Robust and efficient semi‐supervised estimation of average treatment effects with application to electronic health records data

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 Partners' Healthcare.