Havrda and Charvat Entropy-Based Measures to Assess Longitudinal Surrogate Endpoints in Clinical Trials

• Activity Number: 9 - Impact of Using Surrogate Endpoints on Drug Development
• Type: Invited
• Date/Time: Sunday, July 28, 2019 : 2:00 PM to 3:50 PM
• Sponsor: WNAR
• Author(s): María del Carmen Pardo * and Ying Lu and Hua Jin and Qian Zhao
• Companies: Complutense University and Stanford University and South China Normal University and Guangzhou Medical University
• Keywords: Surrogate endpoint; longitudinal data; information theory; Havrda and Charvat entropy

Abstract

The evaluation of new treatments is based on the choice of clinically meaningful clinical endpoints. However, observing such endpoints may require very long follow-up times or may be too expensive to measure. These might be avoided through replacing the true endpoints (T) by surrogate endpoints (S) or biomarkers that can be measured earlier or more cheaply than the true clinical endpoint of interest. Alonso and Molenberghs (2007,2008) redefined surrogacy in terms of the information content that S provides with respect to T. This information can be measured using information theory measures. They based their proposal on the Shannon entropy. However, there are cases where Shannon’s entropy function does not exist or not normally distributed. So we propose to extend their measure to a family of measures based on Havrda and Charvat entropy without that drawback. We define a model when T is a normally distributed, t-distributed or binary distributed clinical endpoints and S are longitudinal continuous biomarkers variables. We estimate the model unknown parameters and plugged into the proposed measures. Finally, we revisited an ophthalmologic case study to illustrate our methodology.