  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.
