A comparison of propensity score-based causal estimators for analyzing partially missing confounder

The propensity scores (PSs) have been developed by modelling the treatment allocation mechanism on observed covariates to recover the balance in observational studies.However, in addition to confounding, missing data often arise in observational studies, and the consequence will be severe if the confounder, a covariate that affects both treatment and outcome, is missing.This study developed an expected-maximization (EM) algorithm to estimate the PS hence the PS-based estimators with confounder missingness under missing at random assumption, and compares the estimator's performance with complete case analysis and multiple imputation approaches.The EM method is most efficient for the stratification and regression estimator, and the multiple imputation approach is efficient for matching and inverse probability weighting estimator.In the simulation, we compared the seconds per iteration to assess the computational burden for different methods of dealing with confounder missingness.The computational time for multiple imputation approaches is significantly higher than the EM and complete case analysis for a given missing percentage and the number of imputations.Therefore, the applied researchers may consider the EM algorithm to deal with missing data problems that provide instant but consistent results.Finally, an application to the breast cancer study and B-aware trial dataset are presented.