On Estimating Optimal Regime for Treatment Initiation Time Based on Restricted Mean Residual Lifetime

TL;DR

This paper develops a nonparametric method to determine the optimal time to start treatment for individual patients based on their characteristics, using restricted mean residual lifetime as a performance measure, addressing challenges of missing data and continuous treatment timing.

Contribution

It introduces a novel approach for estimating individualized treatment initiation times using a nonparametric estimator and analyzes its asymptotic properties under complex missing data mechanisms.

Findings

Estimator is consistent even with incomplete treatment data

Asymptotic distribution follows a weighted chi-squared distribution

Method performs well in simulation and real breast cancer data

Abstract

When to initiate treatment on patients is an important problem in many medical studies such as AIDS and cancer. In this article, we formulate the treatment initiation time problem for time-to-event data and propose an optimal individualized regime that determines the best treatment initiation time for individual patients based on their characteristics. Different from existing optimal treatment regimes where treatments are undertaken at a pre-specified time, here new challenges arise from the complicated missing mechanisms in treatment initiation time data and the continuous treatment rule in terms of initiation time. To tackle these challenges, we propose to use restricted mean residual lifetime as a value function to evaluate the performance of different treatment initiation regimes, and develop a nonparametric estimator for the value function, which is consistent even when treatment initiation times are not completely observable and their distribution is unknown. We also establish the asymptotic properties of the resulting estimator in the decision rule and its associated value function estimator. In particular, the asymptotic distribution of the estimated value function is nonstandard, which follows a weighted chi-squared distribution. The finite-sample performance of the proposed method is evaluated by simulation studies and is further illustrated with an application to a breast cancer data.