Evaluating time to cancer recurrence as a surrogate marker for survival from an information theory perspective

The last two decades have seen a lot of development in the area of surrogate marker validation. One of these approaches places the evaluation in a meta-analytic framework, leading to definitions in terms of trial- and individual-level association. A drawback of this methodology is that different settings have led to different measures at the individual level. Using information theory, Alonso et al. proposed a unified framework, leading to a new definition of surrogacy, which offers interpretational advantages and is applicable in a wide range of situations. In this work, we illustrate how this information-theoretic approach can be used to evaluate surrogacy when both endpoints are of a time-to-event type. Two meta-analyses, in early and advanced colon cancer, respectively, are then used to evaluate the performance of time to cancer recurrence as a surrogate for overall survival.