A Rényi-Divergence-Based Family of Metrics for the Evaluation of Surrogate Endpoints in a Causal Inference Framework

Surrogate endpoints provide several significant advantages in evaluating new drugs, including reduced follow-up times, smaller required sample sizes, and lower overall costs. The Individual Causal Association (ICA), first introduced by Alonso et al. (2015) within the causal inference framework, assesses the validity of a surrogate based on the mutual information between the individual causal treatment effects on both the surrogate and the true endpoint. Mutual information is a specific instance from the broader family of information-theoretic measures known as the Rényi divergence family. In this paper, we extend the ICA by proposing a new family of surrogacy metrics derived from Rényi divergence. We evaluate the performance of this extended family through theoretical analysis and an extensive simulation study. Finally, we provide an illustrative application using clinical trial data from schizophrenia studies.