Evaluating time-to-event surrogates for time-to-event true endpoints: an information-theoretic approach based on causal inference.

Putative surrogate endpoints must undergo a rigorous statistical evaluation before they can be used in clinical trials. Numerous frameworks have been introduced for this purpose. In this study, we extend the scope of the information-theoretic causal-inference approach to encompass scenarios where both outcomes are time-to-event endpoints, using the flexibility provided by D-vine copulas. We evaluate the quality of the putative surrogate using the individual causal association (ICA)-a measure based on the mutual information between the individual causal treatment effects. However, in spite of its appealing mathematical properties, the ICA may be ill defined for composite endpoints. Therefore, we also propose an alternative rank-based metric for assessing the ICA. Due to the fundamental problem of causal inference, the joint distribution of all potential outcomes is only partially identifiable and, consequently, the ICA cannot be estimated without strong unverifiable assumptions. This is addressed by a formal sensitivity analysis that is summarized by the so-called intervals of ignorance and uncertainty. The frequentist properties of these intervals are discussed in detail. Finally, the proposed methods are illustrated with an analysis of pooled data from two advanced colorectal cancer trials. The newly developed techniques have been implemented in the R package Surrogate.