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Simone Lederer, Tjeerd M Dijkstra, and Tom Heskes (2018)

Additive Dose Response Models: Explicit Formulation and the Loewe Additivity Consistency Condition

Frontiers in Pharmacology, 9(31).

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 analyze two data sets of
drug screening that are non-interactive (Cokol et al., 2011; Yadav et al., 2015) and show
that the LACC is mostly violated and Loewe Additivity not defined. Further, we compare
the measurements of the non-interactive cases of both data sets to the theoretical null
reference models in terms of bias and mean squared error. We demonstrate that the
explicit formulation of the null reference model leads to smaller mean squared errors
than the implicit one and is much faster to compute.

10.3389/fphar.2018.00031