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Biometrika Advance Access originally published online on August 5, 2007
Biometrika 2007 94(3):719-733; doi:10.1093/biomet/asm058
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Copyright © 2007 Biometrika Trust

Articles

Survival analysis with temporal covariate effects

Limin Peng and Yijian Huang

Department of Biostatistics, Emory University, Atlanta, Georgia 30322, U.S.A.

lpeng{at}sph.emory.edu

yhuang5{at}sph.emory.edu

Received for publication 1 March 2006. Revision received 1 February 2007.
  Abstract

We propose a natural generalization of the Cox regression model, in which the regression coefficients have direct interpretations as temporal covariate effects on the survival function. Under the conditionally independent censoring mechanism, we develop a smoothing-free estimation procedure with a set of martingale-based equations. Our estimator is shown to be uniformly consistent and to converge weakly to a Gaussian process. A simple resampling method is proposed for approximating the limiting distribution of the estimated coefficients. Second-stage inferences with time-varying coefficients are developed accordingly. Simulations and a real example illustrate the practical utility of the proposed method. Finally, we extend this proposal of temporal covariate effects to the general class of linear transformation models and also establish a connection with the additive hazards model.

Key Words: Censoring • Cox regression • Gaussian process • Linear transformation model • Martingale • Time-varying coefficient


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