Doubly robust estimation of optimal treatment regimes for survival data using an instrumental variable

TL;DR

This paper introduces a new semiparametric, doubly robust method for estimating optimal treatment regimes in survival analysis using instrumental variables, addressing unobserved confounders and model misspecification.

Contribution

It develops a novel estimator that leverages instrumental variables and kernel smoothing to improve the robustness and accuracy of treatment regime estimation in survival data.

Findings

Estimator performs well in simulations under various scenarios.

Method applied successfully to cancer screening trial data.

Provides asymptotic properties and finite sample performance analysis.

Abstract

In survival contexts, substantial literature exists on estimating optimal treatment regimes, where treatments are assigned based on personal characteristics to maximize the survival probability. These methods assume that a set of covariates is sufficient to deconfound the treatment-outcome relationship. However, this assumption can be limited in observational studies or randomized trials in which non-adherence occurs. Therefore, we propose a novel approach to estimating optimal treatment regimes when certain confounders are unobservable and a binary instrumental variable is available. Specifically, via a binary instrumental variable, we propose a semiparametric estimator for optimal treatment regimes by maximizing a Kaplan-Meier-like estimator of the survival function. Furthermore, to increase resistance to model misspecification, we construct novel doubly robust estimators. Since the estimators of the survival function are jagged, we incorporate kernel smoothing methods to improve performance. Under appropriate regularity conditions, the asymptotic properties are rigorously established. Moreover, the finite sample performance is evaluated through simulation studies. Finally, we illustrate our method using data from the National Cancer Institute's prostate, lung, colorectal, and ovarian cancer screening trial.