Asymmetry of the mean-variability tradeoff raises questions about the model in investigations of individual bioequivalence

Abstract

Tradeoff between changes of intraindividual variations of 2 drug formulations and of the difference between their means is a characteristic of a procedure suggested for the determination of individual bioequivalence [Schall and Luus 1993] and to be proposed by the Food and Drug Administration for adoption. Hauck et al. [1996] investigated properties of the tradeoff. Their procedure was applied and extended in the present study. The tradeoff was shown to be asymmetric. Notably, a small change in intrasubject variations can elicit, under various conditions, a comparatively large change in the allowable difference between means which can still be compatible with the declaration of bioequivalence. For instance, when the intraindividual coefficients of variations are 40% and 38% for the reference and test formulations, respectively, the allowable difference between means may increase, as a benefit, by 12.3%. A penalty by 11.2% is elicited if the intrasubject variations of the reference and test products are 40 and 42%, respectively. In addition, 4-period crossover trials were simulated. Ratios of estimated variances of the 2 formulations followed an F-distribution. Distributions of changes in allowable deviations between means were calculated from the tradeoff relationships; generally substantial changes were noted with high probabilities. For example, with an intraindividual variation of 30% there is an estimated 37% probability that a benefit of 10% increase, or larger, is gained by chance in the allowable difference between means, and an additional 36% probability that a penalty of a 10%, or larger, decrease in the allowable difference is suffered. With an intrasubject variation of 40%, the estimated probabilities are 42% and an additional 42% for a 10% expansion and contraction, respectively, of the allowable difference between means. Consequently, the strong asymmetry of the tradeoff could result in very large probabilities for benefits and penalties. Therefore, the investigated model assessing individual bioequivalence does not appear to be suitable for implementation.