A More Efficient, Doubly Robust, Nonparametric Estimator of Treatment Effects in Multilevel Studies

Abstract: When studying treatment effects in multilevel studies, investigators commonly use (semi-)parametric estimators, which make strong parametric assumptions about the outcome, the treatment, and/or the correlation structure between study units in a cluster. We propose a novel estimator of treatment effects that does not make such assumptions. Specifically, the new estimator is shown to be doubly robust, asymptotically Normal, and often more efficient than existing estimators, all without having to make any parametric modeling assumptions about the outcome, the treatment, and the correlation structure. We achieve this by estimating two non-standard nuisance functions in causal inference, the conditional propensity score and the outcome covariance model, using existing existing machine learning methods designed for independent and identically distributed (i.i.d) data. The new estimator is also demonstrated in simulated and real data where the new estimator is drastically more efficient than existing estimators, especially when studying cluster-specific treatment effects.