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Biometrika Advance Access originally published online on June 24, 2009
Biometrika 2009 96(3):601-615; doi:10.1093/biomet/asp026
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© 2009 Biometrika Trust

Article

Pseudo-partial likelihood for proportional hazards models with biased-sampling data

Wei Yann Tsai

Department of Biostatistics, Columbia University, New York, New York 10032, U.S.A. wt5{at}columbia.edu

Received for publication 1 July 2006. Revision received 1 November 2008.
  Abstract

We obtain a pseudo-partial likelihood for proportional hazards models with biased-sampling data by embedding the biased-sampling data into left-truncated data. The log pseudo-partial likelihood of the biased-sampling data is the expectation of the log partial likelihood of the left-truncated data conditioned on the observed data. In addition, asymptotic properties of the estimator that maximize the pseudo-partial likelihood are derived. Applications to length-biased data, biased samples with right censoring and proportional hazards models with missing covariates are discussed.

Key Words: EM Algorithm • Left-truncation • Length-biased data • Missing covariate • Right censoring


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