Efficient estimation for the multivariate Cox model with missing covariates

Missing covariates are a ubiquitous issue in the data analysis. One of the widely-used approaches for efficient parameter estimation is using augmentation based on the semiparametric efficiency theory. However, existing methods for right-censored data with Cox model did not correctly implement augmentation, which may result in inefficient parameter estimation. In this paper, we derive a correct augmentation term for the stratified proportional hazards model with missing covariates. We study the statistical properties of the estimators for known and unknown missing mechanisms. Thus, a popular study design such as the casecohort study design can be handled as a special case. Simulation studies show that our new estimators for an unknown missing mechanism and the case-cohort study design obtain estimation efficiency gains compared with inverse probability weighted estimators. We apply our method to the Atherosclerosis Risk in Communities study under the case-cohort study design.