Loewe additivity

In toxicodynamics and pharmacodynamics, Loewe Additivity (or dose 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 (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

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.

References 

Category:Clinical pharmacology