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因死亡截尾（即被试在结果测量前死亡）情形下因果效应的界限问题。在没有工具变量和/或严格参数假设的情况下，因果效应无法点识别，但在温和约束条件下可建立界限。先前基于主分层框架的部分识别研究主要聚焦于"始终存活者"子群体。本文提出一种全新的非参数统一框架，可为离散型与连续型平方可积结果变量的因果效应提供严格界限。这些界限分别在"始终存活者"、"受保护者"和"受损者"子群体以及全体人群中，在有无单调性和随机占优假设条件下推导得出。核心思想在于利用一组条件概率分布将优化问题重构为积分尾概率期望公式。所提方法适用于任意类型和数量的协变量场景，并可扩展至包含平均因果效应和依从者平均因果效应。最后，我们展示了在不同假设条件下开展的若干模拟研究，以及该方法在"国家支持工作示范"真实数据集上的应用。