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.