PHARM/PCS V5 · Procedure 9 Dose-Response and Potency
Quantal Dose-Response: Probits
Turn percent-responding data into probits and read the ED50, ED16, and ED84 straight from a fitted line.
What it computes
For an all-or-none endpoint (sleep/no sleep, dead/alive, response/no response), the percent of subjects responding is plotted against log dose. Converting percent responding to probit values straightens the S-shaped curve into a line. Linear regression of probit on log(dose) then yields ED50, ED16, and ED84 directly.
Inputs and outputs
You provide
- Log dose and percent responding, one pair per line
PHARM/PCS reports
- The probit regression line, slope and intercept
- ED50, ED16, and ED84
- A probit plot of the data and the fitted line
When to use it
When each subject either responds or doesn't and you want a median effective (or lethal) dose from the proportion responding at each level. This is the all-or-none counterpart to graded Procedure 8; for confidence limits on the ED50 by the Litchfield-Wilcoxon route, see Procedures 46 and 47.
Reading the results
The probit transform straightens the sigmoid, so a straight line is expected; systematic curvature suggests a mixed population, or that log dose isn't the right scale. Groups at 0% or 100% carry no probit and must be corrected or dropped; ED16 and ED84 flank ED50 at ±1 probit and read out the slope (steepness reflects uniformity of susceptibility).
No probit table needed
The 1986 program read probits from the book's Table A.3. V5 computes them directly from the inverse normal distribution, which is slightly more accurate: for the book example the ED50 differs from the printed value by 0.01%. For confidence limits on the ED50, the Litchfield-Wilcoxon procedures, 46 and 47, take the analysis further.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.