One way to do so is the Combenefit method by measuring synergy in terms of volume between the expected and measured effect ( Di Veroli et al., 2016). In this paper we measure synergy as the deviation over the entire response surface. In order to measure all interaction effects, this method has to be applied to many fixed effects or dose ratios. The deviations measured from the isoboles (and hence synergy) are therefore only measured locally for that fixed effects or dose ratios. The general problem with the isobole approaches lies in the use of isoboles at fixed effect or dose ratios. Another way to quantify synergy on the basis of the isobole is to look at the curvature and arc-length of the longest isobole spanned over the measured response ( Cokol et al., 2011). Some suggest to measure synergy as the difference between an observed isobole and a reference isobole calculated from a null-reference model. An isobole is the set of all dose combinations of the compounds that reach the same fixed effect, such as 50% of the maximal effect. Many models are based on the concept of isoboles ( Chou and Talalay, 1984 Gennings and Carter, 1995 Dawson et al., 2000 Minto et al., 2000). Independent of the indecisive opinions about the null reference, there are multiple proposals regarding how synergy can be measured given a null reference model. An alternative is Bliss Independence, which assumes (statistical) independence between the combined compounds.
Other null reference models do not hold that assumption. The popularity of Loewe Additivity is based on its principle of sham combination which assumes no interaction when a compound is combined with itself. Two main principles for non-interactivity have survived the critics: Loewe Additivity ( Loewe, 1928) and Bliss Independence ( Bliss, 1939). For an extensive overview, refer to Greco et al.
Over the last century, many principles of non-interaction have been introduced. Only when deviance from that so-called null reference is observed, can one speak of an interactive effect ( Lederer et al., 2018b). To determine whether a combination of substances exhibits an interaction effect, it is crucial to determine a non-interactive effect. In such a quick scan, one focuses uniquely on the measured response and not on possible mechanisms of action of each compound. Based on that preprocessing scan, those filtered combination candidates can then be examined in greater detail. To quickly scan all interactions, a simple measure is needed. From those screens, one needs to filter for interesting candidates that exhibit an interaction effect. From data generated with high-throughput techniques, one is confronted with massive compound interaction screens. Those interaction effects are usually described as synergistic or antagonistic, dependent on whether the interaction is positive, resulting in greater effects than expected, or negative, resulting in smaller effects than expected. When combining a substance with other substances, one is generally interested in interaction effects. We show this on two datasets of compound combinations that are categorized into synergistic, non-interactive, and antagonistic. Further, we show that computing synergy as lack-of-fit outperforms a parametric approach. In the current study we show that this Explicit Mean Equation outperforms the original implicit formulation of Loewe Additivity and Bliss Independence when measuring synergy in terms of the deviance between measured and expected response, called the lack-of-fit. In a previous study, we introduced, an explicit formulation of the hitherto implicitly defined Loewe Additivity, the so-called Explicit Mean Equation. A non-interactive response is based on a principle of no interaction, such as Loewe Additivity or Bliss Independence. Those promising candidates are chosen based on the deviance between a measured response and an expected non-interactive response. With the help of high-throughput techniques, a huge amount of compound combinations can be screened and filtered for suitable candidates for a more detailed analysis. In synergy studies, one focuses on compound combinations that promise a synergistic or antagonistic effect. 3Center for Integrative Neuroscience, University Tübingen, Tübingen, Germany.2Max Planck Institute for Developmental Biology, Tübingen, Germany.1Data Science, Institute for Computing and Information Sciences, Radbound University, Nijmegen, Netherlands.
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