PHARM/PCS V5 · Procedure 11 Dose-Response and Potency
Relative Potency II: Statistical Analysis
Put confidence limits on a potency ratio, the step that makes the ratio defensible in a report or a publication.
What it computes
Like Procedure 10 but computes 95% (or other) confidence limits on the potency ratio. Requires equal numbers of points (N>2) on each line and the same set of log-dose levels for both drugs. The two regression lines are made parallel via Procedure 7's common-slope construction, and the confidence interval comes from solving the quadratic (Equation 11.3) of Bliss's analysis.
Inputs and outputs
You provide
- Test drug data first, then the standard, each with the same number of points (more than two) at the same log-dose levels
- A confidence level
PHARM/PCS reports
- The common slope of the parallel lines
- Relative potency with asymmetric confidence limits
- A plot of effect against log dose for both preparations
When to use it
When the potency ratio from Procedure 10 needs error bounds for a report or publication; the confidence limits are what make the ratio defensible. Use it once Procedure 6 confirms parallelism and your design meets the equal-N, matched-dose requirement.
Reading the results
The limits are asymmetric because a ratio is a quotient (Fieller's method, which gives the asymmetric confidence limits a ratio requires), so expect uneven spread around the point estimate, and treat very wide or unbounded limits as a warning that the common slope is poorly determined. The Ratio of Means (Procedure 41) applies the same method to ratios outside the potency setting.
More precise than the printed example
The book's worked example rounds intermediate values by hand. V5 carries full precision throughout, and its relative potency of 7.8985 matches the 1986 computer report exactly. Any confidence level is available, where the original was effectively limited to 95% and 99%.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.