Weighted estimated pseudo-partial likelihood method for correlated failure time data with auxiliary covariates

Abstract

This paper considers statistical inferences for correlated failure time data with auxiliary covariates under a marginal model with distinct baseline hazard.We assume that the primary covariate of interest is precisely measured only in a subset of the full study cohort,whereas an auxiliary covariate for the primary covariate is available for all subjects in the study cohort.We first make use of the auxiliary information to empiricallyestimate the relative risk function,and then propose a weighted estimated pseudo-partial likelihood (WEPPL) approachfor the estimation of marginal hazard ratio parameters.The asymptotic properties for the WEPPL estimatorare established when the auxiliary covariate is categorical.The resulting estimator is shown to be consistent and asymptotically normal.Simulation studies are conducted to evaluate the finite sample performance of the proposed estimator.It is shown that the proposed weighted estimator outperforms the unweighted one in efficiency, especially when the dependencies among the failure time are strong.