  A common practice in clinical trials is to evaluate a treatment effect on an
intermediate endpoint when the true outcome of interest would be difficult or
costly to measure. We consider how to validate intermediate endpoints in a
causally-valid way when the trial outcomes are time-to-event. Using
counterfactual outcomes, those that would be observed if the counterfactual
treatment had been given, the causal association paradigm assesses the
relationship of the treatment effect on the surrogate $S$ with the treatment
effect on the true endpoint $T$. In particular, we propose illness death models
to accommodate the censored and semi-competing risk structure of survival data.
The proposed causal version of these models involves estimable and
counterfactual frailty terms. Via these multi-state models, we characterize
what a valid surrogate would look like using a causal effect predictiveness
plot. We evaluate the estimation properties of a Bayesian method using Markov
Chain Monte Carlo and assess the sensitivity of our model assumptions. Our
motivating data source is a localized prostate cancer clinical trial where the
two survival endpoints are time to distant metastasis and time to death.
