A Bayesian Approach to Dose–Response Assessment and Synergy and Its Application to In Vitro Dose–Response Studies

Authors

  • Violeta G. Hennessey,

    1. Department of Biostatistics, The University of Texas Graduate School of Biomedical Sciences at Houston, The University of Texas M.D. Anderson Cancer Center, Houston, Texas 77030, U.S.A.
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  • Gary L. Rosner,

    1. Department of Biostatistics, The University of Texas Graduate School of Biomedical Sciences at Houston, The University of Texas M.D. Anderson Cancer Center, Houston, Texas 77030, U.S.A.
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  • Robert C. Bast Jr,

    1. Department of Experimental Therapeutics, Office of Translational Research, The University of Texas M.D. Anderson Cancer Center, Houston, Texas 77030, U.S.A.
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  • Min-Yu Chen

    1. Department of Obstetrics and Gynecology, Chang Gung Memorial Hospital Linkou Medical Center, Chang Gung University, College of Medicine, Taoyuan 333, Taiwan
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email:vhenness@mdanderson.org

email:glrosner@mdanderson.org

email:rbast@mdanderson.org

email:e12013@adm.cgmh.org.tw

Abstract

Summary In this article, we propose a Bayesian approach to dose–response assessment and the assessment of synergy between two combined agents. We consider the case of an in vitro ovarian cancer research study aimed at investigating the antiproliferative activities of four agents, alone and paired, in two human ovarian cancer cell lines. In this article, independent dose–response experiments were repeated three times. Each experiment included replicates at investigated dose levels including control (no drug). We have developed a Bayesian hierarchical nonlinear regression model that accounts for variability between experiments, variability within experiments (i.e., replicates), and variability in the observed responses of the controls. We use Markov chain Monte Carlo to fit the model to the data and carry out posterior inference on quantities of interest (e.g., median inhibitory concentration IC 50). In addition, we have developed a method, based on Loewe additivity, that allows one to assess the presence of synergy with honest accounting of uncertainty. Extensive simulation studies show that our proposed approach is more reliable in declaring synergy compared to current standard analyses such as the median-effect principle/combination index method (Chou and Talalay, 1984, Advances in Enzyme Regulation22, 27–55), which ignore important sources of variability and uncertainty.

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