Subject-by-Formulation Interaction in Determinations of Individual Bioequivalence: Bias and Prevalence

Abstract

Purpose. 1. To determine properties of the estimated variance component for the subject-by-formulation interaction (σ² _D) in investigations of individual bioequivalence (IBE), and 2. to evaluate the prevalence of interactions in replicate-design studies published by FDA.

Methods. Four-period crossover studies evaluating IBE were simulated repeatedly. Generally, the true bioequivalence of the two formulations, including σ² _D= 0, was assumed, σ² _D was then estimated in a linear mixed-effect model by restricted maximum likelihood (REML). The same method was applied for estimating σ² _D for the data sets of FDA.

Results. 1.σ_D estimated by REML was positively biased. The bias and dispersion of the estimated σ_Dincreased approximately linearly with the estimated within-subject standard deviation for the reference formulation (σ_WR). Only a small proportion of the estimated σ_D exceeded the estimated σ_WR. 2. Distributions of the estimated σ_D were evaluated. At σ_WR = 0.30, a level of estimated σ_D= 0.15 was exceeded, by random chance, with a probability of about 25%. 3. Importantly, the behaviour of the σ² _D values estimated from the FDA data sets was similar to that exhibited by the simulated estimates of σ² _D which were generated under the conditions of true bioequivalence.

Conclusions. 1. σ_D estimated by REML is biased; the bias increases proportionately with the estimated σ_WR. Consequently, exceeding a fixed level of σ_D (e.g., 0.15) does not indicate substantial interaction. 2. The data sets of FDA are compatible with the hypothesis of σ² _D = 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.