An alternative definition of individual bioequivalence

Several definitions of individual bioequivalence of two formulations of a medical treatment (drug) have been proposed recently. These definitions attempt to adapt the criterion of average bioequivalence, which would be deficient if substantive treatment heterogeneity were present. In some of the proposed definitions, relatively large differences of means can be compensated by differences in the measurement-error variances. We propose a definition based on a simple latent-variable model which overcomes this anomaly and need not involve the U.S. Food and Drug Administration's 80/125 rule. Our approach is based on a moment-matching estimator of the discrepancy between the outcomes underlying the subjects' responses. The distribution of this estimator is a linear combination of independent χ² variates; asymptotically, it can be approximated by a normal distribution. Evidence of individual bioequivalence corresponds to rejecting the hypothesis that the discrepancy is greater than a specified threshold. The approach is illustrated by reanalysing two bioequivalence trials.