![]() ![]() ![]() The CI can be computed using the popular CalcuSyn software available at using the following steps: (a) conduct n experiments with drugs A and B alone at a set of doses, (b) construct individual dose-response curves for each drug, (c) for each mortality value M with the drug combination find equivalent single-agent doses D 1 A and D 1 B by inverting the individual dose-response relationships from the previous step, and finally (d) compute n values of the left-hand side of Eq (1) and report the mean and standard deviation of the CI.Īlthough visually attractive, this approach has several limitations: ![]() This equations defines a segment on the plane with dose concentrations ( d A, d B) splitting the positive quadrant into two parts corresponding to synergy and antagonism, and as such is visually attractive. Typically, M = 0.5 is used, then and are half maximum dose concentrations, and we arrive at the Loewe additivity condition on drugs independence Consequently, if the left-hand side, termed Combination Index (CI), is less than one, we claim synergy (lower doses yield the same mortality M) and otherwise antagonism. Where D 1 A and D 1 B are the doses that lead to mortality M when applied individually. Although several statistical packages in R for determination of synergy exist, such as hbim, mixlow, COMBIA, and CImbinator, they lack rigorous statistical testing and computation of the p-value for various treatments/drugs interaction designs under one methodological umbrella, as we propose in the present work.Īdvantages and limitations of Loewe additivity and combination indexĪccording to Loewe, in the case of no interaction between drugs A and B, the drug combination with doses d A and d B leading to the same mortality M must satisfy the so called “median-effect” equation Herein, we discuss the advantages and limitations of these two major definitions, and then apply Bliss definition of independence for determination of statistically significant synergy in popular experimental and clinical trial settings in biology and medicine. There are two main competing definitions of drugs independence: based on (a) Loewe definition of additivity (isobologram approach) and implied combination index (CI) and (b) Bliss definition of independence or, equivalently, Webb fractional product. Despite its fundamental importance in pharmacology, toxicology and experimental medicine, including cancer research, many, sometimes contradictory, definitions of synergy and drugs interaction exist in the literature. ![]() The definition of synergy is one of the most controversial concepts in biology and medicine. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Ĭompeting interests: The authors have declared that no competing interests exist. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.ĭata Availability: All relevant data are within the manuscript and its Supporting Information files.įunding: This research was supported by National Institutes of Health, Cancer Institute (P30 CA23108-37 and 1U01CA196386-01 to E.D. Received: JanuAccepted: OctoPublished: November 25, 2019Ĭopyright: © 2019 Demidenko, Miller. For each design, we developed a specific statistical model and demonstrated how to test for independence, synergy, and antagonism, and compute the associated p-value.Ĭitation: Demidenko E, Miller TW (2019) Statistical determination of synergy based on Bliss definition of drugs independence. We rigorously and consistently extend the Bliss definition to detect statistically significant synergy under various designs: (1) in vitro, when the outcome of a cell culture experiment with replicates is the proportion of surviving cells for a single dose or multiple doses, (2) dose-response methodology, (3) in vivo studies in organisms, when the outcome is a longitudinal measurement such as tumor volume, and (4) clinical studies, when the outcome of treatment is measured by survival. Although Bliss definition is well-known, it remains a theoretical concept and has never been applied for statistical determination of synergy with various forms of treatment outcome. We offer statistical models for estimation of synergy using an established definition of Bliss drugs’ independence. Moreover, methods for statistical determination of synergy that account for variation of response to treatment are underdeveloped and if exist are reduced to the traditional t-test, but do not comply with the normal distribution assumption. Although synergy is a pillar of modern pharmacology, toxicology, and medicine, there is no consensus on its definition despite its nearly one hundred-year history. ![]()
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