In many causal studies, outcomes are censored by death, in the sense that they are neither observed nor defined for units who die. In such studies, the focus is usually on the stratum of always survivors up to a single fixed time s. Building on a recent strand of the literature, we propose an extended framework for the analysis of longitudinal studies, where units can die at different time points, and the main endpoints are observed and well defined only up to the death time. We develop a Bayesian longitudinal principal stratification framework, where units are cross classified according to the longitudinal death status. Under this framework, the focus is on causal effects for the principal strata of units that would be alive up to a time point s irrespective of their treatment assignment, where these strata may vary as a function of s. We can get precious insights into the effects of treatment by inspecting the distribution of baseline characteristics within each longitudinal principal stratum, and by investigating the time trend of both principal stratum membership and survivor-average causal effects. We illustrate our approach for the analysis of a longitudinal observational study aimed to assess, under the assumption of strong ignorability of treatment assignment, the causal effects of a policy promoting start ups on firms survival and hiring policy, where firms hiring status is censored by death.

翻译：在许多因果研究中，结局变量因死亡而截断，即对于死亡个体，这些结局既未被观测到也无法定义。此类研究通常将关注点限定在固定时间点s上的始终存活层。基于近期文献进展，我们提出一个适用于纵向研究的扩展框架——在该框架中，个体可在不同时间点死亡，且主要终点仅能在死亡时间点之前被观测和明确定义。我们构建了一个贝叶斯纵向主分层框架，根据纵向死亡状态对个体进行交叉分类。在此框架下，研究聚焦于那些无论接受何种处理分配都能存活至时间点s的个体的主分层因果效应，且这些分层会随s的变化而变化。通过检视各纵向主分层内基线特征的分布，并探究主分层归属和幸存者平均因果效应的时间趋势，我们可以获得关于处理效应的深刻见解。我们展示了该方法在一项纵向观察性研究中的应用——在强可忽略处理分配假设下，评估一项促进初创企业政策对企业生存和招聘政策的因果效应，其中企业招聘状态因死亡而截断。