We investigate the bounding problem of causal effects in experimental studies in which the outcome is truncated by death, meaning that the subject dies before the outcome can be measured. Causal effects cannot be point identified without instruments and/or tight parametric assumptions but can be bounded under mild restrictions. Previous work on partial identification under the principal stratification framework has primarily focused on the `always-survivor' subpopulation. In this paper, we present a novel nonparametric unified framework to provide sharp bounds on causal effects on discrete and continuous square-integrable outcomes. These bounds are derived on the `always-survivor', `protected', and `harmed' subpopulations and on the entire population with/without assumptions of monotonicity and stochastic dominance. The main idea depends on rewriting the optimization problem in terms of the integrated tail probability expectation formula using a set of conditional probability distributions. The proposed procedure allows for settings with any type and number of covariates, and can be extended to incorporate average causal effects and complier average causal effects. Furthermore, we present several simulation studies conducted under various assumptions as well as the application of the proposed approach to a real dataset from the National Supported Work Demonstration.

翻译：我们研究了实验研究中结果因死亡而截断的因果效应界定问题，即受试者在结果可测量前死亡的情况。在没有工具变量和/或严格的参数假设下，因果效应无法点识别，但在温和约束下可被界定。先前在主要分层框架下的部分识别研究主要关注“始终存活者”子总体。本文提出一种新颖的非参数统一框架，为离散和连续平方可积结果上的因果效应提供尖锐边界。这些边界是在“始终存活者”、“受保护”和“受伤害”子总体以及整个总体上，在有无单调性和随机优势假设的条件下导出的。主要思想是基于一组条件概率分布，利用积分尾部概率期望公式重写优化问题。所提出的程序允许任意类型和数量的协变量设置，并可扩展以包含平均因果效应和依从者平均因果效应。此外，我们展示了在多种假设下进行的若干模拟研究，以及将所提方法应用于来自国家支持工作示范的实际数据集的结果。