  Principal stratification is a causal framework to analyze randomized
experiments with a post-treatment variable between the treatment and endpoint
variables. Because the principal strata defined by the potential outcomes of
the post-treatment variable are not observable, we generally cannot identify
the causal effects within principal strata. Motivated by a real data set of
phase III adjuvant colon clinical trials, we propose approaches to identifying
and estimating the principal causal effects via multiple trials. For the
identifiability, we remove the commonly-used exclusion restriction assumption
by stipulating that the principal causal effects are homogeneous across these
trials. To remove another commonly-used monotonicity assumption, we give a
necessary condition for the local identifiability, which requires at least
three trials. Applying our approaches to the data from adjuvant colon clinical
trials, we find that the commonly-used monotonicity assumption is untenable,
and disease-free survival with three-year follow-up is a valid surrogate
endpoint for overall survival with five-year follow-up, which satisfies both
the causal necessity and the causal sufficiency. We also propose a sensitivity
analysis approach based on Bayesian hierarchical models to investigate the
impact of the deviation from the homogeneity assumption.
