Analysis of Parallel-Line Assays with Multivariate Responses

Abstract

A purpose of comparative parallel-line quantitative assays is to estimate the relative potency of a test drug relative to a standard drug. In a multivariate parallel-line assay several response variables will be measured. One such example occurs when a quantitative response variable is measured over time. In this paper we derive a closed form for the likelihood ratio tests for two hypotheses of interest. We first test for equal slopes; then we test to see if the potency is constant for all response variables. Finally, we present a procedure for obtaining point and interval estimators for relative potency. The procedure allows for covariables and block effects to be included in the analysis. The multivariate approach of this paper has been applied to a single-agent multivariate quantal assay, where the estimation of the median effective dose is the primary purpose. An analysis for this situation appears in Carter and Hubert (1984) and Hubert (1984). Suppose that a standard drug is administered to m experimental units in dosages di1, dim, and a test drug is administered to n experimental units in dosages d21, ..., d2n. The dose metameter is defined to be xij = logio(dij). A response variable Yij is then measured over p characteristics producing the response y[! = (yl, . . . , yp). A general linear model for the experiment may be written as