An Experimental Design for Slope-Ratio Assays

When the response to a drug is a linear function of arithmetic dosage units, the relative potency of two preparations can be computed as a slope-ratio assay. Their dosage-response curves are computed by solving three simultaneous equations to obtain the common intercept $a'$, the slope of the standard, $b_1$, and the slope of the unknown, $b_2$. The method is applicable to certain microbiological assays for the vitamins. Usually several unknowns are assayed at one time with a single standard. Their calculation is simplified when such assays meet the following requirements: (1) restriction of treatments to the zone within which the response is related linearly to the dose, (2) equal spacing of doses on an arithmetic scale beginning with the negative control, (3) an equal number $(k)$ of doses of standard and of each unknown and (4) $r$ replicates for each dose of unknown, $h'$ replicates for the negative control and $h$ replicates for each dose of the standard.