Missingness in covariates is a common problem in survival data. In this article, we propose an importance sampling method for estimating the regression parameters in the proportional hazards model with missing covariates. We also consider the augmented importance sampling method by subtracting the projection term onto the nuisance tangent space. The proposed methods provide consistent and asymptotically normally distributed estimators when the missing-data mechanism depends on outcome variables as well as the observed covariates. Simulation results indicate that the proposed importance sampling estimators are more efficient than the inverse probability weighting estimators for the regression coefficients of the missing covariates, and equally as efficient as or more efficient than the inverse probability weighting estimators for the regression coefficients of the completely observed covariates.
Xu, Qiang ; Paik, Myunghee Cho; Luo, Xiaodong; and Tsai, Wei Yann, "Importance Sampling Estimators for Cox Regression With Missing Covariates" (April 2007). Columbia University Biostatistics Technical Report Series. Working Paper 11.