Statistical detection of synergy: New methods and a comparative study.

Combination therapies are increasingly adopted as the standard of care for various diseases to improve treatment response, minimise the development of resistance and/or minimise adverse events. Therefore, synergistic combinations are screened early in the drug discovery process, in which their potential is evaluated by comparing the observed combination effect to that expected under a null model. Such methodology is implemented in the BIGL R-package which allows for a quick screening of drug combinations. We extend the meanR and maxR tests from this package by allowing non-constant variance of the responses and by extending the list of null models (Loewe, Loewe2, HSA, Bliss). These new tests are evaluated in a comprehensive simulation study under various models for additivity and synergy, various monotherapeutic dose-response models (complete, partial and incomplete responders) and various types of deviation from the constant variance assumption. In addition, the BIGL package is extended with bootstrap confidence intervals for the individual off-axis points and for the overall synergy strength, which were demonstrated to have reliable coverage and can complement the existing tests. We conclude that the differences in performance between the different null models are small and depend on the simulation scenario. As a result, the choice of null model should be driven by expert knowledge on the particular problem. Finally, we demonstrate the new features of the BIGL package and the difference between the synergy models on a real dataset from drug discovery. The BIGL package is available at CRAN (https://CRAN.R-project.org/package=BIGL) and as a Shiny app (https://synergy.openanalytics.eu/app).

BIGL: Biochemically Intuitive Generalized Loewe null model for prediction of the expected combined effect compatible with partial agonism and antagonism.

Clinical efficacy regularly requires the combination of drugs. For an early estimation of the clinical value of (potentially many) combinations of pharmacologic compounds during discovery, the observed combination effect is typically compared to that expected under a null model. Mechanistic accuracy of that null model is not aspired to; to the contrary, combinations that deviate favorably from the model (and thereby disprove its accuracy) are prioritized. Arguably the most popular null model is the Loewe Additivity model, which conceptually maps any assay under study to a (virtual) single-step enzymatic reaction. It is easy-to-interpret and requires no other information than the concentration-response curves of the individual compounds. However, the original Loewe model cannot accommodate concentration-response curves with different maximal responses and, by consequence, combinations of an agonist with a partial or inverse agonist. We propose an extension, named Biochemically Intuitive Generalized Loewe (BIGL), that can address different maximal responses, while preserving the biochemical underpinning and interpretability of the original Loewe model. In addition, we formulate statistical tests for detecting synergy and antagonism, which allow for detecting statistically significant greater/lesser observed combined effects than expected from the null model. Finally, we demonstrate the novel method through application to several publicly available datasets.