PHARM/PCS V5 · Procedure 47 Special Methods
Litchfield and Wilcoxon II
Go beyond the ED50: get ED16 and ED84 with confidence limits, and compare two drugs with a potency ratio and its limits.
What it computes
Extension of Procedure 46: computes ED16, ED84, and their confidence limits, plus the potency ratio and its confidence limits when comparing two quantal dose-response curves.
Inputs and outputs
You provide
- The first drug's data, in the same three columns as Procedure 46: dose, number responding, and number in the group
- Optionally, a second drug in the same format, for a potency comparison
PHARM/PCS reports
- ED50, ED16, and ED84, each with confidence limits
- With two drugs: the potency ratio, its confidence limits, and whether it is significant
- The probit plot against log dose
When to use it
When you want more than the ED50: the ED16 and ED84 that characterize the curve's steepness, or a potency ratio between two quantal curves with confidence limits. It builds directly on Procedure 46 and shares its data format.
Reading the results
The spread between ED16 and ED84 reads out the slope: a narrow spread means a steep, uniform response; a wide one, a shallow curve and a less precise ED50. A potency ratio here carries the same parallelism caveat as the graded case: it's meaningful only when the two curves are parallel.
Faithful to the original method
The procedure implements the full set of Litchfield-Wilcoxon equations, 47.1 to 47.10, and every value in the book's two-drug worked example reproduces within rounding. That includes a potency ratio of 37.1 with limits of 12.5 to 110.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.