Average bioequivalence evaluation: general methods for pilot trials

A Bayesian approach to pilot-pivotal trials for bioequivalence assessment

BACKGROUND

To demonstrate bioequivalence between two drug formulations, a pilot trial is often conducted prior to a pivotal trial to assess feasibility and gain preliminary information about the treatment effect. Due to the limited sample size, it is not recommended to perform significance tests at the conventional 5% level using pilot data to determine if a pivotal trial should take place. Whilst some authors suggest to relax the significance level, a Bayesian framework provides an alternative for informing the decision-making. Moreover, a Bayesian approach also readily permits possible incorporation of pilot data in priors for the parameters that underpin the pivotal trial.

METHODS

We consider two-sequence, two-period crossover designs that compare test (T) and reference (R) treatments. We propose a robust Bayesian hierarchical model, embedded with a scaling factor, to elicit a Go/No-Go decision using predictive probabilities. Following a Go decision, the final analysis to formally establish bioequivalence can leverage both the pilot and pivotal trial data jointly. A simulation study is performed to evaluate trial operating characteristics.

RESULTS

Compared with conventional procedures, our proposed method improves the decision-making to correctly allocate a Go decision in scenarios of bioequivalence. By choosing an appropriate threshold, the probability of correctly (incorrectly) making a No-Go (Go) decision can be ensured at a desired target level. Using both pilot and pivotal trial data in the final analysis can result in a higher chance of declaring bioequivalence. The false positive rate can be maintained in situations when T and R are not bioequivalent.

CONCLUSIONS

The proposed methodology is novel and effective in different stages of bioequivalence assessment. It can greatly enhance the decision-making process in bioequivalence trials, particularly in situations with a small sample size.

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

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 (Gmean) 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 (Cmax) 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 Gmean 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 Gmean 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.

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

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.

Modifications of sequential designs in bioequivalence trials

Bioequivalence (BE) studies are designed to show that two formulations of one drug are equivalent and they play an important role in drug development. When in a design stage, it is possible that there is a high degree of uncertainty on variability of the formulations and the actual performance of the test versus reference formulation. Therefore, an interim look may be desirable to stop the study if there is no chance of claiming BE at the end (futility), or claim BE if evidence is sufficient (efficacy), or adjust the sample size. Sequential design approaches specially for BE studies have been proposed previously in publications. We applied modification to the existing methods focusing on simplified multiplicity adjustment and futility stopping. We name our method modified sequential design for BE studies (MSDBE). Simulation results demonstrate comparable performance between MSDBE and the original published methods while MSDBE offers more transparency and better applicability. The R package MSDBE is available at https://sites.google.com/site/modsdbe/.