发表机构
School of Mathematics, Sun Yat-sen University（中山大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对截断死亡下政策效用未定义的问题，提出主分层框架下的部分识别方法，开发有效估计器并构建约束极小极大优化实现政策学习，兼顾遗憾最小化与生存率保证。
AI 中文摘要
政策评估与学习旨在基于个体特征评估和优化治疗分配规则。当结果因死亡而截断时，一个根本性挑战随之出现，使得常规政策效用无法定义。为应对这一挑战，我们在主分层框架内研究截断死亡下的政策评估与学习。我们提出幸存者平均效用和亚组生存率来评估治疗政策。在治疗可忽略性和单调性假设下，亚组生存率可被点识别，而幸存者平均效用仅能通过尖锐边界部分识别。随后，我们开发了亚组生存率的半参数有效估计器以及幸存者平均效用边界的混合估计器。在此评估框架基础上，我们构建了一个约束极小极大优化问题用于政策学习，该问题最小化相对于基准政策的最坏情况遗憾，同时要求学习到的政策达到不低于基准政策的生存率。我们证明最优政策具有基于两个优先级评分的阈值表示。我们开发了最优政策的估计程序，并建立了遗憾和可行性保证。模拟研究和在MIMIC-III临床数据集上的应用展示了所提出方法的实际性能。
英文摘要
Policy evaluation and learning aim to assess and optimize treatment assignment rules based on individual characteristics. A fundamental challenge arises when outcomes are truncated by death, rendering conventional policy utilities undefined. To address this challenge, we study policy evaluation and learning under truncation by death within the principal stratification framework. We propose the survivor average utility and subgroup survival rates for evaluating treatment policies. Under treatment ignorability and monotonicity, the subgroup survival rates are point identified, whereas the survivor average utility is only partially identified through sharp bounds. We then develop semiparametrically efficient estimators for the subgroup survival rates and hybrid estimators for the survivor average utility bounds. Building on this evaluation framework, we formulate a constrained minimax optimization problem for policy learning that minimizes worst-case regret relative to a benchmark policy while requiring the learned policy to achieve a survival rate no lower than that of the benchmark. We show that the optimal policy admits a threshold representation based on two priority scores. We develop an estimation procedure for the optimal policy and establish regret and feasibility guarantees. Simulation studies and an application to the MIMIC-III clinical dataset demonstrate the practical performance of the proposed methods.
