Limitations of the propensity scores approach: A simulation study

Propensity scores (PS) have been studied for many years, mostly in the aspect of confounder matching in the control and treatment groups. This work is devoted to the problem of estimation of the causal impact of the treatment versus control data in observational studies, and it is based on the simulation of thousands of scenarios and the measurement of the causal outcome. The generated treatment effect was added in simulation to the outcome, then it was retrieved using the PS and regression estimations, and the results were compared with the original known in the simulation treatment values. It is shown that only rarely the propensity score can successfully solve the causality problem, and the regressions often outperform the PS estimations. The results support the old philosophical critique of the counterfactual theory of causation from a statistical point of view.