Statistical Methods in Bioequivalence Studies

Abstract

Bioequivalence studies are an essential part of the evaluation of generic drugs. The most common in-vivo bioequivalence (BE) study design is the two-period two-treatment crossover design. AUC (area under the concentration-time curve) and Cmax (maximum concentration) are obtained from the observed concentration-time profiles for each subject from each treatment under each sequence.

In the BE evaluation of pharmacokinetic crossover studies, the normality of the univariate response variable, e.g. log(AUC) or log(Cmax) is often assumed in the literature without much evidence. Therefore, we investigate the distributional assumption of the normality of response variables, log(AUC), log(Cmax), and log(Tmax) by simulating concentration-time profiles from the two-stage pharmacokinetic models for a wide range of pharmacokinetic parameters and measurement error structures. Our simulation shows that log(AUC) has heavy tails and log(Cmax) is skewed. We study the impact of the non-normality of response variable on the sample size and type I error rate.

Under the normality of the response variable, the most common approach to testing for bioequivalence is the two one-sided tests procedure. We develop the exact analytical formula for the probability of rejection in the two one-sided tests procedure for crossover bioequivalence studies under general parameter settings. Our exact formulas for power and sample size are shown to improve in realistic parameter settings over the previous approximations.

We propose a new unblinded sample size re-estimation strategy. The new total sample size is calculated from our exact power function for the one stage using the estimated variance from the Stage 1 as the true variance. If the sample variance from Stage 1 is smaller than the initial variance from the historical data, then we stop at the end of Stage 1 and analyze Stage 1 data with the standard t- quantile. Otherwise, we collect data from additional subjects. We then analyze the combined data from both Stage 1 and Stage 2 with a new test statistic using the pooled variance of two stages. The exact critical values for the new test statistics are derived as the largest of u for which the following condition holds: the experimentwise type I error rate is exactly alpha.