Comparison of balancing scores using the ANCOVA approach for estimating average treatment effect: a simulation study

In this article, we conducted a simulation study to evaluate the performance of five balancing scores using the Analysis of Covariance (ANCOVA) approach, for adjusting bias in estimating average treatment effects (ATE) in observational studies. The five balancing scores which we used as the covariate(s) in the ANCOVA model were (1) propensity score (P), (2) prognostic score (G), (3) propensity score estimated by prognostic score (PG), (4) prognostic score estimated by propensity score (GP), and (5) both propensity and prognostic scores (P&G). The results of the five balancing scores using the ANCOVA approach were compared to the results of the classic regression approach, which included all observed covariates as the predictors. Simulation results showed that balancing scores P, GP, and (P&G) had the smallest bias and mean squared error (MSE) when the outcome variable and the observed covariates were linearly associated, and PG had the smallest or close to the smallest bias and MSE when the associations were nonlinear, nonadditive and nonlinear & nonadditive.