Generalization of distribution--free confidence intervals for bioavailability ratios

Abstract

The confidence interval approach to bioavailability assessment depends first on selection of the confidence level, usually 95%, and then determination of the confidence limits for the expected bioavailability ratio AUC(Test)/AUC(Reference). In practice, however, it is sometimes of greater interest to know the probability that the expected bioavailability will fall below a critical value, for example 0.75, or within a clinically set bioequivalence range, for example 0.80 to 1.25. Up to now, posterior probability distributions have been suggested, based on classical analysis of variance (ANOVA) with its rather restrictive assumptions, including that of a (logarithmic) normal distribution. In this report, a distribution-free confidence interval based on the Wilcoxon signed-rank statistic has been generalized so that confidence probabilities can be obtained for any given confidence limits. In the case of unimodal and almost symmetrical sampling distributions, the results obtained are very similar to those of the ANOVA-based posterior probability distribution. However, skewed or multimodal sampling distributions are better reflected by the proposed distribution-free method, and more valid information is obtained in these cases, as demonstrated by examples.