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We consider the problem of estimating the effects of a binary treatment on acontinuous outcome of interest from observational data in the absence ofconfounding by unmeasured factors. We provide a new estimator of the populationaverage treatment effect (ATE) based on the difference of novel double-robust(DR) estimators of the treatment-specific outcome means. We compare our newestimator with previously estimators both theoretically and via simulation.DR-difference estimators may have poor finite sample behavior when theestimated propensity scores in the treated and untreated do not overlap. Wetherefore propose an alternative approach, which can be used even in thisunfavorable setting, based on locally efficient double-robust estimation of asemiparametric regression model for the modification on an additive scale ofthe magnitude of the treatment effect by the baseline covariates $X$. Incontrast with existing methods, our approach simultaneously provides estimatesof: i) the average treatment effect in the total study population, ii) theaverage treatment effect in the random subset of the population withoverlapping estimated propensity scores, and iii) the treatment effect at eachlevel of the baseline covariates $X$.  When the covariate vector $X$ is high dimensional, one cannot be certain,owing to lack of power, that given models for the propensity score and for theregression of the outcome on treatment and $X$ used in constructing our DRestimators are nearly correct, even if they pass standard goodness of fittests. Therefore to select among candidate models, we propose a novel approachto model selection that leverages the DR-nature of our treatment effectestimator and that outperforms cross-validation in a small simulation study.

Double-robust and efficient methods for estimating the causal effects of a binary treatment