Misuse of Regression Adjustment for Additional Confounders Following Insufficient Propensity Score Balancing

After propensity score (PS) matching, inverse probability weighting, and stratification or regression adjustment for PS, one may compare different exposure groups with or without further covariate adjustment. In the former case, although a typical application uses the same set of covariates in the PS and the stratification post-PS balancing, several studies adjust for additional confounders in the stratification while ignoring the covariates that have been balanced by the PS. We show the bias arising from such partial adjustments for distinct sets of confounders by PS and regression or stratification. Namely, the stratification or regression after PS balancing causes imbalance in the confounders that have been balanced by the PS if PS-balanced confounders are ignored. We empirically illustrate the bias in the Rotterdam Tumor Bank, in which strong confounders distort the association between chemotherapy and recurrence-free survival. If additional covariates are adjusted for after PS balancing, the covariate sets conditioned in PS should be again adjusted for, or PS should be reestimated by including the additional covariates to avoid bias owing to covariate imbalance.