Pseudo-Partial Likelihood Estimators of Cox Regression Model for Biased Sampling Data with Application to Missing Covariates

Abstract

We obtain a pseudo-partial likelihood for proportional hazards models with biased-sampling data by embedding 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. We also study an application to proportional hazards models with missing covariates. 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 also reported.