Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2022 Feb;10(3):465.
doi: 10.3390/math10030465. Epub 2022 Jan 31.

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

María Del Carmen Pardo  1 , Qian Zhao  2 , Hua Jin  3 , Ying Lu  4
Affiliations

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

María Del Carmen Pardo et al. Mathematics (Basel). 2022 Feb.

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.

Keywords: Havrda and Charvat entropy; clinical trial design; information theory; mutual information; surrogate endpoint.

PubMed Disclaimer

Conflict of interest statement

Conflicts of Interest: The authors declare no conflict of interest.

References

    1. Clinical Trial Endpoints for the Approval of Cancer Drugs and Biologics Guidance for Industry. U.S. Department of Health and Human Services. Available online: Clinical Trial Endpoints for the Approval of Cancer Drugs and Biologics fda.gov (accessed on January 29, 2022).
    1. Kim C; Prasad V Cancer drugs approved on the basis of a surrogate end point and subsequent overall survival: An analysis of 5 years of, U.S.; food and drug administration approvals. JAMA Intern. Med 2015, 175, 1992–1994. 10.1001/jamainternmed.2015.5868. - DOI - PubMed
    1. Schwartz LH; Litière S; de Vries E; Ford R; Gwyther S; Mandrekar S; Shankar L; Bogaerts J; Chen A; Dancey J; et al. RECIST 1.1-update and clarification: From the RECIST committee. Eur. J. Cancer 2016, 62, 132–137. 10.1016/j.ejca.2016.03.081. - DOI - PMC - PubMed
    1. Karrison TG; Maitland ML; Stadler WM; Ratain MJ Design of phase II cancer trials using a continuous endpoint of change in tumor size: Application to a study of sorafenib and erlotinib in non-small-cell lung cancer. J. Natl. Cancer Inst 2007, 99, 1455–1461; Erratum in J. Natl. Cancer Inst. 2007, 99, 1819. - PubMed
    1. Burzykowski T; Coart E; Saad ED; Shi Q; Sommeijer DW; Bokemeyer C; Díaz-Rubio E; Douillard JY; Falcone A; Fuchs CS; et al. Evaluation of continuous tumor-size–based end points as surrogates for overall survival in randomized clinical trials in metastatic colorectal cancer. JAMA Netw. Open 2019, 2, e1911750. 10.1001/jamanetworkopen.2019.11750. - DOI - PMC - PubMed

LinkOut - more resources