Evaluation of surrogate endpoints in randomized experiments with mixed discrete and continuous outcomes

A statistical definition of surrogate endpoints as well as validation criteria was first presented by Prentice. Freedman et al. supplemented these criteria with the so-called proportion explained. Buyse and Molenberghs pointed to inadequacies of these criteria and suggested a new definition of surrogacy based on (i) the relative effect linking the overall effect of treatment on both endpoints and (ii) an individual-level measure of agreement between both endpoints. Using data from a randomized trial, they showed how a potential surrogate endpoint can be studied using a joint model for the surrogate and the true endpoint. Whereas Buyse and Molenberghs restricted themselves to the fairly simple cases of jointly normal and jointly binary outcomes, we treat the situation where the surrogate is binary and the true endpoint is continuous, or vice versa. In addition, we consider the case of ordinal endpoints. Further, Buyse et al. extended the approach of Buyse and Molenberghs to a meta-analytic context. We will adopt a similar approach for responses of a mixed data type.