Sensitivity Analysis for Constructing Optimal Treatment Regimes in the Presence of Non-compliance and Two Active Treatment Options

Existing literature on constructing optimal regimes often focuses on intention-to-treat analyses that completely ignore the compliance behavior of individuals. Instrumental variable-based methods have been developed for learning optimal regimes under endogeneity. However, when there are two active treatment arms, the average causal effects of treatments cannot be identified using a binary instrument, and thus the existing methods will not be applicable. To fill this gap, we provide a procedure that identifies an optimal regime and the corresponding value function as a function of a vector of sensitivity parameters. We also derive the canonical gradient of the target parameter and propose a multiply robust classification-based estimator of the optimal regime. Our simulations highlight the need for and usefulness of the proposed method in practice. We implement our method on the Adaptive Treatment for Alcohol and Cocaine Dependence randomized trial.