Bayesian Information Sharing for Equivalence Testing with an Application to Dose Proportionality Studies
Pub. online: 5 January 2026
Type: Methodology Article
Open Access
Open Access
Area: Biomedical Research
Accepted
19 October 2025
19 October 2025
Published
5 January 2026
5 January 2026
Abstract
Dose proportionality is an essential aspect of pharmacokinetics (PK). We aim to enhance the efficiency of PK studies by incorporating interim analyses and utilizing data from past trials to increase precision and enable early termination of studies if applicable. In this paper, we extend the multisource exchangeability model (MEM) to the setting with correlated data with interim analyses. Simulation results indicate that the MEM estimators are efficient even with smaller sample sizes, although smaller sample sizes may have higher mean square error (MSE) and bias due to early stopping and more liberal data borrowing from non-exchangeable supplementary sources. Our recommendation is to use a constrained MEM approach when considering small sample sizes, with additional caution needed around the equivalence boundary to better control the inflated type I error rate, bias, and MSE. This research extends the application of MEMs from linear regression models to settings with correlated data using linear mixed effects regression models. It also innovatively applies MEMs to equivalence testing in the context of dose proportionality studies, thereby enhancing their efficiency.
Supplementary material
Supplementary MaterialSupplementary Materials for Bayesian Information Sharing and Interim Efficacy Monitoring for Equivalence Testing with an Application to Dose Proportionality Studies
References
Anderson, K. (2024). gsDesign: Group Sequential Design. R package version 3.6.2. https://CRAN.R-project.org/package=gsDesign.
Anderson, P. L., Liu, A. Y., Castillo-Mancilla, J. R., Gardner, E. M., Seifert, S. M., McHugh, C., Wagner, T., Campbell, K., Morrow, M., Ibrahim, M. et al. (2018). Intracellular tenofovir-diphosphate and emtricitabine-triphosphate in dried blood spots following directly observed therapy. Antimicrobial agents and chemotherapy 62(1) 01710-17.
Armitage, P., McPherson, C. and Rowe, B. (1969). Repeated significance tests on accumulating data. Journal of the Royal Statistical Society: Series A (General) 132(2) 235–244. https://doi.org/10.2307/2343787. MR0250405
Chen, N. and Lee, J. J. (2019). Bayesian hierarchical classification and information sharing for clinical trials with subgroups and binary outcomes. Biometrical Journal 61(5) 1219–1231. https://doi.org/10.1002/bimj.201700275. MR4013344
Chen, N. and Lee, J. J. (2020). Bayesian cluster hierarchical model for subgroup borrowing in the design and analysis of basket trials with binary endpoints. Statistical Methods in Medical Research 29(9) 2717–2732. https://doi.org/10.1177/0962280220910186. MR4129440
Durrleman, S. and Simon, R. (1990). Planning and monitoring of equivalence studies. Biometrics 329–336. https://doi.org/10.2307/2531438. MR1060592
Hobbs, B. P., Carlin, B. P., Mandrekar, S. J. and Sargent, D. J. (2011). Hierarchical commensurate and power prior models for adaptive incorporation of historical information in clinical trials. Biometrics 67(3) 1047–1056. https://doi.org/10.1111/j.1541-0420.2011.01564.x. MR2829239
Jennison, C. and Turnbull, B. W. (1999) Group sequential methods with applications to clinical trials. CRC Press. MR1710781
Kaizer, A. M., Koopmeiners, J. S. and Hobbs, B. P. (2018). Bayesian hierarchical modeling based on multisource exchangeability. Biostatistics 19(2) 169–184. https://doi.org/10.1093/biostatistics/kxx031. MR3799610
Kaizer, A. M., Koopmeiners, J. S., Chen, N. and Hobbs, B. P. (2021). Statistical design considerations for trials that study multiple indications. Statistical methods in medical research 30(3) 785–798. https://doi.org/10.1177/0962280220975187. MR4236836
Kotalik, A., Vock, D. M., Hobbs, B. P. and Koopmeiners, J. S. (2022). A group-sequential randomized trial design utilizing supplemental trial data. Statistics in Medicine 41(4) 698–718. https://doi.org/10.1002/sim.9249. MR4386975
Meredith, M. and Kruschke, J. (2022). HDInterval: Highest (Posterior) Density Intervals. R package version 0.2.4. https://CRAN.R-project.org/package=HDInterval.
Plummer, M. (2022). rjags: Bayesian Graphical Models using MCMC. R package version 4-13. https://CRAN.R-project.org/package=rjags.
R Core Team (2022). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.
Schmidli, H., Gsteiger, S., Roychoudhury, S., O’Hagan, A., Spiegelhalter, D. and Neuenschwander, B. (2014). Robust meta-analytic-predictive priors in clinical trials with historical control information. Biometrics 70(4) 1023–1032. https://doi.org/10.1111/biom.12242. MR3295763
Wang, S. K. and Tsiatis, A. A. (1987). Approximately optimal one-parameter boundaries for group sequential trials. Biometrics 193–199. https://doi.org/10.2307/2531959. MR0882780
Yager, J., Castillo-Mancilla, J., Ibrahim, M. E., Brooks, K. M., McHugh, C., Morrow, M., McCallister, S., Bushman, L. R., MaWhinney, S., Kiser, J. J. et al. (2020). Intracellular tenofovir-diphosphate and emtricitabine-triphosphate in dried blood spots following tenofovir alafenamide: the TAF-DBS study. JAIDS Journal of Acquired Immune Deficiency Syndromes 84(3) 323–330.
