Description
Stable supplied Hill/Emax research response and logit.
A pharmacodynamic model relates an exposure or occupancy measure to a response under explicitly supplied parameters. Baseline, maximum increment, half-maximal concentration, effect direction, and observation windows have distinct meanings. Evaluating one model term does not fit the curve or establish its clinical validity.
Stable supplied Hill/Emax research response and logit.
When to use this tool
Use Sigmoid Emax Logit Slope Term when you need this particular response-model term, scale conversion, panel duration, or support calculation.
How to use the tool and how it works
- Enter concentration, ec50, hill, baseline, maximumEffect. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read fraction, logit, effect. Use the output convention below.
For positive concentration, ec50, and hill compute logit=hill*(ln(concentration)-ln(ec50)). Evaluate its logistic fraction using separate positive and negative logit branches, then return effect=baseline+maximumEffect*fraction.1
A sigmoid Emax model uses a half-maximal concentration and a Hill steepness parameter. Evaluating supplied parameters and estimating them reliably from an exposure-response study are separate tasks.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| concentration | Exposure concentration in the same unit as ec50. | Required. Finite number; strictly above 0. |
| ec50 | Positive concentration producing half the maximum increment under the supplied model. | Required. Finite number; strictly above 0. |
| hill | Positive dimensionless Hill steepness parameter. | Required. Finite number; strictly above 0. |
| baseline | Supplied response level at the model's zero-effect baseline. | Required. Finite number. |
| maximumEffect | Signed maximum response increment above baseline; not the final asymptote. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| fraction | Dimensionless fraction under the stated basis. | Required. Finite number. |
| logit | Hill times natural log concentration ratio; a dimensionless model logit. | Required. Finite number. |
| effect | Effect | Required. Finite number. |
{
"input": {
"concentration": 4,
"ec50": 2,
"hill": 2,
"baseline": 1,
"maximumEffect": 10
},
"output": {
"fraction": 0.8,
"logit": 1.3862943611198906,
"effect": 9
}
}Limitations and assumptions
- Concentration and EC50 need the same unit. MaximumEffect is an increment from baseline and may be signed; this evaluates supplied sigmoid parameters without fitting a response curve, establishing a mechanism, or recommending treatment.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a fitted and validated response model when a supplied local term is insufficient. Check exposure units, response direction, baseline, model assumptions, and observation support before comparing effects.
References
-
Calculation and input contract: pharmacodynamics/sigmoid-emax-logit-slope-term — tool.io
-
Donghwan Lee: Parameter estimation for sigmoid Emax models in exposure-response relationship (2017) — Translational and Clinical Pharmacology
Similar or alternative tools
- Emax One Concentration Response Term
Evaluate a supplied one-site research Emax curve without fitting or clinical interpretation.
- PD Hill Curve Halfmax Residual
For positive concentration and ec50 and observedFraction in [0,1] return logConcentrationGap=ln(concentration)-ln(ec50) and halfmaxResidual=observedFraction-0.5.