Independent Action Mixture
Apply independent action as one minus the product of unaffected fractions; statistical independence and compatible effect definitions are caller assumptions.
Description
Predict a mixture effect fraction by multiplying unaffected fractions under independent action.
Independent action, also called response addition, combines component effects under an independence assumption. Each component leaves an unaffected fraction; multiplying those fractions gives the fraction predicted to remain unaffected by all components.1
Supply component effect fractions for their actual mixture doses, using the same response definition, population, and time horizon. Enter 20% as 0.2. These values are response fractions, not concentrations, dose ratios, or hazard quotients.
The tool returns complementary affected and unaffected fractions between zero and one. It predicts a reference response without receiving a measured mixture response, so it cannot determine whether the observed mixture departs from that reference.
When to use Independent Action Mixture
Use it to reproduce an independent-action prediction from already established component responses, or compare that reference with another explicitly named mixture model.
How to use Independent Action Mixture and interpret its calculation
- Enter a nonempty componentEffectFractions list with each value between 0 and 1.
- Confirm the component responses describe the intended mixture doses and compatible endpoints, then run the calculation.
- Read predictedCombinedEffectFraction and remainingUnaffectedFraction. Compare any observed mixture response separately with appropriate uncertainty.
remaining unaffected = product(1 − effect_i); predicted combined effect = 1 − remaining unaffected The prediction multiplies complements rather than adding the affected fractions.
The implementation folds over the list starting from an unaffected fraction of one. Component order does not affect the mathematical result, and no dose-response curve is fitted or inverted.
{
"input": {
"componentEffectFractions": [
0.2,
0.3
]
},
"output": {
"predictedCombinedEffectFraction": 0.44,
"remainingUnaffectedFraction": 0.56
}
}A zero component effect leaves the prediction unchanged. Any component effect of one gives combined effect one. A single component returns its supplied effect, while an empty list or any fraction outside 0–1 is rejected.
Limitations and assumptions
Statistical independence is a model assumption, not something this calculator tests. Correlated responses, shared targets, altered exposure, and interactions can invalidate it.
No observed mixture response, confidence interval, effect-dose matching check, or mechanistic classification is included. A reference prediction is not evidence of synergism, antagonism, or population-level risk without further analysis.
Alternative or Complementary methods
Concentration addition uses potency-normalized concentrations and a shared response model instead of multiplying unaffected fractions. A combination index is another reference comparison with different inputs and conventions.
References
-
Guidelines for the Health Risk Assessment of Chemical Mixtures (1986) — U.S. Environmental Protection Agency
Similar or alternative tools
- Concentration Addition Mixture
Predict response from EC50-normalized concentrations under a common Hill slope.
- Combination Index
Compare two component doses with fitted single-agent target doses using a nonexclusive index.