  We consider the problem of estimating the average treatment effect (ATE) in a
semi-supervised learning setting, where a very small proportion of the entire
set of observations are labeled with the true outcome but features predictive
of the outcome are available among all observations. This problem arises, for
example, when estimating treatment effects in electronic health records (EHR)
data because gold-standard outcomes are often not directly observable from the
records but are observed for a limited number of patients through small-scale
manual chart review. We develop an imputation-based approach for estimating the
ATE that is robust to misspecification of the imputation model. This
effectively allows information from the predictive features to be safely
leveraged to improve efficiency in estimating the ATE. The estimator is
additionally doubly-robust in that it is consistent under correct specification
of either an initial propensity score model or a baseline outcome model. It is
also locally semiparametric efficient under an ideal semi-supervised model
where the distribution of the unlabeled data is known. Simulations exhibit the
efficiency and robustness of the proposed method compared to existing
approaches in finite samples.We illustrate the method by comparing rates of
treatment response to two biologic agents for treatment inflammatory bowel
disease using EHR data from Partner's Healthcare.
