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

M C Pardo ,Hua Jin,Qian Zhao,Ying Lü

doi:10.3390/math10030465

Abstract

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.

Highlights

Surrogate endpoints which can be observed earlier, easier, possibly repeated, or are cost-saving, have been used to replace clinical endpoints in clinical trials
Total tumor response rate and progression–free survival have been used in phase II and phase III cancer clinical trials as surrogate endpoints for overall survival, which often requires a longer trial duration to achieve adequate statistical power
A binary response status, such as the total response based on the RECIST criterion [3], or a continuous response in change of tumor sizes [4] are common primary endpoints

Summary

Introduction

Surrogate endpoints which can be observed earlier, easier, possibly repeated, or are cost-saving, have been used to replace clinical endpoints in clinical trials. We present two new results on the topic of surrogate endpoints based on information-theoretic measure of association (ITMA). To extend H-C entropy to measure the endpoint surrogacy for trials, we define the ITMA under H-C entropy power as the following:. When two binary endpoints have more chance to be concordant, the mutual information will be an increasing function of correlation coefficient of ρ as shown in Proposition 3 Result 3.2.

Model for Longitudinal Continuous Surrogate Biomarkers in Phase II Trials

Findings

Conclusions