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.[1][2][3]

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 (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]

References

  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.
  5. "Github development repository for the R package MDR". 2020-01-20.


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