Sensitivity analysis for constructing optimal regimes in the presence of treatment non-compliance

TL;DR

This paper introduces a sensitivity analysis method for constructing optimal treatment regimes considering treatment non-compliance, especially when multiple treatments are involved and traditional instrumental variable methods are inadequate.

Contribution

It develops a new procedure to identify optimal treatment strategies and value functions using sensitivity parameters, along with a multiply robust estimator applicable in complex treatment settings.

Findings

The proposed method effectively identifies optimal strategies in simulations.

Application to a clinical trial demonstrates practical utility.

The estimator shows robustness under various model specifications.

Abstract

The current body of research on developing optimal treatment strategies often places emphasis on intention-to-treat analyses, which fail to take into account the compliance behavior of individuals. Methods based on instrumental variables have been developed to determine optimal treatment strategies in the presence of endogeneity. However, these existing methods are not applicable when there are two active treatment options and the average causal effects of the treatments cannot be identified using a binary instrument. In order to address this limitation, we present a procedure that can identify an optimal treatment strategy and the corresponding value function as a function of a vector of sensitivity parameters. Additionally, we derive the canonical gradient of the target parameter and propose a multiply robust classification-based estimator for the optimal treatment strategy. Through simulations, we demonstrate the practical need for and usefulness of our proposed method. We apply our method to a randomized trial on Adaptive Treatment for Alcohol and Cocaine Dependence.