Evaluation of Surrogate Endpoints Using Information-Theoretic Measure of Association Based on Havrda and Charvat Entropy

Surrogate endpoints have been used to assess the efficacy of a treatment and can potentially reduce the duration and/or number of required patients for clinical trials. Using information theory, Alonso et al. (2007) proposed a unified framework based on Shannon entropy, a new definition of surrogacy that departed from the hypothesis testing framework. In this paper, a new family of surrogacy measures under Havrda and Charvat (H-C) entropy is derived which contains Alonso’s definition as a particular case. Furthermore, we extend our approach to a new model based on the information-theoretic measure of association for a longitudinally collected continuous surrogate endpoint for a binary clinical endpoint of a clinical trial using H-C entropy. The new model is illustrated through the analysis of data from a completed clinical trial. It demonstrates advantages of H-C entropy-based surrogacy measures in the evaluation of scheduling longitudinal biomarker visits for a phase 2 randomized controlled clinical trial for treatment of multiple sclerosis.