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Combination of Multivariate Bioassay Results

Aage Vølund
Biometrics
Vol. 38, No. 1 (Mar., 1982), pp. 181-190
DOI: 10.2307/2530301
Stable URL: http://www.jstor.org/stable/2530301
Page Count: 10
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Combination of Multivariate Bioassay Results
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Abstract

A multivariate bioassay with r-dimensional response can be considered as a series of r univariate assays with correlated responses and potency estimates that are combined into a common estimate. The combination of a series of multivariate assays may, therefore, be regarded as a two-way combination of kr potency estimates. These arise from k independent assays, each with an r-dimensional response variable. Based on the generalized parallel-line dose-response model, and a multinormal response distribution, asymptotic likelihood ratio tests have been derived to test the homogeneity of the potencies. Also, the maximum likelihood estimate of the combined potency and its asymptotic confidence interval have been determined. These estimates may be calculated explicitly if the assays use the same design and dose levels; if not, an iterative method is required. The methods were developed for the combined analysis of repeated insulin bioassays, an example of which is given. Apart from a complete utilization of experimental data these multivariate methods permit a rather detailed analysis of the homogeneity of the potency from a series of multivariate assays.

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