Bayesian Construction of an Improved Parametric Test for Probability-Based Individual Bioequivalence

• Published in: Biometrical journal Vol. 42; no. 8; pp. 1039 - 1052
• Main Author: Wellek, Stefan
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag Berlin GmbH 01.12.2000; WILEY‐VCH Verlag Berlin GmbH; Wiley-VCH
• Subjects: Distribution theory; Exact power function; Exact sciences and technology; Gauss-Legendre integration; individual bioequivalence; Mathematics; Nonparametric inference; Parametric inference; Probability and statistics; reference prior; Sciences and techniques of general use; Statistics; TIER; Parameter estimation; Bioequivalence; Statistical theory; Non parametric estimation; Probability distribution; Numerical method; Rejection region; Computing; Bayes construction; Gauss Legendre integration; Hypothesis test; Numerical computation; Distribution function; Bayes test; Bayes estimation; Integration; Gauss method; Statistical estimation; Bioavailability; Mean value; Algorithm; Scaling law; Reference model; Posterior probability; Anderson model; Power comparison; Parametric test
• ISSN: 0323-3847; 1521-4036
• DOI: 10.1002/1521-4036(200012)42:8<1039::AID-BIMJ1039>3.0.CO;2-1

Assuming a lognormally distributed measure of bioavailability, individual bioequivalence is defined as originally proposed by Anderson and Hauck (1990) and Wellek (1990; 1993). For the posterior probability of the associated statistical hypothesis with respect to a noninformative reference prior, a numerically efficient algorithm is constructed which serves as the building block of a procedure for computing exact rejection probabilities of the Bayesian test under arbitrary parameter constellations. By means of this tool, the Bayesian test can be shown to maintain the significance level without being over‐conservative and to yield gains in power of up to 30% as compared to the distribution‐free procedure which gained some popularity under the name TIER. Moreover, it is shown that the Bayesian construction also allows scaling of the probability‐based criterion with respect to the proportion of subjects exhibiting bioequivalent responses to repeated administrations of the reference formulation of the drug under study.