Emax Model Calculator

Explicit independently fitted E0+Emaxincrement*d/(ED50+d) response model with nonzero baseline and signed increment. Not the existing normalizedHillEC50fit or a dose recommendation; model fitting, endpoint and extrapolation applicability external.

Description

An Emax model describes a saturating response relative to a fitted baseline.

An Emax model describes a saturating response relative to a fitted baseline.^[1]

A signed maximum response increment allows the modeled response to increase or decrease with dose.

When to use Emax Model Calculator

Use this tool to calculate or review the supplied observations under the stated rules. Establish the chemical, exposure route, endpoint, measurement basis and independently applicable assay or assessment reference.

How to use Emax Model Calculator and understand its results

Establish the chemical, exposure route, endpoint, measurement basis and independently applicable assay or assessment reference.
Enter callerIndependentlyFittedBaselineResponse, callerIndependentlyFittedMaximumResponseIncrement, callerIndependentlyFittedHalfMaximumDose, actualDose, using the field meanings and rules below, then run the tool.
Read result.conditionalEmaxResponse. Use the units and subtraction order below to interpret each value; retain negative differences where returned.
Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.

Input field	Meaning	Value type	Requirement
callerIndependentlyFittedBaselineResponse	Caller independently fitted baseline response	number	Required
callerIndependentlyFittedMaximumResponseIncrement	Caller independently fitted maximum response increment	number	Required
callerIndependentlyFittedHalfMaximumDose	Caller independently fitted half maximum dose	number	Required
actualDose	Actual dose	number	Required

Require a finite baseline and maximum increment, a positive ED50 coordinate and a nonnegative dose. Baseline and increment may be signed. Evaluate the supplied saturable model; the implementation does not fit parameters or constrain the modeled response to a probability range.

response=baseline+maximumIncrement×dose/(ED50+dose)

Use the matching field units and the exact boundary, ordering and reference rules above.

Output field	Meaning	Value type
result	Qualified observed calculation or explicit reference	object
result.conditionalEmaxResponse	Response from the supplied baseline, signed maximum increment and half-maximum dose model.	number

json

{
  "input": {
    "callerIndependentlyFittedBaselineResponse": 1,
    "callerIndependentlyFittedMaximumResponseIncrement": 4,
    "callerIndependentlyFittedHalfMaximumDose": 2,
    "actualDose": 2
  },
  "output": {
    "result": {
      "conditionalEmaxResponse": 3
    }
  }
}

Limitations and assumptions

Chemical identity, route, assay, exposure basis and reference applicability are caller-established. The output supplies no causal conclusion, universal toxicity threshold or authoritative regulatory determination.

Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Extremely large composite outputs are rejected.

Alternative or Complementary methods

For a related step, use Relative Potency Factor Calculator: Relative potency can vary across matched effect levels when response relationships are not parallel. For a complementary comparison, use Probit Slope Calculator: A probit slope describes a relationship between independently transformed response scores and a stated dose coordinate.

References

Emax Model Calculator — tool.io

Similar or alternative tools

Relative Potency Factor Calculator
Relative potency can vary across matched effect levels when response relationships are not parallel.
Probit Slope Calculator
A probit slope describes a relationship between independently transformed response scores and a stated dose coordinate.