An information‐theoretic approach for the evaluation of surrogate endpoints based on causal inference

Summary In this work a new metric of surrogacy, the so‐called individual causal association (ICA), is introduced using information‐theoretic concepts and a causal inference model for a binary surrogate and true endpoint. The ICA has a simple and appealing interpretation in terms of uncertainty reduction and, in some scenarios, it seems to provide a more coherent assessment of the validity of a surrogate than existing measures. The identifiability issues are tackled using a two‐step procedure. In the first step, the region of the parametric space of the distribution of the potential outcomes, compatible with the data at hand, is geometrically characterized. Further, in a second step, a Monte Carlo approach is proposed to study the behavior of the ICA on the previous region. The method is illustrated using data from the Collaborative Initial Glaucoma Treatment Study. A newly developed and user‐friendly R package Surrogate is provided to carry out the evaluation exercise.