Statistical Validation of Surrogate Endpoints: Problems and Proposals

Abstract

Prentice proposed a definition of surrogate endpoints and operational criteria for their validation. Freedman supplemented these criteria with the proportion explained, which is supposed to represent the proportion of the treatment effect upon the true endpoint which is mediated by the surrogate endpoint. In this paper, we argue that the proportion explained should be replaced by other quantities, such as the relative effect linking the effects of treatment on both endpoints and an individual-level measure of agreement between both endpoints. The latter quantity carries over naturally when data are available on several randomized experiments, while the former can be extended to be a trial-level measure of agreement between the effects of treatment of both endpoints. This approach suggests a new definition of surrogacy, and allows one to predict the effect of treatment upon the true endpoint, given its observed effect upon the surrogate endpoint.