Estimating Multiple Treatment Effects Using Two-phase Regression Estimators

We propose a semiparametric two-phase regression estimator with a semiparametric generalized propensity score estimator for estimating average treatment effects in the presence of informative first-phase sampling. The proposed estimator can be easily extended to any number of treatments and does not rely on a prespecified form of the response or outcome functions. The proposed estimator is shown to reduce bias found in standard estimators, such as inverse propensity weighted estimators that ignore the first-phase sample design, and can have improved efficiency compared to the double expansion estimators. Results from simulation studies and from an empirical study of NHANES are presented.