Loewe additivity


In toxicodynamics and pharmacodynamics, Loewe Additivity is one of several common reference models used for measuring the effects of drug combinations

Definition

Let and be doses of compounds 1 and 2 producing in combination an effect. We denote by and the doses of compounds 1 and 2 required to produce effect alone.
quantifies the potency of compound 1 relatively to that of compound 2.
can be interpreted as the dose of compound 2 converted into the corresponding dose of compound 1 after accounting for difference in potency.
Loewe additivity is defined as the situation where or
Geometrically, Loewe additivity is the situation where isoboles are segments joining the points and in the domain.
If we denote by, and the dose-response functions of compound 1, compound 2 and of the mixture respectively, then dose additivity holds when

Testing

The Loewe additivity equation provides a prediction of the dose combination eliciting a given effect. Departure from Loewe additivity can be assessed informally by comparing this prediction to observations. This approach is known in toxicology as the model deviation ratio
This approach can be rooted in a more formal statistical method with the derivation of approximate p⁻values with Monte Carlo simulation, as implemented in the R package MDR.