  Post-randomization events, also known as intercurrent events, such as
treatment noncompliance and censoring due to a terminal event, are common in
clinical trials. Principal stratification is a framework for causal inference
in the presence of intercurrent events. Despite the extensive existing
literature, there lacks generally applicable and accessible methods for
principal stratification analysis with time-to-event outcomes. In this paper,
we specify two causal estimands for time-to-event outcomes in principal
stratification. For estimation, we adopt the general strategy of latent mixture
modeling and derive the corresponding likelihood function. For computational
convenience, we illustrate the general strategy with a mixture of Bayesian
parametric Weibull-Cox proportional model for the outcome. We utilize the Stan
programming language to obtain automatic posterior sampling of the model
parameters via the Hamiltonian Monte Carlo. We provide the analytical forms of
the causal estimands as functions of the model parameters and an alternative
numerical method when analytical forms are not available. We apply the proposed
method to the ADAPTABLE trial to evaluate the causal effect of taking 81 mg
versus 325 mg aspirin on the risk of major adverse cardiovascular events.
