PHARM/PCS V5 · Procedure 8 Dose-Response and Potency
Graded Dose-Response
Fit a graded dose-response line and get the A50, the dose giving half the maximal effect, with confidence limits.
What it computes
Fits a regression line to log(dose) vs. effect for points between 20% and 80% of Emax, then reports the slope, intercept, and A50 (dose giving half-maximal effect) with confidence limits.
Inputs and outputs
You provide
- Dose and effect, one pair per line
- Emax, or leave it blank to have it estimated
- Optionally, how many of the smallest doses to leave out of that estimate
- A confidence level
PHARM/PCS reports
- The estimated Emax, when you did not supply one
- Slope and intercept of the log-dose line
- A50 and log A50, with its standard error and confidence limits
- A plot of effect against log dose, with the fitted line
When to use it
For a continuously graded response (contraction force, blood-pressure change, enzyme rate) measured across doses, when you want the A50, the dose producing half-maximal effect. This is the graded counterpart to the quantal (all-or-none) analysis in Procedure 9; to compare two graded curves, use potency Procedures 10 and 11.
Reading the results
The fit deliberately restricts to the 20-80% band, where log-dose vs. effect is most linear; points near the floor or ceiling curve away and would bias the slope. If an estimated Emax comes back negative or implausible, drop the smallest doses and refit, since a bad Emax poisons the A50.
When you do not know the maximum
Leave Emax blank and the procedure estimates it from a double-reciprocal plot of 1/E against 1/D, then fits the 20 to 80 percent band. The standard error of log A50 uses Bliss's inverse-regression formula and matches the book's printed 0.0344723 exactly.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.