Predictive Potential of Cmax Bioequivalence in Pilot Bioavailability/Bioequivalence Studies, through the Alternative ƒ2 Similarity Factor Method

Abstract

Pilot bioavailability/bioequivalence (BA/BE) studies are downsized trials that can be conducted prior to the definitive pivotal trial. In these trials, 12 to 18 subjects are usually enrolled, although, in principle, a sample size is not formally calculated. In a previous work, authors recommended the use of an alternative approach to the average bioequivalence methodology to evaluate pilot studies' data, using the geometric mean (G_mean) ƒ₂ factor with a cut off of 35, which has shown to be an appropriate method to assess the potential bioequivalence for the maximum observed concentration (C_max) metric under the assumptions of a true Test-to-Reference Geometric Mean Ratio (GMR) of 100% and an inter-occasion variability (IOV) in the range of 10% to 45%. In this work, the authors evaluated the proposed ƒ₂ factor in comparison with the standard average bioequivalence in more extreme scenarios, using a true GMR of 90% or 111% for truly bioequivalent formulations, and 80% or 125% for truly bioinequivalent formulations, in order to better derive conclusions on the potential of this analysis method. Several scenarios of pilot BA/BE crossover studies were simulated through population pharmacokinetic modelling, accounting for different IOV levels. A redefined decision tree is proposed, suggesting a fixed sample size of 20 subjects for pilot studies in the case of intra-subject coefficient of variation (ISCV%) > 20% or unknown variability, and suggesting the assessment of study results through the average bioequivalence analysis, and additionally through G_mean ƒ₂ factor method in the case of the 90% confidence interval (CI) for GMR is outside the regulatory acceptance bioequivalence interval of [80.00-125.00]%. Using this alternative approach, the certainty levels to proceed with pivotal studies, depending on G_mean ƒ₂ values and variability scenarios tested (20-60% IOV), were assessed, which is expected to be helpful in terms of the decision to proceed with pivotal bioequivalence studies.

Keywords: bioequivalence; generic medicinal products; modelling and simulation; pharmacokinetic simulation; pharmacokinetics; pilot studies; ƒ2 factor.

Figure 1

Simulation scheme for pilot bioavailability/bioequivalence (BA/BE) trials.

Figure 2

Distribution of the Test-to-Reference Geometric Least Square Means Ratio (GMR), estimated from the average bioequivalence method, in the form of box plots.

Figure 3

Distribution of the intra-subject coefficient of variation (ISCV%), estimated from the average bioequivalence method, in the form of box plots.

Figure 4

Distribution of the calculated ƒ₂ factor, in the form of box plots.

Figure 5

Relationship between G_mean f₂ factor and Test-to-Reference GMR (above) for all simulated truly bioequivalent (blue) and truly bioinequivalent (red) studies. Vertical dotted lines correspond to 10% and 20% difference between Test and Reference formulations, tested by the average bioequivalence approach. Horizontal dotted lines correspond to ƒ₂ values of 50, 41, and 35.

Figure 6

Variation in sensitivity/power for the bioequivalence evaluation methods (average bioequivalence, centrality of the Test-to-Reference GMR, and A_mean and G_mean ƒ₂ factor evaluated with a cut off of 35) as function of the number of subjects for each tested variability (above) and as function of inter-occasion variability (below), considering a Test product with a lower bioavailability than the Reference product (i.e., true GMR of 90%).

Figure 7

Variation in sensitivity/power for the bioequivalence evaluation methods (average bioequivalence, centrality of the Test-to-Reference GMR, and A_mean and G_mean ƒ₂ factor evaluated with a cut off of 35) as function of the number of subjects for each tested variability (above) and as function of inter-occasion variability (below), considering a Test product with a higher bioavailability than the Reference product (i.e., true GMR of 111%).

Figure 8

Variation in specificity for the bioequivalence evaluation methods (average bioequivalence, centrality of the Test-to-Reference GMR, and A_mean and G_mean ƒ₂ factor evaluated with a cut off of 35) as function of the number of subjects for each tested variability (above) and as function of inter-occasion variability (below), considering a Test product with a lower bioavailability than the Reference product (i.e., true GMR of 80%).

Figure 9

Variation in specificity for the bioequivalence evaluation methods (average bioequivalence, centrality of the Test-to-Reference GMR, and A_mean and G_mean ƒ₂ factor evaluated with a cut off of 35) as function of the number of subjects for each tested variability (above) and as function of inter-occasion variability (below), considering a Test product with a higher bioavailability than the Reference product (i.e., true GMR of 125%).

Figure 10

Variation in precision, negative predictive value (NPV), accuracy, F₁, Matthews’ Correlation Coefficient (MCC), and Cohen’s Kappa (κ) for the bioequivalence evaluation methods (average bioequivalence, centrality of the Test-to-Reference GMR, and A_mean and G_mean ƒ₂ factor evaluated with a cut off of 35) as function of the number of subjects for each tested variability, considering a Test product with a lower bioavailability than the Reference product (i.e., true GMR of 90% and 80%).

Figure 11

Variation in precision, negative predictive value (NPV), accuracy, F₁, Matthews’ Correlation Coefficient (MCC), and Cohen’s Kappa (κ) for the bioequivalence evaluation methods (average bioequivalence, centrality of the Test-to-Reference GMR, and A_mean and G_mean ƒ₂ factor evaluated with a cut off of 35) as function of the number of subjects for each tested variability, considering a Test product with a higher bioavailability than the Reference product (i.e., true GMR of 111% and 125%).

Figure 12

Variation in precision, for the G_mean ƒ₂ factor evaluated with a cut off of 35, 41, and 50 as function of the number of subjects for each tested variability. An ƒ₂ factor of 35, 41, and 50 corresponds to a difference of 20%, 15%, and 10%, respectively, between Test and Reference concentration time-profiles until the Reference t_max.

Figure 13

Newly proposed decision tree for planning and analysis of pilot BA/BE studies.