Abstract: Understanding how treatment effects vary on several key characteristics is critical in the practice of personalized medicine. In such cases, nonparametric estimation of these conditional average treatment effects is often desirable. However, few methods are available owing to the computational difficulty of such estimations. Furthermore, existing nonparametric methods, such as the inverse probability weighting methods, have limitations that hinder their use when the values of propensity scores are close to zero or one. We propose a propensity score regression (PSR) method that allows nonparametric estimation of such conditional average treatment effects in a wide context. The PSR comprises two nonparametric regressions. First, it regresses on the propensity scores together with the characteristics of interest, to obtain an intermediate estimate. Then, it regresses the intermediate estimate on the characteristics of interest only. By including propensity scores as regressors in a nonparametric manner, the PSR eases the computational difficulty substantially while remaining less sensitive to the values of propensity scores. We present its several appealing properties, including consistency and asymptotical normality. In particular, we show the existence of an explicit variance estimator, which we use to assess the analytical behavior of the PSR and its precision. The results of our simulation studies indicate that the PSR outperforms existing methods in various settings with extreme values of propensity scores. We apply our method to the national 2009 flu survey (NHFS) data to investigate the effects of seasonal influenza vaccinations and having paid sick leave across different age groups.

Key words and phrases: Heterogeneous treatment effect, high-dimensional covariates, nonparametric estimation, propensity score.