(M1430-10-65) Comparing a t-Distribution Based Bayesian Approach with the Two One-Sided t-Test (TOST) for Bioequivalence Studies in Real-World Datasets

Purpose: The two one-sided t-test (TOST)¹ has been used as a regulatory standard to evaluate average bioequivalence (BE). Peck et al² compared the performance of TOST with a Bayesian procedure (BEST package3, which assumes the t-distribution, referred to as Bayes_T) using simulated datasets and found that TOST and the Bayes_T procedures perform comparably on Test/Reference (T/R) ratio data following the lognormal distribution, while Bayes_T is more accurate, requiring fewer subjects when data follow the normal distribution or contain extreme values². In this study, real-world BE study datasets were used to compare the performance of Bayes_T with TOST in different BE scenarios comprising lognormal T/R data and inclusion of extreme values.

Methods: Real-world BE datasets were assembled from two-treatment, two-period (2x2), crossover BE studies in abbreviated new drug applications (ANDAs) submitted to the US. Food and Drug Administration between 2020-2021. 2,341 BE pharmacokinetic parameter datasets (811 C_MAX, 754 AUC_T, and 776 AUC_I) were reported, 97.39% of which met BE criteria using TOST. BE performance of TOST and Bayes_T was compared on these datasets, along with Shapiro-Wilk normality tests, extreme value assessments (2.5 interquartile range as criteria), and skewness analyses. The BE acceptance range of 0.8000-1.2500 was used for both TOST and Bayes_T assessments.

Results: BE conclusions using TOST and Bayes_T agreed in 2,314 (98.85%) of the datasets and disagreed on BE in 27 datasets. Agreement or non-agreement between the two approaches was categorized as follows: 1) TOST BE, Bayes_T BE; 2) TOST not-BE(NBE), Bayes_T NBE; 3) TOST BE, Bayes_T NBE; and 4) TOST NBE, Bayes_T BE. In each category, normality tests and extreme value assessments were conducted. The results are reported in Table 1. In Category 4 (TOST NBE, Bayes_T BE (N=20, including 7 C_MAX, 6 AUC_T, and 7 AUC_I)), the log-transformed T/R ratios of all datasets rejected normality and 19 datasets included extreme values. Notably, among these 19 datasets, six datasets included extreme values in logT and log(T/R), but not logR, eight datasets had extreme values in logR and log(T/R), and five datasets had no extreme values in either logT or logR (only in log(T/R)). The log-transformed T/R ratios of 19 datasets were highly skewed (absolute values of skewness greater than 1). The absolute differences between the confidence/credible bounds (upper or lower) from TOST and Bayes_T were also large, ranging from 0.004 to 0.887 (median = 0.046). For Category 3 (TOST BE, Bayes_T NBE (N=7, all C_MAX datasets)), all log-transformed T/R ratios didn’t reject normality and contained no extreme values. The estimated confidence/credible bounds for both approaches were close to either of BE boundaries (0.8000 or 1.2500) and the absolute differences between the confidence/credible bounds (upper or lower) from TOST and Bayes_T were small, ranging from 0.002 to 0.026 (median = 0.010). Four datasets were moderately to highly skewed (absolute values of skewness greater than 0.5) and the other three datasets were nearly symmetrical (absolute values of skewness within 0.5). For Categories 1 and 2, datasets with agreement of both approaches, the log-transformed T/R ratios of 608 datasets rejected normality and 475 of them included extreme values, of which 57 datasets had extreme values only in logT and log(T/R), 77 datasets had extreme values only in logR and log(T/R), and 295 datasets have no extreme values in either logT or logR (only in log(T/R)). Regarding skewness, the log(T/R) of 1352 datasets were approximately symmetrical, 609 datasets were moderately skewed, and 353 datasets were highly skewed. Table 1 shows that in log(T/R) datasets that rejected normality with extreme values, the average sample sizes of the datasets from Categories 1 and 2 (e.g., 43 and 41) were higher than that of the datasets in Category 4 (i.e., 36).

Conclusion: In 2,341 ANDA datasets, Bayes_T and TOST agree on BE in 98.85% cases. When TOST rejected BE and Bayes_T concluded BE, the results were consistent with Peck et al², indicating that the t-distribution based Bayesian approach can be a useful complementary tool for datasets rejecting normality and/or include extreme values in log-transformed T/R ratios. Skewness may be another contributing factor to discordance of BE between TOST and Bayes_T. The cases with inconsistent BE conclusions from TOST and Bayes_T warrant further analysis.

References: 1. Schuirmann DJ. (1987). A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. J Pharmacokinet Biopharm. 15:657-680.
2. Peck, C., Campbell, G., Yoo, I., Feng, K., Hu, M., & Zhao, L. (2022). Comparing a Bayesian Approach (BEST) with the Two One-Sided t-Tests (TOSTs) for Bioequivalence Studies. The AAPS Journal, 24(5), 97.
3. Kruschke JK. (2013). Bayesian estimation supersedes the t test. J Exp Psychol Gen. 142:573-603.

Acknowledgements: Conflict of Interest: The authors declare no competing interests. Disclaimer: This article reflects the views of the authors and should not be construed to represent FDA’s views or policies.