Learning Robust Treatment Rules for Censored Data

There is a fast-growing literature on estimating optimal treatment rules directly by maximizing the expected outcome. In biomedical studies and operations applications, censored survival outcome is frequently observed, in which case the truncated mean survival time and survival probability are of great interest. In this paper, we propose two robust criteria for learning optimal treatment rules with censored survival outcomes; the former one targets an optimal treatment rule maximizing the truncated mean survival time, where the cutoff is specified by a given quantile such as median; the latter one targets an optimal treatment rule maximizing buffered survival probabilities, where the predetermined threshold is adjusted to account for the truncated mean survival time. We develop a sampling-based difference-of-convex algorithm for learning the proposed optimal treatment rules, and provide theoretical justifications for them. In simulation studies, our estimators show improved performance compared to existing methods. We also demonstrate the proposed method using AIDS clinical trial data.

💡 Research Summary

The paper addresses the problem of learning individualized treatment rules when the outcome of interest is a right‑censored survival time. While most existing work focuses on maximizing the expected (mean) survival time, this objective can be inadequate in settings where the distribution of survival times is skewed or where decision makers are particularly concerned with the lower tail (early failures). To fill this gap, the authors propose two robust criteria that explicitly target tail performance.

The first criterion is based on Conditional Value‑at‑Risk (CVaR). For a given quantile level γ∈(0,1) (e.g., the median), they define a quantile‑indexed truncated mean survival time V₁^γ(d)=E