Cox regression analysis with missing covariates via multiple imputation

TL;DR

This paper introduces a robust nonparametric multiple imputation method for Cox regression with missing covariates, leveraging predictive models and nearest neighbor imputation, and compares it with the AIPW method through simulations and a real dataset.

Contribution

It proposes a novel nonparametric imputation approach for Cox regression with missing data that is robust to model mis-specification, improving bias reduction.

Findings

The nonparametric method is robust to model mis-specification.

Both methods reduce bias from non-ignorable missingness.

The nonparametric approach performs well in simulations and real data.

Abstract

We consider the situation of estimating Cox regression in which some covariates are subject to missing, and there exists additional information (including observed event time, censoring indicator and fully observed covariates) which may be predictive of the missing covariates. We propose to use two working regression models: one for predicting the missing covariates and the other for predicting the missing probabilities. For each missing covariate observation, these two working models are used to define a nearest neighbor imputing set. This set is then used to nonparametrically impute covariate values for the missing observation. Upon the completion of imputation, Cox regression is performed on the multiply imputed datasets to estimate the regression coefficients. In a simulation study, we compare the nonparametric multiple imputation approach with the augmented inverse probability weighted (AIPW) method, which directly incorporates the two working models into estimation of Cox regression. We show that all approaches can reduce bias due to non-ignorable missing mechanism. The proposed nonparametric imputation method is robust to mis-specification of either one of the two working models and robust to mis-specification of the link function of the two working models. In contrast, the AIPW method is not robust to mis-specification of the link function of the two working models and is sensitive to the selection probability. We apply the approaches to a breast cancer dataset from Surveillance, Epidemiology and End Results (SEER) Program .