Sample size determination in bioequivalence studies using statistical assurance

Bioequivalence (BE) trials aim to demonstrate that the 90% confidence interval of the T/R-ratio of the pharmacokinetic metrics between two formulations (test [T] and reference [R]) of a drug is fully included in the acceptance interval [0.80, 1.25]. Traditionally, the sample size of BE trials is based on a power calculation based on the intrasubject variability coefficient of variation (CV) and the T/R-ratio of the metrics. Since the exact value of the T/R-ratio is not known prior to the trial, it is often assumed that the difference between the treatments does not exceed 5%. Hence, uncertainty about the T/R-ratio is expressed by using a fixed value for the sample size calculation. We propose to characterise the uncertainty about the T/R-ratio by a (normal) distribution for the log(T/R-ratio), with an assumed mean of  log θ = 0.00 (i.e. θ = 1.00) and a standard deviation σ_u , which quantifies the uncertainty. Evaluating this distribution leads to the statistical assurance of the BE trial.

The assurance of a clinical trial can be derived by integrating the power over the distribution of the input parameters, in this case, the assumed distribution of the log(T/R)-ratio. Because it is an average power, the assurance can be interpreted as a measure of the probability of success that does not depend on a specific assumed value for the log(T/R)-ratio. The relationship between power and assurance will be analysed by comparing the numerical outcomes.

Using the assurance concept, values of the standard deviation for the distribution of potential log(T/R)-ratios can be chosen to reflect the magnitude of uncertainty. For most practical cases (i.e. when 0.95 ≤ θ ≤ 1.05), the sample size is not, or only slightly, changed when σ = |log(θ)|.

The advantage of deriving the assurance for BE trials is that uncertainty is directly expressed as a parameter of variability.