Tests for individual and population bioequivalence based on generalized p-values.

Bioequivalence studies are a vital part of drug development. The average bioequivalence approach is the standard method of assessment to conclude whether the generic product is bioequivalent to the innovator product. Of late, debates are on whether the average bioequivalence approach adequately addresses drug interchangeability as it considers only population mean for the evaluation especially when highly variable drug products and narrow therapeutic index drugs are dealt with. Hence, the alternative approaches like population bioequivalence and individual bioequivalence assessment approaches emerge as they consider inter/intra-subject variance and subject- by-formulation variance along with population mean. The objective of the study was to apply different bioequivalence assessment approaches in a replicate bioequivalence study to evaluate the drug interchangeability. This was an open-label, single-dose, randomized, balanced, two-treatment, three-period, three-sequence, partial replicate crossover bioequivalence study of omeprazole enteric-coated tablet 20 mg conducted on 48 normal healthy subjects under fed conditions. The plasma concentration of omeprazole was analyzed by a validated bioanalytical method to determine the pharmacokinetic and statistical parameters to assess average bioequivalence, population bioequivalence, and individual bioequivalence. In this study, test formulation was shown to be bio-inequivalent to the reference formulation by average bioequivalence, population bioequivalence, and individual bioequivalence approaches. The outcome of the evaluation clearly states that the bioequivalence outcome of all these approaches are the same. Obviously, it does not mean that these three approaches provide the same outcome though the consideration of variances varies. Certainly, population bioequivalence and individual bioequivalence approach will be more accurate for the assessment of drug interchangeability.

Nowadays, the bootstrap is one of the most prominent representatives of resampling techniques, especially with respect to their daily use. It is typically applied in situations which are not analytically tractable due to the complexity of the underlying statistical estimation or testing problem, where it is common practice to run a Monte-Carlo algorithm instead of calculating the exact bootstrap. This makes the bootstrap an easy to handle and also a very flexible tool, which, of course, must always be critically looked at before being applied. This is also the case when using the bootstrap to calculate confidence intervals for statistically evaluating the bioequivalence of two formulations of a drug as recommended in the 1997 draft of the Food and Drug Administration (FDA) guidance (]). Here, the bootstrap seems to be a sensible way to cope with the analytical problems related to the recently proposed and rather complex measures for assessing population and individual bioequivalence. In this paper, we briefly review the different concepts of bioequivalence and two approaches for measuring the individual and population bioequivalence, namely the moment-based and the probability-based approaches, where the focus is on individual bioequivalence. We then concentrate on the bootstrap percentile interval, which has been considered by the FDA.

The concept of interchangeable pharmaceutical products has been examined in great detail in the literature. Anderson and Hauck proposed a statistical random coefficient model to study ‘switchability’, and coined the phrase ‘individual bioequivalence’ which they defined with a probability-based inequality. Since that paper there has been considerable work and discussion. The Food and Drug Administration has recommended the introduction of individual bioequivalence (IBE) and population bioequivalence (PBE) methods in a draft guidance document. The proposal in the draft guidance includes criteria for IBE and PBE and recommends the use of non-parametric bootstrap 95 per cent upper confidence intervals for the conclusion of either IBE or PBE. However, this method requires intensive computations. We have developed an alternative confidence interval procedure to assess IBE by the FDA recommended criteria. This method utilizes Howe's approximation I to a Cornish–Fisher expansion. Our proposed method is applicable to balanced or unbalanced data in a broad class of extended cross-over designs, and can be easily programmed using readily available software. Copyright © 2000 John Wiley & Sons, Ltd.

Bioequivalence studies are conducted to demonstrate equivalence in the bioavailability of the active ingredient in different formulations. The U.S. Food and Drug Administration (FDA) requires pharmaceutical companies to show bioequivalence between different formulations or generic companies to show bioequivalence between generic drugs and brand drugs before approval. A recent FDA guidance on bioequivalence proposes criteria for assessment of population bioequivalence (PBE) and individual bioequivalence (IBE) in a four-period cross-over design. In this paper, computer simulation is used to compare modified large sample (MLS) upper bounds with those proposed by the FDA to test for both PBE and IBE. The comparison criteria are the ability to maintain the stated test size and the simulated power of tests based on these bounds.

Average bioequivalence is used to assess pharmacokinetic properties of proposed generic drug before they are marketed. The limitations of average bioequivalence have led the U.S. Food and Drug Administration to propose the use of popUlation bioequivalence and individual bioequivalence. In this study, bootstrap confidence intervals were used to evaluate population bioequivalence and individual bioequivalence in the context of a 2 x 4 crossover experimental design. Two bioequivalence criteria were compared: the mean-squared difference criterion and a probability-based criterion. Simulations were conducted to study the properties of the bootstrap confidence intervals under each criterion in establishing population bioequivalence or individual bioequivalence. Various inter-subject, within-subject, and subject-by-formulation interaction variance components were considered.

In recent years, as more generic drug products become available, it is a concern not only whether generic drug products that have been approved based on the regulation of average bioequivalence will have the same quality, safety and efficacy as that of the brand-name drug product, but also whether the approved generic drug products can be used interchangeably. In its recent draft guidance, the U.S. Food and Drug Administration (FDA) recommends that individual bioequivalence (IBE) be assessed using the method proposed by Hyslop, Hsuan, and Holder to address drug switchability. The FDA suggests that a 2x4 cross-over design be considered for assessment of IBE, while a 2x3 cross-over design may be used as an alternative design to reduce the length and cost of the study. Little or no information regarding the statistical procedures under 2x3 cross-over designs is discussed in the guidance. In this paper, a detailed statistical procedure for assessment of IBE under 2x3 cross-over designs is derived. The main purpose of this paper, however, is to derive an IBE test under an alternative 2x3 design and show that the resulting IBE test is better than that under a 2x3 cross-over design and is comparable to or even better than that under a 2x4 cross-over design. Our conclusions are supported by theoretical considerations and empirical results. Furthermore, a method of determining the sample sizes required for IBE tests to reach a given level of power is proposed.

A practical approach for evaluating population and individual bioequivalence

We propose an approach for comparing directly the reference and test blood concentration × time profiles of subjects in a bioequivalence trial under a crossover design. We compare the test and reference profiles via the construction of two regions, namely, an acceptable region based on the reference profile and another region based on reflecting the test profile about the reference profile. Also, we describe how to construct these regions if the assay for measuring the concentration has a lower limit of detection and how to adjust the reference and test concentrations of the n subjects participating in a bioequivalence trial. If the test and reference formulations are bioequivalent, then the area displaced by the latter region should be less than the area displaced by the acceptable region. Therefore, we construct a ratio of these areas for each subject. Then we calculate upper confidence limits for quantiles, either under the assumption of lognormality or based on a bootstrapping algorithm, to investigate population and/or individual bioequivalence.

This chapter contains sections titled: Introduction Brief history Study designs and statistical models Population bioequivalence Individual bioequivalence Disaggregate criteria Other approaches Average bioequivalence in replicate designs Example: The antihypertensive patch dataset Conclusions References

Update to the PhRMA perspective on population and individual bioequivalence.

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Recent work, beginning with that of Anderson and Hauck in 1990, has led to a general acceptance of the need to ensure switchability in bioequivalence testing for approval of generic drugs. In other applications of bioequivalence testing, prescribability may be sufficient. However, there is less acceptance of the need to change statistical procedures and study designs from those currently used to assess the current criterion of average bioequivalence. We propose easily interpreted measures of switchability and prescribability. These measures provide bases for assessing conditions under which average bioequivalence is not sufficient to ensure switchability and prescribability, and hence for which a procedure for individual or population bioequivalence is required. The required conditions are sufficiently tight that they cannot be presumed to hold. Thus, there are reasonable conditions for which current practice is not sufficient. An outcome of this development is a connection between two current approaches for assessing individual bioequivalence.

The performances of three statistical approaches for assessing in vitro equivalence was evaluated with a set of 55 scenarios of realistic test (T) and reference (R) cascade impactor (CI) profiles (originally employed by the Product Quality Research Institute to evaluate the chi-square ratio statistic: CSRS) by comparing the outcomes against experts' opinion (surrogate for the truth). The three methods were (A) a stepwise aerodynamic particle size distribution (APSD) equivalence test integrating population bioequivalence (PBE) testing of impactor-sized mass (ISM) with the CSRS (PBE-CSRS approach), previously suggested by the USFDA; (B) the combination of PBE testing of single actuation content and ISM with the newly suggested modified CSRS (PBE-mCSRS approach), a method employing reference variance scaling; and (C) EMA's average bioequivalence (ABE approach). Based on Monte-Carlo simulations, both PBE-CSRS and ABE approaches resulted in high misclassification rates, the former with highest false-pass rate and the latter with highest false-fail rate at both ≥ 50% and ≥ 80% classification threshold values (the % of simulations or experts necessary to judge a given scenario as equivalent). Based on DeLong's tests, the PBE-mCSRS approach showed significantly better overall agreement with experts' opinion compared to the other approaches. Comparison of CSRS with mCSRS (both without PBE) suggested that the more discriminatory characteristics of the mCSRS method is based on the integration of variance scaling into the mCSRS method. Contrary to the ABE approach, the application of PBE-mCSRS approach for assessing APSD profiles of three dry powder inhaler (DPI) formulations supported the pharmacokinetic bioequivalence assessment of these formulations.

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