Power comparison for propensity score methods

We compared four propensity score (PS) methods using simulations: maximum likelihood (ML), generalized boosting models (GBM), covariate balancing propensity scores (CBPS), and generalized additive models (GAM). Although these methods have been shown to perform better than the ML in estimating causal treatment effects, no comparison has been conducted in terms of type I error and power, and the impact of treatment exposure prevalence on PS methods has not been studied. In order to fill these gaps, we considered four simulation scenarios differing by the complexity of a propensity score model and a range of exposure prevalence. Propensity score weights were estimated using the ML, CBPS and GAM of logistic regression and the GBM. We used these propensity weights to estimate the average treatment effect among treated on a binary outcome. Simulations showed that (1) the CBPS was generally superior across the four scenarios studied in terms of type I error, power and mean squared error; (2) the GBM and the GAM were less biased than the CBPS and the ML under complex models; (3) the ML performed well when treatment exposure is rare.