Indicators of Evidence for Bioequivalence

Abstract

Some equivalence tests are based on two one-sided tests, where in many applications the test statistics are approximately normal. We define and find evidence for equivalence in Z-tests and then one-and two-sample binomial tests as well as for t-tests. Multivariate equivalence tests are typically based on statistics with non-central chi-squared or non-central F distributions in which the non-centrality parameter λ is a measure of heterogeneity of several groups. Classical tests of the null λ ≥ λ 0 versus the equivalence alternative λ < λ 0 are available, but simple formulae for power functions are not. In these tests, the equivalence limit λ 0 is typically chosen by context. We provide extensions of classical variance stabilizing transformations for the non-central chi-squared and F distributions that are easy to implement and which lead to indicators of evidence for equivalence. Approximate power functions are also obtained via simple expressions for the expected evidence in these equivalence tests.

Multivariate Assessment for Bioequivalence Based on the Correlation of Random Effect

“…9 Although several average bioequivalence (ABE) studies have been generated, there are a limited number of multivariate analyses. 9,12,25,26 In the present study, we adapted an advanced bioequivalence test model based on multivariate analysis for pharmacokinetic studies and compared the results from a multivariate HGLM and two conventional independent LMMs in real datasets. Because pharmacokinetic parameters such as AUC and C max are highly correlated, these correlations need to be incorporated into the multivariate model, which deals with multiple endpoints simultaneously.…”

“…2 , 9 , 24 Although these markers were relatively independent of AUC, their usefulness is limited due to the low power caused by their discrete nature or the assumption of normality for random effects. 25 , 26 Essentially, bioequivalence is a multivariate endpoint from the same biological sample measurements, and correlation between primary endpoints has to be considered for clearly appropriate analysis. 9 , 27 However, currently accepted practice usually involves univariate bioequivalence analysis.…”

“… 9 Although several average bioequivalence (ABE) studies have been generated, there are a limited number of multivariate analyses. 9 , 12 , 25 , 26 …”

Evidence for goodness of fit in Karl Pearson chi-squared statistics

“…In Section 1.3 the evidence against the desired model in the chi-squared statistic and the calibration scale for this evidence is described, based on earlier work by Kulinskaya et al (2008), Morgenthaler & Staudte (2012, 2013, 2016. It is then shown that this evidence is essentially an estimate of the square root of the symmetrized Kullback & Leibler (1951) divergence between the null and alternative chi-square models.…”

“…It works! Why it works was explained when a foundational rationale for this calibration scale was described in Morgenthaler & Staudte (2012, 2013, 2016, for exponential families, among others; and for the difference of two proportions in Prendergast & Staudte (2014).…”