An information-theoretic approach to surrogate-marker evaluation with failure time endpoints

Over the last decades, the evaluation of potential surrogate endpoints in clinical trials has steadily been growing in importance, not only thanks to the availability of ever more potential markers and surrogate endpoints, also because more methodological development has become available. While early work has been devoted, to a large extent, to Gaussian, binary, and longitudinal endpoints, the case of time-to-event endpoints is in need of careful scrutiny as well, owing to the strong presence of such endpoints in oncology and beyond. While work had been done in the past, it was often cumbersome to use such tools in practice, because of the need for fitting copula or frailty models that were further embedded in a hierarchical or two-stage modeling approach. In this paper, we present a methodologically elegant and easy-to-use approach based on information theory. We resolve essential issues, including the quantification of “surrogacy” based on such an approach. Our results are put to the test in a simulation study and are applied to data from clinical trials in oncology. The methodology has been implemented in R.