Bayesian principal stratification with longitudinal data and truncation by death

In causal studies, outcomes are often ‘censored by death,’ meaning they are not observed or defined for units that die. These studies typically focus on the stratum of ’always survivors’ up to a single fixed time s. An extension is proposed for the analysis of longitudinal studies where units may die at different times and outcomes observed and well-defined only up to the respective moment of death. A Bayesian longitudinal principal stratification approach is developed, where units are cross-classified based on their death status over time. This method focuses on causal effects for principal strata of units that would survive until time s, regardless of treatment assignment, with these strata varying as a function of s. The approach provides insights into treatment effects by examining the distribution of baseline characteristics within each longitudinal principal stratum and the time trends of both stratum membership and survivor-average causal effects. The methodology is illustrated in a longitudinal observational study assessing the causal effects of a policy promoting start-ups on firms’ survival and hiring decisions, assuming strong ignorability of treatment assignment, where firms’ hiring decisions may be censored by death.