Combination Index Calculator: How to Use It

The combination index (CI) calculator determines whether two or more drugs interact synergistically, additively, or antagonistically based on their individual and combined dose-response data. You enter the doses (or concentrations) of each drug needed to achieve a given effect alone and in combination, and the calculator returns a CI value where CI < 1 indicates synergy, CI = 1 indicates additivity, and CI > 1 indicates antagonism. This tool is widely used in pharmacology and cancer research to design multi-drug regimens.

Formula

The most common formula for two drugs is the isobologram equation:

CI = (C₁ / D₁) + (C₂ / D₂)

• C₁ = dose of drug 1 in the combination that produces a given effect (e.g., 50% inhibition)
• D₁ = dose of drug 1 alone that produces the same effect
• C₂ = dose of drug 2 in the combination that produces that effect
• D₂ = dose of drug 2 alone that produces that effect

All doses must be in the same units (e.g., mg/kg, µM). The CI is unitless. For three or more drugs, the equation extends to the sum of all (C_i/D_i) terms.

Worked Example

Using the defaults from the calculator: Drug 1 alone requires 10 mg for 50% effect, drug 2 alone requires 20 mg. In combination, only 5 mg of drug 1 and 10 mg of drug 2 are needed for the same effect.

1. Compute the ratio for drug 1: 5 / 10 = 0.5
2. Compute the ratio for drug 2: 10 / 20 = 0.5
3. Add the ratios: 0.5 + 0.5 = 1.0

The CI is 1.0, which means the combination is purely additive. If the combination doses were lower (e.g., 4 mg and 8 mg), the CI would be 0.8, indicating synergy.

When to Use the Combination Index

The CI is used when you have dose-response data for each drug alone and for the combination at a fixed ratio. It is most valid when the dose-response curves are parallel and the effect level is the same (e.g., IC50). Common applications include:

• Cancer combination chemotherapy screening
• Antimicrobial combination testing
• Evaluating drug-herb or drug-supplement interactions
• Optimizing dosing to reduce toxicity while maintaining efficacy

The CI is a snapshot at one effect level. You often calculate it at multiple effect levels (e.g., IC25, IC50, IC75) to see if synergy changes with dose.

How to Choose the Right Model

The simple CI formula above assumes mutually exclusive drug action (both drugs act on the same pathway). If the drugs act independently, the mutually non-exclusive formula is more appropriate:

CI = (C₁/D₁) + (C₂/D₂) + (C₁×C₂)/(D₁×D₂)

This adds a product term, which always gives a higher CI (less synergy) than the simple formula. The Chou-Talalay method (a widely cited approach) uses a median-effect equation that incorporates the slope of the dose-response curve. Most modern software (like CompuSyn or CalcuSyn) uses that method, but the basic CI calculator here gives a quick estimate when you only have the effective doses.

Common Mistakes and Pitfalls

• Mixing units: All doses must be in the same unit. Convert mg to µg or µM to nM before calculating.
• Using different effect levels: D₁ and C₁ must correspond to the same effect (e.g., both IC50). If drug 1 alone gives 50% at 10 mg but the combination gives 70%, the CI is not valid.
• Ignoring the slope: The simple formula assumes parallel dose-response curves. If slopes differ significantly, the CI may be misleading.
• Rounding too early: Keep at least three significant figures in intermediate steps.

Limitations of the Combination Index

The CI is a mathematical description, not a biological proof. It cannot distinguish between true synergy and experimental error. It also assumes that the drugs do not affect each other’s metabolism or distribution. In vivo, drug interactions can be pharmacokinetic (e.g., one drug inhibits the other’s clearance) rather than pharmacodynamic, which the CI does not capture. Always validate CI results with independent experiments, such as isobolograms or combination dose-response curves.

Frequently Asked Questions

What does a CI of 0.5 mean?

A CI of 0.5 indicates moderate synergy: the combination achieves the same effect using only half the dose that would be predicted from the individual drugs. The lower the CI, the stronger the synergy. A CI of 0.7–0.9 is often considered slight synergy, while below 0.3 is strong synergy.

Can I use the CI for more than two drugs?

Yes, the formula extends to any number of drugs: CI = Σ (C_i/D_i). For three drugs, add the third ratio. The mutually non-exclusive version becomes more complex with multiple interaction terms, but the simple additive version works for a quick estimate.

What if my drugs have different units?

You must convert all doses to the same unit. For example, if drug 1 is in mg/kg and drug 2 is in µg/mL, convert both to molar concentrations (µM) or to the same mass unit. The CI is unitless, but only if the ratios are consistent.

Is a CI of exactly 1 always additive?

Yes, mathematically CI = 1 means the combination effect equals the sum of individual effects (additivity). In practice, due to experimental variability, values between 0.9 and 1.1 are often considered additive. Statistical analysis (e.g., confidence intervals) is needed to determine if a deviation from 1 is significant.

Does the CI change with the effect level?

It can. Synergy may be present at low effect levels but not at high ones, or vice versa. That’s why researchers often calculate CI at multiple effect levels (e.g., IC25, IC50, IC75) and plot CI versus fraction affected (Fa). A CI that remains below 1 across a wide range indicates robust synergy.

What is the difference between CI and isobologram?

An isobologram is a graph that shows the combination doses needed for a fixed effect. The line connecting the individual effective doses (D₁ and D₂) represents additivity. Points below the line indicate synergy, points above indicate antagonism. The CI is the numerical expression of that same relationship: CI = (C₁/D₁) + (C₂/D₂).

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in d1 | Dose of drug 1 alone | mg | 10 | 0
in d2 | Dose of drug 2 alone | mg | 20 | 0
in c1 | Dose of drug 1 in combination | mg | 5 | 0
in c2 | Dose of drug 2 in combination | mg | 10 | 0
out ci | Combination Index (CI) | - | (c1/d1) + (c2/d2) | 3
out fa | Fraction affected (Fa) | - | 0.5 | 2