Addressing substantial covariate imbalance with propensity score stratification and balancing weights: connections...

Propensity score (PS) weighting methods are commonly used to adjust for confounding in observational treatment comparisons. However, in the setting of substantial covariate imbalance, PS values may approach 0 and 1, yielding extreme weights and inflated variance of the estimated treatment effect. Adaptations of the standard inverse probability of treatment weights (IPTW) can reduce the influence of extremes, including trimming methods that exclude people with PS values near 0 or 1. Alternatively, overlap weighting (OW) optimizes criteria related to bias and variance, and performs well compared to other PS weighting and matching methods. However, it has not been compared to propensity score stratification (PSS). PSS has some of the same potential advantages; being insensitive extreme values. We sought to compare these methods in the setting of substantial covariate imbalance to generate practical recommendations.

Analytical derivations were used to establish connections between methods, and simulation studies were conducted to assess bias and variance of alternative methods.

We find that OW is generally superior, particularly as covariate imbalance increases. In addition, a common method for implementing PSS based on Mantel-Haenszel weights (PSS-MH) is equivalent to a coarsened version of OW and can perform nearly as well. Finally, trimming methods increase bias across methods (IPTW, PSS and PSS-MH) unless the PS model is re-fit to the trimmed sample and weights or strata are re-derived. After trimming with re-fitting, all methods perform similarly to OW.

These results may guide the selection, implementation and reporting of PS methods for observational studies with substantial covariate imbalance.