Combination Index
Calculate a nonexclusive two-agent median-effect combination index including the product term; materially distinct from the simple Loewe isobole sum and dependent on externally fitted single-agent curves.
Description
Calculate a nonexclusive two-agent combination index from supplied median-effect fits and component doses.
A median-effect dose describes the dose giving an affected fraction of one half, while the fitted slope describes how response changes with dose. Combination-index calculations compare mixture component doses with the doses predicted to produce the same effect when each agent is used alone.1
This tool uses exactly two externally fitted single-agent curves and the nonexclusive index convention, which adds a product term to the two normalized dose ratios. That convention is an assumption selected for the analysis; the calculator does not infer mechanisms from the data.
Each component dose and its median-effect dose must use compatible units, and both curves must describe the same effect definition and assay conditions. The returned index is dimensionless. It is not a measured mixture response or a statistical test of synergy.
When to use Combination Index
Use it to reproduce a specified nonexclusive median-effect calculation after fitting single-agent curves and identifying a common target affected fraction.
How to use Combination Index and interpret its calculation
- Enter exactly two componentDoses, medianEffectDoses, and medianEffectSlopes in corresponding agent order. Component doses may be zero; median-effect doses and slopes must be positive.
- Enter targetAffectedFraction strictly between 0 and 1 and run the calculation.
- Read singleAgentTargetDoses, doseRatios, and nonexclusiveCombinationIndex. Verify that the tested combination produces the intended effect before interpreting the index.
Dx_i = Dm_i × [fa/(1 − fa)]^(1/m_i); r_i = D_i/Dx_i; CI = r1 + r2 + r1 × r2 Dm is the median-effect dose, m the supplied slope, fa the target affected fraction, and D the mixture dose.
The implementation first inverts each supplied curve at the target, then normalizes the component dose by that target dose. An index below one, equal to one, or above one is below, on, or above this chosen reference, respectively; interpretation requires effect-matched experimental evidence.
{
"input": {
"componentDoses": [
2,
4
],
"medianEffectDoses": [
10,
20
],
"medianEffectSlopes": [
1,
1
],
"targetAffectedFraction": 0.5
},
"output": {
"singleAgentTargetDoses": [
10,
20
],
"doseRatios": [
0.2,
0.2
],
"nonexclusiveCombinationIndex": 0.44
}
}At target fraction 0.5, each single-agent target dose equals its median-effect dose. Zero component doses are accepted; both zero give index zero, which is not evidence that zero dose produces the target effect. Target fractions zero and one are rejected.
Limitations and assumptions
No single-agent fitting, observed combination response, confidence interval, or mechanism selection is performed. Input doses alone cannot establish synergism or antagonism.
The product term makes this index different from a simple dose-addition sum. Extreme fractions or fitted parameters can produce nonfinite intermediate results and be rejected.
Alternative or Complementary methods
Use a straight-line isobole when the intended reference is the sum of normalized doses without a product term. Independent action combines supplied effect fractions under a different assumption and should be reported by its own model name.
References
Similar or alternative tools
- Isobologram Analysis
Calculate the simple two-agent dose-ratio sum and its signed deviation from one.
- Independent Action Mixture
Combine supplied component effect fractions through independent unaffected fractions.