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.

Equivalence tests for ratio of means in bioequivalence studies under crossover design

There are several problems concerning the statistical definition of average bioequivalence provided by the U.S. Food and Drug Administration. We proposed a ratio of means based on the original bioavailability measure as the definition for average bioequivalence. Under the log-normal distribution assumption, we proposed a hypothesis testing-based method and a confidence interval-based method to answer the question of whether the ratio of means falls into a predetermined interval. For the hypothesis testing-based method, we decomposed the null two-sided hypothesis of the ratio of means into two one-sided hypotheses. With the intersection-union theorem for asymptotic tests, we constructed two asymptotic size-α tests for the original null hypothesis. The method of variance estimation recovery was adopted to develop the confidence interval-based method. Simulation studies showed that the proposed methods can maintain the empirical type I error rate closely at the nominal level and is as powerful as the two one-sided t-test for testing the ratio of means under different settings. The application of the proposed methods was illustrated through six datasets in real-world examples.

Multivariate Assessment for Bioequivalence Based on the Correlation of Random Effect

Background and Objective

Bioequivalence tests are fundamental step in assessing the equivalence in bioavailability between a test and reference product. In practice, two separate linear mixed models (LMMs) with random subject effects, which have an area under the concentration-time curve (AUC) and the peak concentration (C_max) as the responses, have become the gold standard for evaluating bioequivalence. Recently, Lee et al developed a multivariate hierarchical generalized linear model (HGLM) for several responses that modeled correlations among multivariate responses via correlated random effects. The objective of this study was to apply this multivariate analysis to the bioequivalence test in practice and to compare the performance of multivariate HGLM and separate LMMs.

Methods

Three pharmacokinetic datasets, fixed-dose combination (naproxen and esomeprazole), tramadol and fimasartan data were analyzed. We compared the 90% confidence interval (CI) for the geometric mean ratio (GMR) of a test product to a reference product using the multivariate HGLM and two conventional separate LMMs.

Results

We found that the 90% CIs for the GMRs of both AUC and C_max from the multivariate HGLM were narrower than those from the separate LMMs: (0.843, 1.152) vs (0.825, 1.177) for C_max of esomeprazole in fixed-dose combination data; (0.805, 0.931) vs (0.797, 0.941) for C_max in tramadol data; (0.801, 1.501) vs (0.762, 1.578) for C_max and (1.163, 1.332) vs (1.009, 1.341) for AUC in fimasartan data, consistent with the random subject effects from two separate LMMs being highly correlated in the three datasets (correlation coefficient r = 0.883; r = 0.966; r = 0.832).

Conclusion

This multivariate HGLM had good performance in the bioequivalence test with multiple endpoints. This method would provide a more reasonable option to reduce the 90% CI by adding correlation parameters and thus an advantage especially in evaluating the bioequivalence of highly variable drugs with broad 90% CIs.

Simultaneous confidence regions for multivariate bioequivalence

Demonstrating bioequivalence of several pharmacokinetic (PK) parameters, such as AUC and C_max , that are calculated from the same biological sample measurements is in fact a multivariate problem, even though this is neglected by most practitioners and regulatory bodies, who typically settle for separate univariate analyses. We believe, however, that a truly multivariate evaluation of all PK measures simultaneously is clearly more adequate. In this paper, we review methods to construct joint confidence regions around multivariate normal means and investigate their usefulness in simultaneous bioequivalence problems via simulation. Some of them work well for idealised scenarios but break down when faced with real-data challenges such as unknown variance and correlation among the PK parameters. We study the shapes of the confidence regions resulting from different methods, discuss how marginal simultaneous confidence intervals for the individual PK measures can be derived, and illustrate the application to data from a trial on ticlopidine hydrochloride. An R package is available.

A Bioequivalence Test by the Direct Comparison of Concentration-versus-Time Curves Using Local Polynomial Smoothers

In order to test if two chemically or pharmaceutically equivalent products have the same efficacy and/or toxicity, a bioequivalence (BE) study is conducted. The 80%/125% rule is the most commonly used criteria for BE and states that BE cannot be claimed unless the 90% CIs for the ratio of selected pharmacokinetics (PK) parameters of the tested to the reference drug are within 0.8 to 1.25. Considering that estimates of these PK parameters are derived from the concentration-versus-time curves, a direct comparison between these curves motivates an alternative and more flexible approach to test BE. Here, we propose to frame the BE test in terms of an equivalence of concentration-versus-time curves which are constructed using local polynomial smoother (LPS). A metric is presented to quantify the distance between the curves and its 90% CIs are calculated via bootstrapping. Then, we applied the proposed procedures to data from an animal study and found that BE between a generic drug and its brand name cannot be concluded, which was consistent with the results by applying the 80%/125% rule. However, the proposed procedure has the advantage of testing only on a single metric, instead of all PK parameters.

The use of asymmetric distributions in average bioequivalence

Generic drugs have been commercialized in numerous countries. Most of these countries approve the commercialization of a generic drug when there is evidence of bioequivalence between the generic drug and the reference drug. Generally, the pharmaceutical industry is responsible for the bioequivalence test under the supervision of a regulatory agency. This procedure is concluded after a statistical data analysis. Several agencies adopt a standard statistical analysis based on procedures that were previously established. In practice, we face situations in which this standard model does not fit to some sets of bioequivalence data. In this study, we propose an evaluation of bioequivalence using univariate and bivariate models based on an extended generalized gamma distribution and a skew-t distribution, under a Bayesian perspective. We introduce a study of the empirical power of hypothesis tests for univariate models, showing advantages in the use of an extended generalized gamma distribution. Three sets of bioequivalence data were analyzed under these new procedures and compared with the standard model proposed by the majority of regulatory agencies. In order to verify that the asymmetrical distributions are usually better fitted for the data, when compared with the standard model, model discrimination methods were used, such as the Deviance Information Criterion (DIC) and quantile-quantile plots. The research concluded that, in general, the use of the extended generalized gamma distribution may be more appropriate to model bioequivalence data in the original scale. Copyright © 2016 John Wiley & Sons, Ltd.

Modelling household finances: A Bayesian approach to a multivariate two-part model

We contribute to the empirical literature on household finances by introducing a Bayesian multivariate two-part model, which has been developed to further our understanding of household finances. Our flexible approach allows for the potential interdependence between the holding of assets and liabilities at the household level and also encompasses a two-part process to allow for differences in the influences on asset or liability holding and on the respective amounts held. Furthermore, the framework is dynamic in order to allow for persistence in household finances over time. Our findings endorse the joint modelling approach and provide evidence supporting the importance of dynamics. In addition, we find that certain independent variables exert different influences on the binary and continuous parts of the model thereby highlighting the flexibility of our framework and revealing a detailed picture of the nature of household finances.

Likelihood approach for evaluating bioequivalence of highly variable drugs

Bioequivalence (BE) is required for approving a generic drug. The two one-sided tests procedure (TOST, or the 90% confidence interval approach) has been used as the mainstream methodology to test average BE (ABE) on pharmacokinetic parameters such as the area under the blood concentration-time curve and the peak concentration. However, for highly variable drugs (%CV > 30%), it is difficult to demonstrate ABE in a standard cross-over study with the typical number of subjects using the TOST because of lack of power. Recently, the US Food and Drug Administration and the European Medicines Agency recommended similar but not identical reference-scaled average BE (RSABE) approaches to address this issue. Although the power is improved, the new approaches may not guarantee a high level of confidence for the true difference between two drugs at the ABE boundaries. It is also difficult for these approaches to address the issues of population BE (PBE) and individual BE (IBE). We advocate the use of a likelihood approach for representing and interpreting BE data as evidence. Using example data from a full replicate 2 × 4 cross-over study, we demonstrate how to present evidence using the profile likelihoods for the mean difference and standard deviation ratios of the two drugs for the pharmacokinetic parameters. With this approach, we present evidence for PBE and IBE as well as ABE within a unified framework. Our simulations show that the operating characteristics of the proposed likelihood approach are comparable with the RSABE approaches when the same criteria are applied.

Use of Bayesian methods for multivariate bioequivalence measures

In this paper, we introduce a Bayesian analysis for bioequivalence data assuming multivariate pharmacokinetic measures. With the introduction of correlation parameters between the pharmacokinetic measures or between the random effects in the bioequivalence models, we observe a good improvement in the bioequivalence results. These results are of great practical interest since they can yield higher accuracy and reliability for the bioequivalence tests, usually assumed by regulatory offices. An example is introduced to illustrate the proposed methodology by comparing the usual univariate bioequivalence methods with multivariate bioequivalence. We also consider some usual existing discrimination Bayesian methods to choose the best model to be used in bioequivalence studies.