Optimal statistical design of radioimmunoassays and competitive protein-binding assays.

The statistical analysis of radioimmunoassay and competitive protein binding assay data is complex. Because the response variable (percent counts) is not lineraly related to log dose, a logit transformation of the response variable usually is performed to permit linear regression analysis. This transformation induces marked heterogeneity of variance, so that iterative weighted regression programs have been used to achieve the best standard curve and the most precise dose estimates of unknowns. In this study several parameters of assay design are investigated in order to establish those designs yielding antigen concentration estimates of highest precision as well as estimates of comparable precision by either simple linear regression analysis or by the more complex weighted regression technique. Unknown estimates of highest precision are obtained when 1) the present counts of the standard doses covers a range of approximately 80 percent to 20 percent, 2) the number of standard dose levels is eight or more, 3) the number of replicates at each dose level is two or more, and 4) the percent counts of the unknowns also are within the range 80 percent ot 20 percent. Under these conditions, also, simple linear regression yields unknown estimates of comparable precision to weighted regression and therefore may be safely used.