Nonparametric tests for treatment effect heterogeneity in observational studies

We consider the problem of testing for treatment effect heterogeneity in observational studies and propose a nonparametric test based on multisample $U$-statistics. To account for potential confounders, we use reweighted data where the weights are determined by estimated propensity scores. The proposed method does not require any parametric assumptions on the outcomes and bypasses the need for modelling the treatment effect for each study subgroup. We establish the asymptotic normality for the test statistic and demonstrate its superior numerical performance over several competing approaches via simulation studies. Two real data applications are discussed: an employment programme evaluation study and a mental health study of China's one-child policy.