A Bayesian Approach to Dose–Response Assessment and Synergy and Its Application to In Vitro Dose–Response Studies
Article first published online: 11 MAR 2010
© 2010, The International Biometric Society
Volume 66, Issue 4, pages 1275–1283, December 2010
How to Cite
Hennessey, V. G., Rosner, G. L., Bast Jr, R. C. and Chen, M.-Y. (2010), A Bayesian Approach to Dose–Response Assessment and Synergy and Its Application to In Vitro Dose–Response Studies. Biometrics, 66: 1275–1283. doi: 10.1111/j.1541-0420.2010.01403.x
- Issue published online: 11 MAR 2010
- Article first published online: 11 MAR 2010
- Received February 2009. Revised November 2009. Accepted January 2010.
- Combination index method;
- Drug interaction;
- Emax model;
- Interaction index;
- Loewe additivity model;
- Median-effect principle
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 Regulation 22, 27–55), which ignore important sources of variability and uncertainty.