Validation of surrogate endpoints in cancer clinical trials via principal stratification with an application to a prostate cancer trial.

Increasing attention has been focused on the use and validation of surrogate endpoints in cancer clinical trials. Previous literature on validation of surrogate endpoints are classified into four approaches: the proportion explained approach; the indirect effects approach; the meta-analytic approach; and the principal stratification approach. The mainstream in cancer research has seen the application of a meta-analytic approach. However, VanderWeele (2013) showed that all four of these approaches potentially suffer from the surrogate paradox. It was also shown that, if a principal surrogate satisfies additional criteria called one-sided average causal sufficiency, the surrogate cannot exhibit a surrogate paradox. Here, we propose a method for estimating principal effects under a monotonicity assumption. Specifically, we consider cancer clinical trials which compare a binary surrogate endpoint and a time-to-event clinical endpoint under two naturally ordered treatments (e.g. combined therapy vs. monotherapy). Estimation based on a mean score estimating equation will be implemented by the expectation-maximization algorithm. We will also apply the proposed method as well as other surrogacy criteria to evaluate the surrogacy of prostate-specific antigen using data from a phase III advanced prostate cancer trial, clarifying the complementary roles of both the principal stratification and meta-analytic approaches in the evaluation of surrogate endpoints in cancer.