Inference for Dynamic Treatment Regimes using Overlap Sampling Splitting

Abstract

Dynamic treatment regime is a sequence of decision rules mapping patient informa- tion at a specific time to a recommended treatment, with the goal of maximizing long-term clinical outcome. However, the inference for the estimator of optimal regime is challenging due to the nonregularity resulting from the maximize operator. In this paper, we review methods for estimating optimal regimes and discuss the problem of nonregularity. We propose a novel approach based on sample splitting to construct valid confidence sets for both the optimal regime and the maximized value function. Additionally, we conduct a hypothesis test to compare the optimal regime to the treatment regime used in usual clinical practice. We evaluate the proposed approach using simulated data from the Sequential Multiple Assignment Randomized Trials (SMART) design and assess the coverage of the confidence sets and the power of the hypothesis test.