Covariate adjusted nonparametric methods under propensity analysis

Propensity score is one of the most commonly used score functions in adjusting for covariates effect in statistical inference. It is important to understand the impact with propensity score in case some of the prespecified covariates are severely imbalanced. In this article, we performed simulation evaluation the empirical type 1 error and empirical power under scenario of imbalanced covariates in several nonparametric two sample tests with propensity score or with other covariate adjustments. Our results suggest common propensity score approaches might have type 1 error inflation at scenarios with severe imbalanced covariates or model is mis-specified.