Subject-by-formulation interaction in determinations of individual bioequivalence: bias and prevalence

1. To determine properties of the estimated variance component for the subject-by-formulation interaction (sigma D2) in investigations of individual bioequivalence (IBE), and 2, to evaluate the prevalence of interactions in replicate-design studies published by FDA.

Four-period crossover studies evaluating IBE were simulated repeatedly. Generally, the true bioequivalence of the two formulations, including sigma D2 = 0, was assumed. sigma D2 was then estimated in a linear mixed-effect model by restricted maximum likelihood (REML). The same method was applied for estimating sigma D2 for the data sets of FDA.

1. sigma D estimated by REML was positively biased. The bias and dispersion of the estimated sigma D increased approximately linearly with the estimated within-subject standard deviation for the reference formulation (sigma WR). Only a small proportion of the estimated sigma D exceeded the estimated sigma WR. 2. Distributions of the estimated sigma D were evaluated. At sigma WR = 0.30, a level of estimated sigma D = 0.15 was exceeded, by random chance, with a probability of about 25%. 3. Importantly, the behaviour of the sigma D2 values estimated from the FDA data sets was similar to that exhibited by the simulated estimates of sigma D2 which were generated under the conditions of true bioequivalence.

1. sigma D estimated by REML is biased; the bias increases proportionately with the estimated sigma WR. Consequently, exceeding a fixed level of sigma D (e.g., 0.15) does not indicate substantial interaction. 2. The data sets of FDA are compatible with the hypothesis of sigma D2 = 0. Consequently, they do not demonstrate the prevalence of subject-by-formulation interaction. Therefore, it could be sufficient and reasonable to evaluate bioequivalence from 2-period crossover studies.