High-throughput techniques allow for massive screening of drug combinations. To find combinations that exhibit an interaction effect, one filters for promising compound combinations by comparing to a response without interaction. A common principle for no interaction is Loewe Additivity which is based on the assumption that no compound interacts with itself and that two doses from different compounds having the same effect are equivalent. It then should not matter whether a component is replaced by the other or vice versa. We call this assumption the Loewe Additivity Consistency Condition (LACC). We derive explicit and implicit null reference models from the Loewe Additivity principle that are equivalent when the LACC holds. Of these two formulations, the implicit formulation is the known General Isobole Equation (Loewe, 1928), whereas the explicit one is the novel contribution. The LACC is violated in a significant number of cases. In this scenario the models make different predictions.We implemented the code to model several dose-response curves and non-interaction models, among which the General Isobole Equation (implicit formulation of Loewe Additivity), the Explicit Mean Equation (explicit formulation of the Loewe Additivity) and Bliss Indepence. Building up on these null-reference models, we implement two methods to compute synergy: a parametric one where interaction effects are implemented within the shape-determination and a so-called lack-of-fit approach, where synergy is measured in terms of the deviance between measured and expected response.This code was generated for the analyses conducted in "Lederer, S., Dijkstra, T.M.H., Heskes, T., (2018). 'Additive Dose Response Models: Explicit Formulation and the Loewe Additivity Consistency Condition'. Frontiers in Pharmacology, 9, 31" and "Lederer, S., Dijkstra, T.M.H., Heskes, T., (2019). 'Additive Dose Response Models: Defining Synergy'. Frontiers in Pharmacology, 10, 1384."

Date Submitted: 2021-02-07