Model-Based Approach for Designing an Efficient Bioequivalence Study for Highly Variable Drugs

The statistical procedures as outlined by the European Medicines Agency (EMA) and United States Food and Drug Administration (FDA) guidelines for bioequivalence testing of highly variable drugs (HVDs) are complex. Additionally, the sample size is affected by clinical study designs or practical real-world problems, such as dropout rate or study budget. To overcome these difficulties, we propose a model-based approach for the selection of a study design with a sample size that satisfies the bioequivalence criteria using simulation studies based on a pharmacokinetic (PK) model. The designed approach was implemented using a simulation procedure considering some conventionally measured factors, such as geometric mean ratio and within-subject coefficient of variation, with various PK information important in determining bioequivalence. All simulation results were assessed according to the EMA and FDA guidelines. Furthermore, power calculations from simulation results were interpreted with regard to PK characteristics and compared among 2 × 2, 3 × 3, and 2 × 4 crossover designs to determine the efficient design considering appropriate sample size and duration of the clinical study. The proposed approach can be applied to bioequivalence studies of all drugs. However, the current study was targeted at HVDs, which are highly likely to require detailed decision making for sample size and study design.

Pharmacokinetics, Bioequivalence, and Safety Studies of Pantoprazole Sodium Enteric-Coated Tablets in Healthy Subjects

This study aimed to evaluate the bioequivalence of 2 pantoprazole sodium enteric-coated tablet formulations, a generic formulation and a branded formulation, and to investigate their pharmacokinetic and safety profiles. The study was designed as a single-center, randomized, open-label, single-dose, dual-period, and 2-sequence crossover trial, and was divided into fasting and postprandial human bioequivalence trials. In the first trial, 36 subjects were fasted overnight before they were given generic or branded tablets (during 2 separate administration periods). Separately, 42 subjects were provided a high-fat meal 1 hour before the drugs were administered. Blood specimens of each subject were obtained up to 24 hours after drug administration. No significant differences were observed between the pharmacokinetic profiles of the generic and branded pantoprazole sodium enteric-coated tablets. Bioequivalence was evaluated using 90% confidence intervals for the ratio of test/reference log area under the concentration-time curve over 24 hours, log area under the concentration-time curve to infinity (AUC_0-∞ ), and log peak concentration (C_max ). The 90% confidence intervals of the least squares geometric mean ratio of C_max , area under the concentration-time curve from time zero to the last measurable concentration (AUC_0-t ), and AUC_0-∞ of 36 subjects in the fasting trial and of 40 of 41 subjects in the postprandial trial (C_max [41], AUC_0-t [41], and AUC_0-∞ [40]) were in accordance with the bioequivalence criteria. No severe adverse effects were detected. The generic and branded pantoprazole sodium enteric-coated tablets were considered bioequivalent with similar safety profiles.

Algorithms for evaluating reference scaled average bioequivalence: power, bias, and consumer risk

The determination of the bioequivalence between highly variable drug products involves the evaluation of reference scaled average bioequivalence. The European and US regulatory authorities suggest different algorithms for the implementation of this approach. Both algorithms are based on approximations reflected in lower than the achievable power or higher than the nominal consumer risk of 5%. To overcome these deficiencies, a new class of algorithms, the so-called Exact methods, was earlier introduced. However, their applicability was limited. We propose 2 modifications which make their computation simpler and also applicable with any study design. Four algorithms were evaluated in simulated 3-period and 4-period bioequivalence studies: Hyslop's approach recommended by the US FDA, the method of average bioequivalence with expanding limits requested by the European EMA, and 2 versions of the new Exact methods. At small sample sizes, the Exact methods had substantially higher statistical power than Hyslop's algorithm and had lower consumer risk than the method of average bioequivalence with expanding limits. Similarly to the Hyslop's algorithm, higher than 5% consumer risk was observed only with either unbalanced study design or with additional regulatory requirements. The improved Exact algorithms compare favorably with the alternative procedures. They are based on the bias correction method of Hedges. The recognition that the scaled difference statistics is measured with bias has important practical implications when results of pilot bioequivalence studies are evaluated and, at the same time, calls for the revision of the statistical theory of RSABE and its related methods.

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.

An Exact Procedure for the Evaluation of Reference-Scaled Average Bioequivalence

Reference-scaled average bioequivalence (RSABE) has been recommended by Food and Drug Administration (FDA), and in its closely related form by European Medicines Agency (EMA), for the determination of bioequivalence (BE) of highly variable (HV) and narrow therapeutic index (NTI) drug products. FDA suggested that RSABE be evaluated by an approximating procedure. Development of an alternative, numerically exact approach was sought. A new algorithm, called Exact, was derived for the assessment of RSABE. It is based upon the observation that the statistical model of RSABE follows a noncentral t distribution. The parameters of the distribution were derived for crossover and parallel-group study designs. Simulated BE studies of HV and NTI drugs compared the power and consumer risk of the proposed Exact method with those recommended by FDA and EMA. The Exact method had generally slightly higher power than the FDA approach. The consumer risks of the Exact and FDA procedures were generally below the nominal error risk with both methods except for the partial replicate design under certain heteroscedastic conditions. The estimator of RSABE was biased; simulations demonstrated the appropriateness of Hedges' correction. The FDA approach had another, small but meaningful bias. The confidence intervals of RSABE, based on the derived exact, analytical formulas, are uniformly most powerful. Their computation requires in standard cases only a single-line program script. The algorithm assumes that the estimates of the within-subject variances of both formulations are available. With each algorithm, the consumer risk is higher than 5% when the partial replicate design is applied.

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.