Isobologram Analysis

Measure geometric deviation from a two-agent Loewe isobole at a caller-fixed effect level; negative deviations alone do not establish synergy without matched effects and uncertainty.

Description

Calculate normalized dose sums and signed departures from a two-agent straight-line additive isobole.

An isobologram compares doses of two agents that produce a specified effect. A straight-line dose-addition reference connects the doses at which each agent alone produces that same effect. A combination can then be compared with that reference using normalized dose contributions.^[1]

For this tool, each single-agent reference dose must correspond to the same effect level and experimental context as the mixture dose pairs. The tool receives doses only; it cannot verify that the observed effects match.

A normalized sum of one lies on the reference line. The signed deviation is the sum minus one: negative is below the line and positive is above it. These are geometric scores; evidence of synergy or antagonism also requires effect-matched data, justified assumptions, and uncertainty analysis.

When to use Isobologram Analysis

Use it to reproduce a two-agent dose-addition calculation for prepared, effect-matched dose pairs, or to inspect where hypothetical pairs fall relative to supplied reference doses.

How to use Isobologram Analysis and interpret its calculation

Enter exactly two positive singleAgentTargetDoses, one for each agent at the same target effect.
Enter a nonempty mixtureDosePairs matrix with two nonnegative doses per row. Match each column to its reference agent and use compatible units within that column.
Run the calculation and read normalizedDoseSums and additivityDeviations in row order. Confirm target-effect matching before interpreting interaction direction.

S = dA / DA + dB / DB; deviation = S − 1

DA and DB are single-agent target doses; dA and dB are mixture component doses.

The implementation calculates the two dose ratios and adds them. It does not fit a response curve, produce a plot, add a product interaction term, or calculate a statistical significance test.

json

{
  "input": {
    "singleAgentTargetDoses": [
      10,
      20
    ],
    "mixtureDosePairs": [
      [
        2,
        8
      ],
      [
        5,
        10
      ]
    ]
  },
  "output": {
    "normalizedDoseSums": [
      0.6,
      1
    ],
    "additivityDeviations": [
      -0.4,
      0
    ]
  }
}

A pair [0, 0] is numerically accepted and scores zero with deviation −1. It is not evidence that zero dose achieves the target effect. A zero reference dose or a row with other than two entries is rejected.

Limitations and assumptions

The straight-line reference assumes the relevant dose-addition relationship is appropriate at the chosen effect. Curved isoboles, varying relative potency, and alternative response-independence models can lead to different comparisons.

No measured effects, fitted parameters, confidence bounds, mechanism labels, or replicate variation are inputs. The signed deviation alone cannot establish a biological interaction.

Alternative or Complementary methods

Use fitted single-agent curves to establish target doses when they are not supplied directly. A nonexclusive median-effect combination index includes an additional product term, so its numerical score is not interchangeable with this simple dose sum.

References

Searching for Drug Synergy in Complex Dose–Response Landscapes Using an Interaction Potency Model (Yadav et al., 2015) — Computational and Structural Biotechnology Journal

Similar or alternative tools

Combination Index
Calculate target doses and a nonexclusive two-agent index from supplied median-effect fits.
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Compare combined mutations with a multiplicative fitness reference for a distinct interaction problem.