Flexible regression approach to propensity score analysis and its relationship with matching and weighting

In propensity score analysis, the frequently used regression adjustment involves regressing the outcome on the estimated propensity score and treatment indicator. This approach can be highly efficient when model assumptions are valid, but can lead to biased results when the assumptions are violated. We extend the simple regression adjustment to a varying coefficient regression model that allows for nonlinear association between outcome and propensity score. We discuss its connection with some propensity score matching and weighting methods, and show that the proposed analytical framework can shed light on the intrinsic connection among some mainstream propensity score approaches (stratification, regression, kernel matching, and inverse probability weighting) and handle commonly used causal estimands. We derive analytic point and variance estimators that properly take into account the sampling variability in the estimated propensity score. Extensive simulations show that the proposed approach possesses desired finite sample properties and demonstrates competitive performance in comparison with other methods estimating the same causal estimand. The proposed methodology is illustrated with a study on right heart catheterization.