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Biometrika Advance Access originally published online on June 22, 2009
Biometrika 2009 96(3):617-633; doi:10.1093/biomet/asp027
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© 2009 Biometrika Trust

Article

Pseudo-partial likelihood estimators for the Cox regression model with missing covariates

Xiaodong Luo

Department of Psychiatry, Mount Sinai School of Medicine, New York, New York 10029, U.S.A. Xiaodong.Luo{at}mssm.edu

Wei Yann Tsai

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

Qiang Xu

Food and Drug Administration, Silver Spring, Maryland 20993, U.S.A. Qiang.Xu{at}fda.hhs.gov

Received for publication 1 May 2007. Revision received 1 November 2008.
  Abstract

By embedding the missing covariate data into a left-truncated and right-censored survival model, we propose a new class of weighted estimating functions for the Cox regression model with missing covariates. The resulting estimators, called the pseudo-partial likelihood estimators, are shown to be consistent and asymptotically normal. A simulation study demonstrates that, compared with the popular inverse-probability weighted estimators, the new estimators perform better when the observation probability is small and improve efficiency of estimating the missing covariate effects. Application to a practical example is reported.

Key Words: Augmented estimator • Biased sampling data • Embedding missing data • Left-truncation • Martingale structure • Right censoring • U-statistic


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