Multivariate bioassay, combination of bioassays, and Fieller's theorem

In this paper alternative methods for estimating the relative potency, its confidence intervals, and testing for proportionality are developed for multivariate bioassays. The test and estimate are based on the smaller characteristic root and the corresponding characteristic vector of a 2 X 2 matrix. The same idea is applied in combining several symmetric parallel-line bioassays. Also, multivariate versions of Fieller's theorem are explicitly stated to obtain exact and asymptotic confidence intervals for the relative potency.