An insight into the properties of a two-stage design in bioequivalence studies

Performance Evaluation of Interim Analysis in Bioequivalence Studies

Under current bioequivalence guidelines in Japan, it is mandatory to establish bioequivalence using a single pivotal study. Clinical trials with limited resources usually have a pre-defined maximum permissible number of participants. In this manuscript, we considered a trial design that would allow for bioequivalence evaluation at an interim analysis in which the total number of participants takes into account the resource constraints. Then, available options at the interim analysis are group sequential designs and adaptive designs, A comparison of the performance of the two methods under same maximum participant number has not been conducted thus far. So we examined which method should be used by conducting a simulation study. Since bioequivalence is expected to be achieved at the interim analysis, a study design using a Pocock-type alpha spending function is preferrable. Simulation results using a Pocock-type alpha spending function showed similar performance between group sequential and adaptive designs. Consequently, due to statistical and operational complexity, it is preferable to choose group sequential designs for bioequivalence study in Japan.

Pharmacokinetics and Bioequivalence of 2 Azithromycin Tablet Formulations: A Randomized, Open-Label, 2-Stage Crossover Study in Healthy Volunteers

The current study aimed to assess the bioequivalence of a new branded azithromycin with the reference formulation. An open-label, randomized, 2-stage, crossover study design was implemented involving 77 healthy volunteers under fasting conditions. Each volunteer received a single dose of 250-mg azithromycin tablets test and reference formulations separated by a 21-day washout period. Twenty-two samples were collected at pre-dose and until 72 hours post-dose. Azithromycin concentrations were analyzed using a high-performance liquid chromatography-mass spectrometry validated method following a solid-phase plasma extraction. Noncompartmental analysis was carried out to estimate the pharmacokinetic parameters, which were compared between the test and reference products using a multivariate analysis of variance. The difference between C_max and AUC_0-72 of the test and reference formulation was not significant. The 94.1% confidence intervals of ln-transformed C_max and AUC_0-72 of azithromycin were within the bioequivalence acceptance limits of 80%-125%, therefore it can be concluded that the tested formulation is bioequivalent to the reference formulation.

A Three-Treatment Two-Stage Design for Selection of a Candidate Formulation and Subsequent Demonstration of Bioequivalence

This paper introduces a two-stage bioequivalence design involving the selection of one out of two candidate formulations at an initial stage and quantifies the overall power (chance of ultimately showing bioequivalence) in a range of scenarios with CVs ranging from 0.1 to 1. The methods introduced are derivates of the methods invented in 2008 by Diane Potvin and co-workers (Pharm Stat. 7(4): 245-262, 2008). The idea is to test the two candidate formulations independently in an initial stage, making a selection of one of these formulations basis of the observed point estimates, and to run, when necessary, a second stage of the trial with pooling of data. Alpha levels are identified which are shown to control the maximum type I error at 5%. Results, expressed as powers and sample sizes, are also published for scenarios where the two formulations are far apart in terms of the match against the reference (one GMR being 0.80, the other GMR being 0.95) and in scenarios where the two test formulations have an actual better match (one GMR being 0.90, the other GMR being 0.95). The methods seem to be compliant with wording of present guidelines from EMA, FDA, WHO, and Health Canada. Therefore the work presented here may be useful for companies developing drugs whose approval hinges on in vivo proof of bioequivalence and where traditional in vitro screening methods (such as dissolution trials) may have poor ability to predict the best candidate.

10th Anniversary of a Two-Stage Design in Bioequivalence. Why Has it Still Not Been Implemented?

PURPOSE

In 2010 the European Medicines Agency allowed a two-stage design in bioequivalence studies. However, in the public domain there are mainly articles describing the theoretical and statistical base for the application of the two-stage design. One of the reasons seems to be the lack of practical guidance for the Sponsors on when and how the two-stage design can be beneficial in bioequivalence studies.

METHODS

Different variants with positive and negative outcomes have been evaluated, including a pivotal study, pilot + pivotal study and two-stage study. The scientific perspective on the two-stage bioequivalence study has been confronted with the industrial one.

RESULTS

Key information needed to conduct a bioequivalence study - such as in vitro data and pharmacokinetics - have been listed and organized into a decision scheme. Advantages and disadvantages of the two-stage design have been summarized.

CONCLUSION

The use of the two-stage design in bioequivalence studies seems to be a beneficial alternative to the 2 × 2 crossover study. Basic information on the properties of the active substance and the characteristics of the drug form are needed to make an initial decision to carry out the two-stage study.

Two-Stage Adaptive Designs for Three-Treatment Bioequivalence Studies

Bioequivalence (BE) studies are most often conducted as crossover trials, and therefore establishing their required sample size necessitates specification of the within-person variance. Given that this specification is often difficult in practice, there has been great interest in recent years in the use of adaptive designs for BE trials. However, while numerous methods for this have now been presented, their focus has been solely on two-treatment BE studies. In some instances, it will be desired to incorporate more than a single test and reference formulation into a BE trial. It would therefore be useful to establish methodology for the design of adaptive multi-treatment BE trials, to acquire the benefits in the two-treatment setting in this more complex situation. Here, we achieve this for three-treatment studies by extending previously proposed designs for two-treatment trials. First, we discuss the additional design considerations that arise when multiple comparisons are made. Next, an extensive simulation study is employed to compare the performance of the proposed procedures. With this, we demonstrate that two-stage designs with desirable statistical operating characteristics can be readily identified for three-treatment BE trials. Supplementary materials for this article are available online.

Controlling type 1 error rate for sequential, bioequivalence studies with crossover designs

Sample size reestimation in a crossover, bioequivalence study can be a useful adaptive design tool, particularly when the intrasubject variability of the drug formulation under investigation is not well understood. When sample size reestimation is done based on an interim estimate of the intrasubject variability and bioequivalence is tested using the pooled estimate of intrasubject variability, type 1 error inflation will occur. Type 1 error inflation is caused by the pooled estimate being a biased estimator of the intrasubject variability. The type 1 error inflation and bias of the pooled estimator of variability are well characterized in the setting of a two-arm, parallel study. The purpose of this work is to extend this characterization to the setting of a crossover, bioequivalence study with sample size reestimation and to propose an estimator of the intrasubject variability that will prevent type 1 error inflation.

A comparison of group sequential and fixed sample size designs for bioequivalence trials with highly variable drugs

PURPOSE

A drug is defined as highly variable if its intra-individual coefficient of variation (CV) is greater than or equal to 30%. In such a case, bioequivalence may be assessed by means of methods that take the (high) variability into account. The Scaled Average Bioequivalence (SABE) approach is such a procedure and represents the recommendations of FDA. The aim of this investigation is to compare the performance characteristics of classical group sequential designs (GSD) and fixed design settings for three-period crossover bioequivalence studies with highly variable drugs, where the SABE procedure is utilized.

METHODS

Monte Carlo simulations were performed to assess type I error rate, power, and average sample size for GSDs with Pocock's and O'Brien-Fleming's stopping rules and various timings of the interim analysis and for fixed design settings.

RESULTS

Based on our investigated scenarios, the GSDs show comparable properties with regard to power and type I error rate as compared to the corresponding fixed designs. However, due to an advantage in average sample size, the most appealing design is Pocock's approach with interim analysis after 50% information fraction.

CONCLUSIONS

Due to their favorable performance characteristics, two-stage GSDs are an appealing alternative to fixed sample designs when assessing bioequivalence in highly variable drugs.

Two-stage designs versus European scaled average designs in bioequivalence studies for highly variable drugs: Which to choose?

The usual approach to determine bioequivalence for highly variable drugs is scaled average bioequivalence, which is based on expanding the limits as a function of the within-subject variability in the reference formulation. This requires separately estimating this variability and thus using replicated or semireplicated crossover designs. On the other hand, regulations also allow using common 2 × 2 crossover designs based on two-stage adaptive approaches with sample size reestimation at an interim analysis. The choice between scaled or two-stage designs is crucial and must be fully described in the protocol. Using Monte Carlo simulations, we show that both methodologies achieve comparable statistical power, though the scaled method usually requires less sample size, but at the expense of each subject being exposed more times to the treatments. With an adequate initial sample size (not too low, eg, 24 subjects), two-stage methods are a flexible and efficient option to consider: They have enough power (eg, 80%) at the first stage for non-highly variable drugs, and, if otherwise, they provide the opportunity to step up to a second stage that includes additional subjects.

Two-stage designs for cross-over bioequivalence trials

The topic of applying two-stage designs in the field of bioequivalence studies has recently gained attention in the literature and in regulatory guidelines. While there exists some methodological research on the application of group sequential designs in bioequivalence studies, implementation of adaptive approaches has focused up to now on superiority and non-inferiority trials. Especially, no comparison of the features and performance characteristics of these designs has been performed, and therefore, the question of which design to employ in this setting remains open. In this paper, we discuss and compare 'classical' group sequential designs and three types of adaptive designs that offer the option of mid-course sample size recalculation. A comprehensive simulation study demonstrates that group sequential designs can be identified, which show power characteristics that are similar to those of the adaptive designs but require a lower average sample size. The methods are illustrated with a real bioequivalence study example.

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/.

Two-stage designs in bioequivalence trials

PURPOSE

The aim of this study is to assess the current status of non-fixed sample size designs in bioequivalence trials with a focus on two-stage adaptive approaches.

METHODS

We searched PubMed and Google Scholar from inception to October 2014. Regulatory guidelines were obtained from the public domain. Different methods were compared by Monte Carlo simulations for their impact on the patient's and producer's risks.

RESULTS

Add-on designs, group sequential designs and adaptive two-stage sequential designs are currently accepted to demonstrate bioequivalence in various regulations. All three approaches may inflate the patient's risk if applied inconsiderately. Direct transfer of methods developed for superiority testing to bioequivalence is not warranted. Published two-stage frameworks maintain the type I error and generally the desired power. Adaptation based on the observed T/R ratio observed in the first stage should be applied with caution. Monte Carlo simulations are an efficient tool to explore the operating characteristics of methods.

CONCLUSIONS

Validated two-stage frameworks can be applied without requiring the sponsor to perform own simulations-which could further improve power based on additional assumptions. Two-stage designs are both ethical and economical alternatives to fixed sample designs.

Statistical comparison of dissolution profiles to predict the bioequivalence of extended release formulations

Appropriate setting of dissolution specification of extended release (ER) formulations should include precise definition of a multidimensional space of complex definition and interpretation, including limits in dissolution parameters, lag time (t-lag), variability, and goodness of fit. This study aimed to set dissolution specifications of ER by developing drug-specific dissolution profile comparison tests (DPC tests) that are able to detect differences in release profiles between ER formulations that represent a lack of bioequivalence (BE). Dissolution profiles of test formulations were simulated using the Weibull and Hill models. Differential equations based in vivo-in vitro correlation (IVIVC) models were used to simulate plasma concentrations. BE trial simulations were employed to find the formulations likely to be declared bioequivalent and nonbioequivalent (BE space). Customization of DPC tests was made by adjusting the delta of a recently described tolerated difference test (TDT) or the limits of rejection of f2. Drug ka (especially if ka is small), formulation lag time (t-lag), the number of subjects included in the BE studies, and the number of sampled time points in the DPC test were the factors that affected the most these setups of dissolution specifications. Another recently described DPC test, permutation test (PT), showed excellent statistical power. All the formulations declared as similar with PT were also bioequivalent. Similar case-specific studies may support the biowaiving of ER drug formulations based on customized DPC tests.

Futility rules in bioequivalence trials with sequential designs

Health Canada, the US Food and Drug Administration, as well as the European Medicines Agency consider sequential designs acceptable for bioequivalence studies as long as the type I error is controlled at 5%. The EU guideline explicitly asks for specification of stopping rules, so the goal of this work is to investigate how stopping rules may affect type I errors and power for recently published sequential bioequivalence trial designs. Using extensive trial simulations, five different futility rules were evaluated for their effect on type I error rates and power in two-stage scenarios. Under some circumstances, notably low sample size in stage 1 and/or high variability power may be very severely affected by the stopping rules, whereas type I error rates appear less affected. Because applicants may initiate sequential studies when the variability is not known in advance, achieving sufficient power and thereby complying with certain guideline requirements may be challenging and application of optimistic futility rules could possibly be unethical. This is the first work to investigate how futility rules affect type I errors and power in sequential bioequivalence trials.

On the statistical model of the two-stage designs in bioequivalence assessment

OBJECTIVES

Two-stage clinical designs are currently recommended by the regulatory authorities for the assessment of bioequivalence (BE). A specific statistical methodology was recently proposed by the European Medicines Agency (EMA). The aims of this article are to elaborate on the suggested statistical design from the EMA and to compare it with the existing statistical methods reported in the literature.

METHODS

Monte Carlo simulations were used to simulate the conditions of a two-stage BE design. The starting sample size was either 24 or 48, whereas the coefficient of variation of the within-subject variability was equal to 20% and 40%. Several geometric mean ratio levels of the BE metric were considered. Under each condition, 1,000,000 studies were simulated.

KEY FINDINGS

The overall performance, in terms of percentage of BE acceptance, is identical. The additional term, 'sequence × stage', suggested in the EMA method is in most cases nonsignificant. The same results were obtained regardless of the type (fixed or random) of the effect applied to the 'subjects' term.

CONCLUSIONS

Any BE study either finished or in progress which relies on the existing literature methodology leads to the same percentage of BE acceptance as if it was analysed with the recently proposed EMA method.