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It is avail- able for download when Phoenix is purchased. And can be used to provide floating licenses for WinNonlin 5.x is backwards compatible with WinNonlin 5.0. Note: Contact Pharsight customer support (support@pharsight.

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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. INTRODUCTION Bioequivalence testing is a general requirement for companies developing generic medicines, testing food effects, making formulation changes, or developing extensions to existing approved medicines where absorption rate and extent to the systemic circulation determines safety and efficacy. Throughout many countries and jurisdictions, the common way of testing for bioequivalence is to compare the pharmacokinetics of the new formulation (“test”) with that of the known formulation (“reference”). Using non-compartmental analysis, the primary metrics derived in bioequivalence studies are most often the area under the concentration time curve until the last sampling point ( AUC t) and the maximum observed concentration ( C max) for both the test and the reference. A confidence interval is then constructed on basis of two one-sided t tests, typically at a nominal α level of 5%.

The most common designs for bioequivalence testing are the two-treatment, two-sequence, two-period randomized crossover design and the randomized two-group parallel design. The former is considerably more common than the latter and the design of choice for active ingredients whose half-lives are not prohibitively long (–). To evaluate the data obtained in a bioequivalence trial, companies must use validated software but in the absence of datasets with known results, it is difficult to actually know if the software acquired correctly performs the task it is supposed to do and therefore, it is practically impossible to validate software in-house beyond installation qualification and operational qualification. On that basis, we recently published a paper in this journal with reference datasets for the two-treatment, two-sequence, two-period crossover trials and where the datasets were evaluated with different software packages.

Since trials with two parallel groups are the second most common type of bioequivalence studies and published datasets with known results are scarce, the purpose of this paper is to propose reference datasets for two-group parallel trials and derive 90% confidence intervals with different statistical software packages in order to establish consensus results that can be used—together with the datasets—to qualify or validate software analyzing the outcomes from parallel group bioequivalence trials. It is outside the scope of this paper to discuss more than two groups or the other design options that exist such as replicate designs. For validation purposes, datasets should be of varying complexity in terms of imbalance, outliers, range, heteroscedasticity, and point estimate in order to cover any situation which can reasonably be expected to occur in practice. It is not the aim of this work to validate any software or to advocate for or against any specific software package. This is a dataset simulated on basis of a log-normal distribution, where the simulated GMR was 1.1 and with slight imbalance ( N T = 31, N R = 29) and homoscedasticity (CV R = CV T = 0.05).

Although a CV of 0.05 is not realistic for any drug tested in humans; variabilities at this level are often seen with orally inhaled products (e.g., delivered dose). Applicants in Europe may choose the parallel bioequivalence model for their testing. To qualify for approval on basis of such data, the actual requirement is a 90% confidence interval with a 15% equivalence margin corresponding to an acceptance range of 85.00–117.65% when a multiplicative model is used. 3 where t 1 − α, ν is the one-sided critical value of Student’s t distribution at ν degrees of freedom for the given α (in this paper 0.05) and MSE is the mean square error (estimated pooled variance). R and SAS are script-/code-based applications. Examples of scripts used for these two software packages are uploaded as a supplementary material.

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They should be adapted to the user’s preferences. The OpenOffice Calc spreadsheet is also uploaded as a supplementary material. Phoenix/WinNonlin natively does not offer evaluations based on the Welch correction. A workaround (,) was used in generating results given in Table. The Welch correction appears to be impossible in the menu-driven software packages EquivTest/PK and Kinetica.

DISCUSSION The conventional t test is fairly robust against violations of homoscedasticity but quite sensitive to unequal group sizes. Furthermore, preliminary testing for equality of variances is flawed and should be avoided.

If assumptions are violated, the t test becomes liberal, i.e., the patient’s risk might exceed the nominal level and an alternative (e.g., based on the Welch correction) is suggested (,). FDA’s guidance states: “For parallel designs equal variances should not be assumed”.

In WinNonlin, a somewhat cumbersome workaround allows a Welch correction for construction of the confidence interval, whereas in EquivTest/PK and Kinetica, there appears to be no option to evaluate two-group parallel designs with the Welch correction for unequal variances. Due to limitations of WinNonlin (fixed factors are restricted to 1000 levels), we were not able to process datasets P7–P11 with the published workaround. Kinetica consistently arrived at confidence intervals that differed from the other packages if datasets had unequal group sizes (i.e., P2, P5–7, P10–P11). A similar phenomenon was noted in a previous publication presenting balanced and imbalanced reference datasets for two-treatment, two-sequence, two-period crossover bioequivalence trials.

Although we do not have access to Kinetica’s source code, it is noted that when group sizes are equal (that is, when N T = N R), Eq. can be simplified to. The results coincide with Kinetica’s that we found for the investigated datasets. Equation is stated in the user manual. While it is outside the scope of this paper to specifically debate any specific software’s general fitness for bioequivalence evaluations, the fact that different packages arrive at different results with identical datasets underscore the need for proper validation. The datasets and evaluations presented here are relatively simple; in various areas of drug development, much more sophisticated statistical models with many more numerical settings are available.

Examples include mixed effect models used for longitudinal data or replicated bioequivalence trials, and survival or time-to-event trials evaluated by Kaplan-Meier derivatives, to mention but a few. To help companies qualify or validate their software for such evaluations, we call for other authors to publish datasets of varying complexity with known results that can be confirmed by multiple statistical packages. CONCLUSION This paper releases 11 datasets into the public domain along with proposed consensus results in order to help companies qualify and validate their statistical software for evaluation of bioequivalence trials with two treatment groups. The datasets are evaluated with different statistical packages with and without the assumption of equal variances for the construction of the 90% confidence interval. Not all packages are able to use a Welch correction for unequal variances when analyzing the datasets and not all packages can handle the largest datasets. In addition, one package seemed to arrive at results that stand in contrast to others. We propose the results obtained with R, which are identical to those obtained with SAS (and WinNonlin, where possible) to be targeted by companies qualifying or validating their software.

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Prodigy albums. The datasets are available as supplementary material.