We propose a semiparametric two-phase regression estimator with a semiparametric generalized propensity score estimator for estimating average treatment effects in the presence of the 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 that ignore the first-phase sample design, and can have improved efficiency compared to the inverse propensity weighted estimators. Results from simulation studies and from an empirical study of NHANES are presented.
"Estimating multiple treatment effects using two-phase semiparametric regression estimators." Electron. J. Statist. 7 2737 - 2761, 2013. https://doi.org/10.1214/13-EJS856