Description
Hill response sensitivity to natural log concentration at a supplied occupancy fraction.
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.
Hill response sensitivity to natural log concentration at a supplied occupancy fraction.
When to use this tool
Use PD Log Concentration Effect Elasticity 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 fraction, hill, maximumEffect. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read fractionSlope, effectSlope, relativeElasticity. Use the output convention below.
For fraction in [0,1] and positive hill return fractionSlope=hill*fraction*(1-fraction), effectSlope=maximumEffect*fractionSlope, and relativeElasticity=hill*(1-fraction).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| fraction | Dimensionless fraction under the stated basis. | Required. Finite number; minimum 0; maximum 1. |
| hill | Positive dimensionless Hill steepness parameter. | Required. Finite number; strictly above 0. |
| maximumEffect | Signed maximum response increment above baseline; not the final asymptote. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| fractionSlope | Derivative of fraction with respect to natural log concentration. | Required. Finite number. |
| effectSlope | Effect Slope | Required. Finite number. |
| relativeElasticity | Hill*(1-fraction); fractional-response elasticity, with an endpoint formula limit. | Required. Finite number. |
{
"input": {
"fraction": 0.5,
"hill": 2,
"maximumEffect": 10
},
"output": {
"fractionSlope": 0.5,
"effectSlope": 5,
"relativeElasticity": 1
}
}Limitations and assumptions
- Slopes are with respect to natural log concentration under the Hill model. RelativeElasticity refers to the fractional response, not the baseline-inclusive effect; its zero-fraction value is a formula limit rather than a defined observed log response.
- 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
Similar or alternative tools
- Sigmoid Emax Logit Slope Term
Stable supplied Hill/Emax research response and logit.
- Emax One Concentration Response Term
Evaluate a supplied one-site research Emax curve without fitting or clinical interpretation.