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

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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

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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

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  1. ^ Greco, W.R.; Bravo, G.; Parsons, J. (1995). "The Search for Synergy: A Critical Review from a Response Surface Perspective". Pharmacol. Rev. 47 (2): 331–385. PMID 7568331.
  2. ^ Loewe, S. (1926). "Effect of combinations: mathematical basis of problem". Arch. Exp. Pathol. Pharmakol. 114: 313–326. doi:10.1007/BF01952257. S2CID 19783017.
  3. ^ Tang, J.; Wennerberg, J.K.; Aittokallio, T. (2015). "What Is Synergy? The Saariselkä Agreement Revisited". Frontiers in Pharmacology. 6: 181. doi:10.3389/fphar.2015.00181. PMC 4555011. PMID 26388771.
  4. ^ Belden, J. B.; Gilliom, R.; Lydy, M.J. (2007). "How well can we predict the toxicity of pesticide mixtures to aquatic life?". Integr. Environ. Assess. Manag. 3 (3): 364–72. doi:10.1002/ieam.5630030307. PMID 17695109. S2CID 16438339.
  5. ^ "Github development repository for the R package MDR". GitHub. 2020-01-20.