Estimating optimal treatment regimes in survival contexts using an instrumental variable

Abstract

There is extensive literature on the estimation of the optimal individualized treatment regime in a survival context, which dictates treatment to maximize the expected survival probability. Those methods are based on the key assumption that we can collect all the confoundings in the observational studies or in the randomized trials with noncompliance. However, the assumption sometimes is too restrictive to be applied and the violation would yield bias on the estimation of the optimal regime. In the article, we propose a method to learn the optimal regime when some of the confoundings are not observed and a valid binary instrumental variable is available. Specifically, we establish the estimator for the potential survival function under any given treatment regime and for the optimal regime by maximizing the potential survival function under a prespecified class of regimes. We also propose the doubly robust estimator to avoid possibly wrong assignment of the nuisance model. Since the estimators of the potential survival function is jagged, we utilize the kernel smoothed technique to relieve the burden of the optimization. Asymptotic properties of the proposed estimators are provided, moreover, simulation results confirm the finite sample performance when unmeasured confounding exists. Our methods are also examined and illustrated by a real-world example to dictate personalized colorectal cancer screening.