Alternative Analysis Approaches for the Assessment of Pilot Bioavailability/Bioequivalence Studies

Abstract

Pilot bioavailability/bioequivalence (BA/BE) studies are usually conducted and analysed similarly to pivotal studies. Their analysis and interpretation of results usually rely on the application of the average bioequivalence approach. However, due to the small study size, pilot studies are inarguably more sensitive to variability. The aim of this work is to propose alternative approaches to the average bioequivalence methodology, in a way to overcome and reduce the uncertainty on the conclusions of these studies and on the potential of test formulations. Several scenarios of pilot BA/BE crossover studies were simulated through population pharmacokinetic modelling. Each simulated BA/BE trial was analysed using the average bioequivalence approach. As alternative analyses, the centrality of the test-to-reference geometric least square means ratio (GMR), bootstrap bioequivalence analysis, and arithmetic (A_mean) and geometric (G_mean) mean ƒ₂ factor approaches were investigated. Methods performance was measured with a confusion matrix. The G_mean ƒ₂ factor using a cut-off of 35 was the most appropriate method in the simulation conditions frame, enabling to more accurately conclude the potential of test formulations, with a reduced sample size. For simplification, a decision tree is also proposed for appropriate planning of the sample size and subsequent analysis approach to be followed in pilot BA/BE trials.

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

Figure 1

Pilot bioavailability/bioequivalence (BA/BE) trials simulation scheme.

Figure 2

Distribution of ƒ₂ similarity factor as a function of mean difference. ƒ₂ similarity factor is derived from the mean squared difference and can be calculated as a function of the reciprocal of the mean squared-root transformation of the sum of square differences at all points. An average difference of 10%, 15%, and 20% from all measured time points results in a ƒ₂ value of 50 (red dotted lines), 41 (green dotted lines) and 35 (blue dotted lines), respectively.

Figure 3

Variation of sensitivity for the bioequivalence evaluation methods (average bioequivalence, centrality of the test-to-reference GMR, bootstrap bioequivalence analysis, and A_mean and G_mean ƒ₂ factor evaluated with a cut-off of 35) as function of the number of subjects, per tested variability for the different pharmacokinetic model parameters.

Figure 4

Variation of sensitivity for A_mean and G_mean ƒ₂ factor evaluated with a cut-off of 35, 41, and 50, as function of the number of subjects, per tested variability for the different pharmacokinetic model parameters.

Figure 5

Variation of specificity for the bioequivalence evaluation methods (average bioequivalence, centrality of the test-to-reference GMR, bootstrap bioequivalence analysis, and A_mean and G_mean ƒ₂ factor evaluated with a cut-off of 35) as function of the number of subjects, per tested variability for the different pharmacokinetic model parameters.

Figure 6

Variation of precision for the bioequivalence evaluation methods (average bioequivalence, centrality of the test-to-reference GMR, bootstrap bioequivalence analysis, and A_mean and G_mean ƒ₂ factor evaluated with a cut-off of 35) as function of the number of subjects, per tested variability for the different pharmacokinetic model parameters.

Figure 7

Variation of negative predictive value (NPV) for the bioequivalence evaluation methods (average bioequivalence, centrality of the test-to-reference GMR, bootstrap bioequivalence analysis, and A_mean and G_mean ƒ₂ factor evaluated with a cut-off of 35) as function of the number of subjects, per tested variability for the different pharmacokinetic model parameters.

Figure 8

Variation of accuracy for the bioequivalence evaluation methods (average bioequivalence, centrality of the test-to-reference GMR, bootstrap bioequivalence analysis, and A_mean and G_mean ƒ₂ factor evaluated with a cut-off of 35) as a function of the number of subjects, per tested variability for the different pharmacokinetic model parameters.

Figure 9

Variation of F₁ for the bioequivalence evaluation methods (average bioequivalence, centrality of the test-to-reference GMR, bootstrap bioequivalence analysis, and A_mean and G_mean ƒ₂ factor evaluated with a cut-off of 35) as a function of the number of subjects, per tested variability for the different pharmacokinetic model parameters.

Figure 10

Variation of Matthews correlation coefficient (MCC) for the bioequivalence evaluation methods (average bioequivalence, centrality of the test-to-reference GMR, bootstrap bioequivalence analysis, and A_mean and G_mean ƒ₂ factor evaluated with a cut-off of 35) as function of the number of subjects, per tested variability for the different pharmacokinetic model parameters.

Figure 11

Variation of Cohen’s κ for the bioequivalence evaluation methods (average bioequivalence, centrality of the test-to-reference GMR, bootstrap bioequivalence analysis, and A_mean and G_mean ƒ₂ factor evaluated with a cut-off of 35) as a function of the number of subjects, per tested variability for the different pharmacokinetic model parameters.

Figure 12

Relationship between G_mean f₂ factor and test-to-reference GMR (above) or absolute LSM difference (below), and number of subjects (colour gradient), for all simulated true bioequivalent (blue) and true bioinequivalent (red) studies. Vertical dotted lines correspond to the maximum 20% difference between test and reference formulations, tested by the average bioequivalence approach. Horizontal dotted lines correspond to the tested cut-off values for ƒ₂ of 50, 41, and 35.

Figure 13

Proposed decision tree for the planning and analysis of pilot BA/BE studies.