In toxicodynamics and pharmacodynamics, Loewe additivity (or dose additivity) is one of several common reference models used for measuring the effects of drug combinations.^[1][2][3]

Definition[edit]

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 (assuming this conditions uniquely define them, i.e. that the individual dose-response functions are bijective). 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[edit]

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 (MDR).^[4]

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.^{[5][clarification needed]}

References[edit]