Quantile-optimal Treatment Regimes with Censored Data

Abstract

The problem of estimating an optimal treatment regime has received considerable attention recently. However, most of the earlier work in this area has focused on estimating a mean-optimal treatment regime based on completely observed data. We investigate a new quantile criterion for estimating an optimal treatment regime with right-censored survival outcomes. When the outcome distribution is skewed or when the censoring is heavy, the quantile criterion is easy to interpret and provides an attractive measure of treatment effect. In contrast, the mean criterion often cannot be reliably estimated in such settings. We propose a nonparametric approach to robustly estimate the quantile-optimal treatment regime from a class of candidate treatment regimes without imposing an outcome regression model. We derive a nonstandard converge rate and a non-normal limiting distribution for the estimated parameters indexing the optimal treatment regime using advanced empirical processes theory. Such a theory has not been established in any earlier work for survival data. We also extend the method to a two-stage dynamic setting. We illustrate the practical utility of the proposed new method for single-stage estimation through Monte Carlo studies and an application to a clinical trial data set, and we also examine the performance of the proposed method for two-stage estimation through Monte Carlo studies.