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

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.