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Reference Datasets for Studies in a Replicate Design Intended for Average Bioequivalence with Expanding Limits
Abstract
In order to help companies qualify and validate the software used to evaluate bioequivalence trials in a replicate design intended for average bioequivalence with expanding limits, this work aims to define datasets with known results. This paper releases 30 reference datasets into the public domain along with proposed consensus results. A proposal is made for results that should be used as validation targets. The datasets were evaluated by seven different software packages according to methods proposed by the European Medicines Agency. For the estimation of CVwR and Method A, all software packages produced results that are in agreement across all datasets. Due to different approximations of the degrees of freedom, slight differences were observed in two software packages for Method B in highly incomplete datasets. All software packages were suitable for the estimation of CVwR and Method A. For Method B, different methods for approximating the denominator degrees of freedom could lead to slight differences, which eventually could lead to contrary decisions in very rare borderline cases.
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Proposals are being made for changes in bioequivalence criteria, the so- called 'population' and 'individual' bioequivalence methodologies. The proposed criteria require assumptions that have not yet been validated, including the equality of intra-subject variances. More data are needed about the different sources of variation. This type of information was provided by a single dose, two-formulation, four-period trial of phenytoin that used a replicated design. There were no formulation effects, thus each subject provided four observations from which intra-subject variances could be estimated; the individual intra-subject variances were equal within each formulation and were uncorrelated with individual means. This was true on both original and log-transformed scales. Observations of area under the time by concentration curve and maximum observed concentration were analyzed as the total study and within each of the two replications. Bioequivalence inferences were the same for all three analyses, indicating that for this drug 'individual' bioequivalence is not likely to be needed.
In order to help companies qualify and validate the software used to evaluate bioequivalence trials with two parallel treatment groups, this work aims to define datasets with known results. This paper puts a total 11 datasets into the public domain along with proposed consensus obtained via evaluations from six different software packages (R, SAS, WinNonlin, OpenOffice Calc, Kinetica, EquivTest). Insofar as possible, datasets were evaluated with and without the assumption of equal variances for the construction of a 90% confidence interval. Not all software packages provide functionality for the assumption of unequal variances (EquivTest, Kinetica), and not all packages can handle datasets with more than 1000 subjects per group (WinNonlin). Where results could be obtained across all packages, one showed questionable results when datasets contained unequal group sizes (Kinetica). A proposal is made for the results that should be used as validation targets.
It is difficult to validate statistical software used to assess bioequivalence since very few datasets with known results are in the public domain, and the few that are published are of moderate size and balanced. The purpose of this paper is therefore to introduce reference datasets of varying complexity in terms of dataset size and characteristics (balance, range, outlier presence, residual error distribution) for 2-treatment, 2-period, 2-sequence bioequivalence studies and to report their point estimates and 90% confidence intervals which companies can use to validate their installations. The results for these datasets were calculated using the commercial packages EquivTest, Kinetica, SAS and WinNonlin, and the non-commercial package R. The results of three of these packages mostly agree, but imbalance between sequences seems to provoke questionable results with one package, which illustrates well the need for proper software validation.
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.
Studies in bioequivalence are the commonly accepted method to demonstrate therapeutic equivalence between two medicinal products. Savings in time and cost are substantial when using bioequivalence as an established surrogate marker of therapeutic equivalence. For this reason the design, performance and evaluation of bioequivalence studies have received major attention from academia, the pharmaceutical industry and health authorities. Bioequivalence Studies in Drug Development focuses on the planning, conducting, analysing and reporting of bioequivalence studies, covering all aspects required by regulatory authorities. This text presents the required statistical methods, and with an outstanding practical emphasis, demonstrates their applications through numerous examples using real data from drug development. Includes all the necessary pharmacokinetic background information. Presents parametric and nonparametric statistical techniques. Describes adequate methods for power and sample size determination. Includes appropriate presentation of results from bioequivalence studies. Provides a practical overview of the design and analysis of bioequivalence studies. Presents the recent developments in methodology, including population and individual bioequivalence. Reviews the regulatory guidelines for such studies, and the existing global discrepancies. Discusses the designs and analyses of drug-drug and food-drug interaction studies. Bioequivalence Studies in Drug Development is written in an accessible style that makes it ideal for pharmaceutical scientists, clinical pharmacologists, and medical practitioners, as well as biometricians working in the pharmaceutical industry. It will also be of great value for professionals from regulatory bodies assessing bioequivalence studies.
DRUG DEVELOPMENT AND CLINICAL PHARMACOLOGY Aims of This Book Drug Development Clinical Pharmacology Statistics in Clinical Pharmacology Structure of the Book HISTORY AND REGULATION OF BIOEQUIVALENCE When and How BE Studies Are Performed Why Are BE Studies Performed? Deciding When Formulations Are Bioequivalent Potential Issues with TOST Bioequivalence Current International Regulation TESTING FOR AVERAGE BIOEQUIVALENCE Background Linear Model for 2 x 2 Data Applying the TOST Procedure Carry-over, Sequence, and Interaction Effects Checking Assumptions Made about the Linear Model Power and Sample Size for ABE in the 2 x 2 Design Example Where Test and Reference Are Not ABE Nonparametric Analysis Some Practical Issues BE STUDIES WITH MORE THAN TWO PERIODS Background Three-period Designs Within-subject Variability Robust Analyses for Three Period Designs Four-Period Designs Designs with More than Two Treatments Nonparametric Analyses of Tmax Technical Appendix: Efficiency Tables of Data DEALING WITH UNEXPECTED BE CHALLENGES Restricted Maximum Likelihood Modelling Failing BE and the DER Assessment Simulation Data-Based Simulation Carry-Over Optional Designs Determining Trial Size What Outliers are and How to Handle Their Data Bayesian BE Assessment Technical Appendix THE FUTURE AND RECENT PAST OF BE TESTING Brief History Individual and Population BE Scaled Average BE CLINICAL PHARMACOLOGY SAFETY STUDIES Background First-time-in-humans Sub-chronic Dosing Studies Food-Effect Assessment and DDIs Dose-Proportionality Technical Appendix QTC Background Modelling of QTc Data Interpreting the QTc Modelling Findings Design of a Thorough QTc Study in the Future Technical Appendix CLINICAL PHARMACOLOGY EFFICACY STUDIES Background Sub-chronic Dosing Phase IIa and the Proof of Concept Methodology Studies POPULATION PHARMACOKINETICS Population and Pharmacokinetics Absolute and Relative Bioavailability Age and Gender Pharmacokinetic Studies Ethnicity Liver Disease Kidney Disease Technical Appendix Epilogue Bibliography Index
The two one-sided test procedure (TOST) has been used for average bioequivalence testing since 1992 and is required when marketing new formulations of an approved drug. TOST is known to require comparatively large numbers of subjects to demonstrate bioequivalence for highly variable drugs, defined as those drugs having intra-subject coefficients of variation greater than 30%. However, TOST has been shown to protect public health when multiple generic formulations enter the marketplace following patent expiration. Recently, scaled average bioequivalence (SABE) has been proposed as an alternative statistical analysis procedure for such products by multiple regulatory agencies. SABE testing requires that a three-period partial replicate cross-over or full replicate cross-over design be used. Following a brief summary of SABE analysis methods applied to existing data, we will consider three statistical ramifications of the proposed additional decision rules and the potential impact of implementation of scaled average bioequivalence in the marketplace using simulation. It is found that a constraint being applied is biased, that bias may also result from the common problem of missing data and that the SABE methods allow for much greater changes in exposure when generic-generic switching occurs in the marketplace.
The construction and analysis of an experimental design, in which there are t2 experimental units for t treatments, are presented. The design is suitable for experiments in which the treatments are applied to experimental units in a sequence over two periods and where an estimate of the treatments x periods interaction is required. Least squares estimators for the various effects are obtained and the analysis of variance of a numerical example is presented to illustrate the application of the results to experimental data.
Restricted maximum likelihood (REML) is now well established as a method for estimating the parameters of the general Gaussian linear model with a structured covariance matrix, in particular for mixed linear models. Conventionally, estimates of precision and inference for fixed effects are based on their asymptotic distribution, which is known to be inadequate for some small-sample problems. In this paper, we present a scaled Wald statistic, together with an F approximation to its sampling distribution, that is shown to perform well in a range of small sample settings. The statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias. This approach has the advantage that it reproduces both the statistics and F distributions in those settings where the latter is exact, namely for Hotelling T2 type statistics and for analysis of variance F-ratios. The performance of the modified statistics is assessed through simulation studies of four different REML analyses and the methods are illustrated using three examples.
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.
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