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Loewe additivity is one of several reference models used in the analysis of combined dose response in pharmacology. Originally proposed by Siegfried Loewe and H. Muischnek, the model is based on the intuition that a compound should not be expected to interact with itself. Loewe additivity forms the basis of several combination analysis approaches, including the Combination Index method, the isobologram method , and the response surface model of Greco, Park and Rustum.

Definition
Suppose that a dose $D_{A}$ of a particular drug A and a dose $D_{B}$ of another drug B are administered together to a particular cell population, tissue, organ or other target, and that these combined doses produce the effect X. The combined dose of $D_{A}$ of drug A and $D_{B}$ of drug B is said to be Loewe additive if


 * $$1=\frac{D_A}{{ID}_{X,A}}+\frac{D_B}{{ID}_{X,B}}$$

where $ID_{X,A}$ is the dose of drug A alone required to produce the effect X in the same context, and $ID_{X,B}$ is the dose of drug B alone required to produce the effect X in the same context. If every possible pair of doses of drugs A and B is Loewe additive, then the overall drug combination is also referred to as Loewe additive. This is the sense in which the designation is usually applied (to a pair of drugs overall), but it can also be used to describe a subset of possible doses (e.g. stating that a combination is "additive at high doses").

Less formally, to say that a combination is Loewe additive is to say that dose pairs producing a given effect are formed from complimentary proportions of the individual doses required to produce that effect. So, if one needs M of drug A to produce a particular effect (say, killing 99% of tumor cells), and one needs N of drug B to produce the same effect, then one can also expect half of M of drug A combined with half of N of drug B to produce that effect; the same is true of two-thirds of M of drug A combined with one-third of N of drug B, or one tenth of M of drug A combined with nine tenths of N of drug B. Graphically, this means that when plotted in a two-dimensional space where the x-dimension represents the dose of drug A and the y-dimension represents the dose of drug B, all the dose pairs that produce a given effect lie along a straight diagonal line. This fact is the basis of the isobologram approach to combination analysis.