 3105-D McGavran-Greenberg Hall, Campus Box 7420, Chapel Hill, North Carolina, 27516, U.S.A. dzeng{at}bios.unc.edu

Qingxia Chen

Department of Biostatistics, Vanderbilt University, 1161 21st Avenue South, S-2323 Medical Center North, Nashville, Tennessee, 37232, U.S.A. cindy.chen{at}vanderbilt.edu

Joseph G. Ibrahim

Department of Biostatistics, University of North Carolina, 3109 McGavran-Greenberg Hall, Campus Box 7420, Chapel Hill, North Carolina, 27516, U.S.A. ibrahim{at}bios.unc.edu

Received for publication 1 March 2008. Revision received 1 October 2008.
  Abstract

We propose a class of transformation models for multivariate failure times. The class of transformation models generalize the usual gamma frailty model and yields a marginally linear transformation model for each failure time. Nonparametric maximum likelihood estimation is used for inference. The maximum likelihood estimators for the regression coefficients are shown to be consistent and asymptotically normal, and their asymptotic variances attain the semiparametric efficiency bound. Simulation studies show that the proposed estimation procedure provides asymptotically efficient estimates and yields good inferential properties for small sample sizes. The method is illustrated using data from a cardiovascular study.

Key Words: Gamma frailty model • Linear transformation model • Proportional hazards model • Semiparametric efficiency


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