Estimating multiple treatment effects in two-phase observational data
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We propose three estimators: Two-phase Regression (TPR), Generalized Method of Moments (GMM), and Empirical Likelihood (EL) estimators to estimate multiple treatment effects in two-phase observational data. They use semiparametric generalized propensity scores in estimating average treatment effects in the presence of informative first-phase sampling. The proposed estimators can be easily extended to any number of treatments and do not rely on a prespecified form of the treatment selection func- tions. All of the three proposed estimators have considered the first phase and second phase inclusion probabilities in their propensity scores to eliminate the biases resulted from ignoring survey sampling designs and selection bias. The proposed TPR estimator which deals with continuous response is shown to have improved efficiency compared to the double expansion estimators using sieve semiparametric regressions. The GMM and EL estimators, which estimate treatment effects defined through generalized estimating equations, reduce Monte Carlo variance by adding covariates and combing all the gen- eralized estimating equations in treatment groups. Results from simulation studies and real data studies for three estimators are presented.