A practical approach for evaluating population and individual bioequivalence

Levothyrox® New and Old Formulations: Are they Switchable for Millions of Patients?

In France, more than 2.5 million patients are currently treated with levothyroxine, mainly as the marketed product Levothyrox^®. In March 2017, at the request of French authorities, a new formulation of Levothyrox^® was licensed, with the objective of avoiding stability deficiencies of the old formulation. Before launching this new formulation, an average bioequivalence trial, based on European Union recommended guidelines, was performed. The implicit rationale was the assumption that the two products, being bioequivalent, would also be switchable, allowing substitution of the new for the old formulation, thus avoiding the need for individual calibration of the dosage regimen of thyroxine, using the thyroid-stimulating hormone level as the endpoint, as required for a new patient on initiating treatment. Despite the fact that both formulations were shown to be bioequivalent, adverse drug reactions were reported in several thousands of patients after taking the new formulation. In this opinion paper, we report that more than 50% of healthy volunteers enrolled in a successful regulatory average bioequivalence trial were actually outside the a priori bioequivalence range. Therefore, we question the ability of an average bioequivalence trial to guarantee the switchability within patients of the new and old levothyroxine formulations. We further propose an analysis of this problem using the conceptual framework of individual bioequivalence. This involves investigating the bioavailability of the two formulations within a subject, by comparing not only the population means (as established by average bioequivalence) but also by assessing two variance terms, namely the within-subject variance and the variance estimating subject-by-formulation interaction. A higher within individual variability for the new formulation would lead to reconsideration of the appropriateness of the new formulation. Alternatively, a possible subject-by-formulation interaction would allow a judgement on the ability, or not, of doctors to manage patients effectively during transition from the old to the new formulation.

Testing for bioequivalence of highly variable drugs from TR-RT crossover designs with heterogeneous residual variances

Traditional bioavailability studies assess average bioequivalence (ABE) between the test (T) and reference (R) products under the crossover design with TR and RT sequences. With highly variable (HV) drugs whose intrasubject coefficient of variation in pharmacokinetic measures is 30% or greater, assertion of ABE becomes difficult due to the large sample sizes needed to achieve adequate power. In 2011, the FDA adopted a more relaxed, yet complex, ABE criterion and supplied a procedure to assess this criterion exclusively under TRR-RTR-RRT and TRTR-RTRT designs. However, designs with more than 2 periods are not always feasible. This present work investigates how to evaluate HV drugs under TR-RT designs. A mixed model with heterogeneous residual variances is used to fit data from TR-RT designs. Under the assumption of zero subject-by-formulation interaction, this basic model is comparable to the FDA-recommended model for TRR-RTR-RRT and TRTR-RTRT designs, suggesting the conceptual plausibility of our approach. To overcome the distributional dependency among summary statistics of model parameters, we develop statistical tests via the generalized pivotal quantity (GPQ). A real-world data example is given to illustrate the utility of the resulting procedures. Our simulation study identifies a GPQ-based testing procedure that evaluates HV drugs under practical TR-RT designs with desirable type I error rate and reasonable power. In comparison to the FDA's approach, this GPQ-based procedure gives similar performance when the product's intersubject standard deviation is low (≤0.4) and is most useful when practical considerations restrict the crossover design to 2 periods.

Evaluation of bioequivalence for highly variable drugs with scaled average bioequivalence

Bioequivalence studies are performed to demonstrate in vivo that two pharmaceutically equivalent products (in the US) or alternative pharmaceutical products (in the EU) are comparable in their rate and extent of absorption. By definition, for highly variable drugs (HVDs), the estimated within-subject variability is >30%. HVDs often fail to meet current regulatory acceptance criteria for average bioequivalence (ABE). The determination of the bioequivalence of HVDs has been a vexing problem since the inception of the current regulations. It is of concern not only to the generic industry but also to the innovator industry. This article reviews the definition of HVDs, the present regulatory recommendations and the approaches proposed in the literature to deal with the bioequivalence problems of HVDs. The approach of scaled ABE (SABE) is proposed as the most adequate procedure to solve the problem. It is demonstrated that SABE has firm theoretical foundations. In fact, statistical tests similar to SABE are used in various fields, such as psychology and quality control. Algorithms and numerical examples are presented to calculate SABE from the data in conventional two-period and replicate-design studies. The most important feature of SABE is that a fixed sample size is adequate to demonstrate bioequivalence regardless of within-subject variability. The conditions for reaching consistent regulatory decisions with SABE are discussed. The required sample size, for a given statistical power, depends on the regulatory criteria. Sample sizes with different criteria are demonstrated and compared with those arising from a recent informal US FDA proposal. Pragmatic considerations lead to modifications of the theoretical concept of SABE. Several modifications are proposed, including reference scaling, restriction on the estimated geometric mean ratios and possibly limiting SABE to only secondary bioequivalence metrics such as the maximum concentration. Each proposal has its own merit but is also a source of new controversy. Overall, the statistical evaluation of SABE is more complex than that of ABE, which means higher regulatory burden. Standardized open software could be very useful in this regard. A small program script is presented to calculate SABE confidence limits.

Kullback-Leibler divergence for evaluating bioequivalence

In this paper we propose a methodology for evaluating the bioequivalence of two formulations of a drug that encompasses not only average bioequivalence (ABE), but also the more recently introduced measures of population bioequivalence (PBE) and individual bioequivalence (IBE). The latter two measures are concerned with prescribability (PBE) and switchability (IBE). The main idea is to use the Kullback-Leibler divergence (KLD) as a measure of discrepancy between the distributions of the two formulations. Two formulations are declared bioequivalent if the upper bound of a level-alpha confidence interval for the KLD is less than a given goalpost to be set by a regulator. This new methodology overcomes many of the disadvantages of the corresponding measures recommended by the FDA. In particular the KLD: (i) possesses the natural hierarchical property that IBE => PBE => ABE; (ii) satisfies the properties of a true distance metric; (iii) is invariant to monotonic transformations of the data; (iv) generalizes easily to the multivariate case where equivalence on more than one parameter (for example, AUC, C(max) and T(max)) is required; and (v) is applicable over a wide range of distributions of the response variable (for example, those in the exponential family). The performance of the KLD relative to the metric proposed in guidance by the FDA for the evaluation of individual bioequivalence is evaluated using a simulation study. Previously published retrospective analyses using the FDA-proposed metric are contrasted with those based on the KLD. It is concluded that the KLD is a viable alternative to the FDA-proposed metric and that its mathematical and statistical properties make it a readily interpretable measure of the differences between formulations.

Assessing individual bioequivalence using the structural equation model

The structural equation model (SEM) is introduced as a useful approach for assessing individual bio-equivalence. SEM parameters are estimated using a partial likelihood analysis and the hypotheses of individual bioequivalence is evaluated in a disaggregate way, testing separately the hypothesis concerning SEM parameters, and assessing the overall hypothesis of individual bioequivalence using the intersection-union principle. Limits of bioequivalence for SEM parameters are proposed and a power analysis is carried out.

Limits for the scaled average bioequivalence of highly variable drugs and drug products

PURPOSE

To provide a rational procedure for establishing regulatory bioequivalence (BE) limits that can be applied in determinations of scaled average BE for highly-variable (HV) drugs and drug products.

METHODS

Two-period crossover BE investigations with either 24 or 36 subjects were simulated with assumptions of a coefficient of variation of 10, 20, 30, or 40%. The decline in the fraction of accepted studies was recorded as the ratio of geometric means (GMR) for the two formulations was raised from 1.00 to 1.45. Acceptance of BE was evaluated by scaled average BE, assuming various BE limits, and, for comparison, by unscaled average BE. A procedure for calculating exact confidence limits in two-period studies is presented, and an approximate method, based on the linearization of the regulatory model, is applied.

RESULTS

A mixed model is proposed for average BE. Accordingly, at low variabilities, the BE limit is constant, +/-BELo, generally log(1.25). Beyond a logarithmic, limiting, "switching" variability (sigma(o)), in the region of HV drugs, the approach of scaled average BE is applied with limits of +/-(BEL(o)/sigma(o)). It is demonstrated that the performance of the mixed model corresponds to these expectations. The effect of sigma(o), and of the resulting BE limits is also demonstrated. Scaled average BE, with all reasonable limits for HV drugs, requires fewer subjects than an unscaled average BE. In two-period studies, the exact and approximate methods calculating confidence limits yield very comparable inferences.

CONCLUSIONS

Scaled average BE can be effectively applied, with the recommended limits, for determining the BE of HV drugs and drug products. The limiting, "switching" variability (sigma(o)) will have to be established by regulatory authorities.

Assessment of average, population and individual bioequivalence in two- and four-period crossover studies

The aim of bioequivalence studies is to assess the equivalence of two pharmaceutical formulations of the same active drug substance. Currently three types of bioequivalence are distinguished: average, population and individual bioequivalence. Average and population bioequivalence can be assessed in two-period (non-replicated) crossover studies, whereas individual bioequivalence requires three- or four-period replicated studies, with a preference for four-period studies. The PC-program BIOEQV80 is presented for the statistical analysis of average and population bioequivalence from two-period crossover studies. The program BIOEQ2X2 is presented for the statistical analysis of all three types of bioequivalence from four-period replicated crossover studies. The statistical aspects of population and individual bioequivalence are based on a recent Guidance issued by the US Food and Drug Administration.

Population and individual bioequivalence: lessons from real data and simulation studies

The Food and Drug Administration (FDA) has proposed replacing the 1992 average bioequivalence (ABE) with population and individual bioequivalence (PBE & IBE), as outlined in the preliminary draft guidance of December 1997, which was subsequently replaced by the draft guidances of August 1999 and resolved in the final guidance of October 2000. This has led to considerable public debate among regulatory, academic, and industry experts at numerous conferences (e.g., FDA/AAPS March 1998, FDA/AAPS August-September 1999, FDA Pharmaceutical Sciences Advisory Committee September 1999) and in the literature. The final guidance calls for ABE to remain as the primary criterion by which new formulations may be judged ready for access to the marketplace. In addition, the FDA recommends the use of replicate study designs for the specific drug classes of controlled-release formulations and highly variable drugs. The final guidance also alludes to the possibility of a sponsor requesting alternative criteria such as PBE and IBE following consultation with the FDA. This procedure amounts to a data collection period during which data suitable to evaluate the operating characteristics of PBE and IBE would be generated, analyzed, and discussed among interested parties. A comprehensive review of currently available databases is useful in determining the ultimate value of this data collection period. This report provides an update to the previous publication by the authors. In all, 28 data sets from 20 replicate cross-over bioequivalence studies have been analyzed (n = 12-96) using the statistical methodology in the most recent FDA draft guidance. The results are presented below. ABE Pass: ABE Fail: Total: AUC/Cmax AUC/Cmax AUC/Cmax AUC/Cmax Pass PBE & IBE 20/14 1/3 21/17 Pass IBE only 1/0 0/0 1/0 Fail PBE and IBE 0/2 0/1 0/3 Fail IBE only 2/3 4/5 6/8 Total 23/19 5/9 28/28 Review of the database reveals many interesting features, most notably the lack of consistent results within a given data set across all three criteria. The sensitivity of subject-by-formulation interaction to sample size and inherent variability of the compounds is further explored through simulation studies. It is concluded that additional simulation assessments must be considered when evaluating the value of a data collection period for PBE and IBE assessment. It will be shown that definitive conclusions regarding some of the operating characteristics of PBE and IBE can be achieved through a combination of data-driven hypotheses followed by simulation studies to further evaluate the hypotheses. Some recommendations for further data collection will be made.