A Parametric Confidence Interval for a Moment-Based Scaled Criterion for Individual Bioequivalence

Abstract

Confidence intervals of proposed individual bioequivalence metrics are difficult to determine in closed form because their stochastic distributions are unknown. In this article, it is shown that, with slightly modified weights, the Relative Individual Risk (RIR) moment-based scaled statistic for individual bioequivalence that was presented by Schall and Williams has an exact noncentral Fisherʼns F distribution with noncentrality parameter given by a scaled squared difference in formulations means. This can be approximated by a central F with adjusted degrees of freedom from which it follows that an upper (1-α) confidence bound for RIR is given by $UL = \frac{{(\widehat{RIR} + 1)}}{{F_{\alpha ,v,df_{ER} } }} - 1$ where is the least square estimate of RIR; df _ER is the degrees of freedom associated with the reference intrasubject variance estimate, ν is the subject-by-formulation degrees of freedom adjusted for noncentrality and α is the significance level. Individual bioequivalence is concluded if UL does not exceed the regulatory limit. The performance of this confidence interval was investigated by comparing its experimental bioequivalence rate to that of the unweighted metric under known parameter situations through simulations of two formulations in a fully replicated study design. Results showed that the proposed metric is slightly less biased and more precise than the unweighted metric.