Identification and Estimation of the Probabilities of Potential Outcome Types Using Covariate Information in Studies with Non-compliance

Abstract

We propose novel identification conditions and a statistical estimation method for the probabilities of potential outcome types using covariate information in randomized trials in which the treatment assignment is randomized but subject compliance is not perfect. Different from existing studies, the proposed identification conditions do not require strict assumptions such as the assumption of monotonicity. When the probabilities of potential outcome types are identifiable through the proposed conditions, the problem of estimating the probabilities of potential outcome types is reduced to that of singular models. Thus, the probabilities cannot be evaluated using standard statistical likelihood-based estimation methods. Rather, the proposed identification conditions show that we can derive consistent estimators of the probabilities of potential outcome types via the method of moments, which leads to the asymptotic normality of the proposed estimators through the delta method under regular conditions. We also propose a new statistical estimation method based on the bounded constrained augmented Lagrangian method to derive more efficient estimators than can be derived through the method of moments.