PHARM/PCS V5 · Procedure 46 Special Methods
Litchfield and Wilcoxon I: Confidence Limits of ED50
Estimate an ED50 or LD50 with 95% confidence limits from all-or-none dose-response data, using every dose, including the 0% and 100% groups.
What it computes
Computes the ED50 and its 95% confidence limits from quantal dose-response data with 0% and 100% endpoints corrected via Table A.12. Uses a two-pass probit regression.
Inputs and outputs
You provide
- For each dose: the dose, the number responding, and the number in the group
PHARM/PCS reports
- ED50 with 95% confidence limits
- The probit plot against log dose
When to use it
When you need an ED50 (or LD50) with defensible confidence limits from all-or-none dose-response data, the classic bioassay endpoint. It's a more complete treatment than the basic probit fit (Procedure 9); Procedure 47 extends it to ED16/ED84 and potency comparisons.
Reading the results
The Litchfield-Wilcoxon method specifically handles the awkward 0% and 100% points a plain probit regression can't use, correcting rather than discarding them. Its confidence limits depend on the fitted slope, so a shallow or poorly-determined slope widens them considerably; read the slope alongside the ED50.
Nothing thrown away
Plain probit regression cannot use a dose where no animal, or every animal, responded. The Litchfield-Wilcoxon method corrects those 0% and 100% points with the book's Table A.12 instead of discarding them. V5 computes probits directly rather than reading them from a table, and the book's worked example reproduces exactly, including the published limits of 3.48 to 5.43.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.