Efficient estimation for the multivariate Cox model with missing covariates

Youngjoo Cho, Soyoung Kim and Kwang Woo Ahn

Statistica Neerlandica, 2025, vol. 79, issue 1

Abstract: Missing covariates are a ubiquitous issue in 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 the 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 case‐cohort 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.

Date: 2025
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