Bayesian Dynamic Borrowing for Vaccine Efficacy Studies in Pediatric Population
Pub. online: 21 July 2026
Type: Statistical Data Science
Open Access
Open Access
Received
21 November 2025
21 November 2025
Accepted
28 June 2026
28 June 2026
Published
21 July 2026
21 July 2026
Abstract
Pediatric vaccine efficacy studies face enrollment challenges, often resulting in underpowered studies to confirm vaccine efficacy. To address the challenge, this paper proposes a novel Two-Tier Bayesian dynamic borrowing framework that selectively incorporates two heterogeneous sources of historical data of adult populations into pediatric studies. The method employs similarity metrics based on intermediate outcomes, such as immunological markers, to dynamically determine borrowing weights via overlap coefficients, ensuring that only comparable data are utilized. Power priors are constructed with weights reflecting this similarity, while a cap on the effective sample size helps maintain control of the maximum information to borrow. Simulation studies demonstrate that the proposed approach improves power, reduces estimation bias and maintains type I error control, thus offering a robust and practical strategy for pediatric vaccine study design.
Supplementary material
Supplementary MaterialThe R code used to reproduce the simulation results is provided as online Supplementary Material.
References
Baumann L, Sauer LD, Kieser M (2025). A basket trial design based on power priors. Statistics in Biopharmaceutical Research, 17(3): 446–456. https://doi.org/10.1080/19466315.2024.2402275.
Callegaro A, Karkada N, Aris E, Zahaf T (2023). Vaccine clinical trials with dynamic borrowing of historical controls: Two retrospective studies. Pharmaceutical Statistics, 22(3): 475–491. https://doi.org/10.1002/pst.2283.
Callegaro A, Luo Y, Karkada N, Zahaf T (2024). Dynamic borrowing of historical controls adjusting for covariates in vaccine efficacy clinical trials. Pharmaceutical Statistics, 23(5): 630–644. https://doi.org/10.1002/pst.2384.
Chan IS, Bohidar NR (1998). Exact power and sample size for vaccine efficacy studies. Communications in Statistics – Theory and Methods, 27(6): 1305–1322. https://doi.org/10.1080/03610929808832160.
Chen MH, Guan Z, Lin M, Sun M (2025). Power priors for leveraging historical data: Looking back and looking forward. Journal of Data Science, 23(1): 1–30. https://doi.org/10.6339/24-JDS1161.
Chen MH, Guan Z, Sun M, Zhong J (2024). A unified Bayesian decision rule-based approach for Bayesian design of clinical trials using historical data. In: Biostatistics in Biopharmaceutical Research and Development: 80-Years of Contributions and Dedications from the Deming Conference (DG Chen, ed.), 195–217. Springer, New York, NY.
Chen MH, Ibrahim JG, Lam P, Yu A, Zhang Y (2011). Bayesian design of non-inferiority trials for medical devices using historical data. Biometrics, 67(3): 1163–1170. https://doi.org/10.1111/j.1541-0420.2011.01561.x.
Chen MH, Ibrahim JG, Zeng D, Hu K, Jia C (2014). Bayesian design of superiority clinical trials for recurrent events data with applications to bleeding and transfusion events in myelodyplastic syndrome. Biometrics, 70(4): 1003–1013. https://doi.org/10.1111/biom.12215.
De Santis F, Gubbiotti S (2023). Borrowing historical information for non-inferiority trials on COVID-19 vaccines. The International Journal of Biostatistics, 19(1): 177–189. https://doi.org/10.1515/ijb-2021-0120.
Gamalo-Siebers M, Savic J, Basu C, Zhao X, Gopalakrishnan M, Gao A, et al. (2017). Statistical modeling for Bayesian extrapolation of adult clinical trial information in pediatric drug evaluation. Pharmaceutical Statistics, 16(4): 232–249. https://doi.org/10.1002/pst.1807.
Han Z, Zhang Q, Tiwari R, Bai T (2025). Bayesian borrowing with multiple heterogeneous historical studies using order restricted normalized power prior. Statistics in Medicine, 44(3–4): e10302. https://doi.org/10.1002/sim.10302.
Han Z, Zhang Q, Wang M, Ye K, Chen MH (2023). On efficient posterior inference in normalized power prior Bayesian analysis. Biometrical Journal, 65(5): 2200194 https://doi.org/10.1002/bimj.202200194.
Hobbs BP, Carlin BP, Mandrekar SJ, Sargent DJ (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.
Huang Y, Hejazi NS, Blette B, Carpp LN, Benkeser D, ..., Gilbert PB (2023). Stochastic interventional vaccine efficacy and principal surrogate analyses of antibody markers as correlates of protection against symptomatic COVID-19 in the COVE mRNA-1273 trial. Viruses, 15(10): 2029. https://doi.org/10.3390/v15102029.
Ibrahim JG, Chen MH (2000). Power prior distributions for regression models. Statistical Science, 15(1): 46–60. https://doi.org/10.1214/ss/1009212673.
Inman HF, Bradley JEL (1989). The overlapping coefficient as a measure of agreement between probability distributions and point estimation of the overlap of two normal densities. Communications in Statistics-Theory and Methods, 18(10): 3851–3874. https://doi.org/10.1080/03610928908830127.
Jiang Y, Simon S, Mayo MS, Gajewski BJ (2015). Modeling and validating Bayesian accrual models on clinical data and simulations using adaptive priors. Statistics in Medicine, 34(4): 613–629. https://doi.org/10.1002/sim.6359.
Jin M, Feng D, Liu G (2020). Bayesian approaches on borrowing historical data for vaccine efficacy trials. Statistics in Biopharmaceutical Research, 12(3): 284–292. https://doi.org/10.1080/19466315.2020.1736617.
Jin M, Li Q, Kaur A (2021). Bayesian design for pediatric clinical trials with binary endpoints when borrowing historical information of treatment effect. Therapeutic Innovation & Regulatory Science, 55(2): 360–369. https://doi.org/10.1007/s43441-020-00220-5.
Li W, Chen MH, Tan H, Dey DK (2015). Bayesian design of non-inferiority clinical trials with co-primary endpoints and multiple dose comparison. In: Applied Statistics in Biomedicine and Clinical Trials Design – Selected Papers from 2013 ICSA/ISBS Joint Statistical Meetings (Z Chen, A Liu, Y Qu, L Tang, N Ting, Y Tsong, eds.), 17–33. Springer, New York, NY.
Li W, Chen MH, Wang X, Dey DK (2018). Bayesian design of non-inferiority clinical trials via the Bayes factor. Statistics in Biosciences, 10(2): 439–459. https://doi.org/10.1007/s12561-017-9200-5.
Liu M, Bunn V, Hupf B, Lin J, Lin J (2021). Propensity-score-based meta-analytic predictive prior for incorporating real-world and historical data. Statistics in Medicine, 40(22): 4794–4808. https://doi.org/10.1002/sim.9095.
Malec D (2001). A closer look at combining data among a small number of binomial experiments. Statistics in Medicine, 20(12): 1811–1824. https://doi.org/10.1002/sim.782.
Morita S, Thall PF, Müller P (2008). Determining the effective sample size of a parametric prior. Biometrics, 64(2): 595–602. https://doi.org/10.1111/j.1541-0420.2007.00888.x.
Morita S, Thall PF, Müller P (2012). Prior effective sample size in conditionally independent hierarchical models. Bayesian Analysis, 7(3): 591–614. https://doi.org/10.1214/12-BA720.
Moss J, Tveten M (2019). kdensity: An R package for kernel density estimation with parametric starts and asymmetric kernels. Journal of Open Source Software, 4(42): 1566. https://doi.org/10.21105/joss.01566.
Neuenschwander B, Weber S, Schmidli H, O’Hagan A (2020). Predictively consistent prior effective sample sizes. Biometrics, 76(2): 578–587. https://doi.org/10.1111/biom.13252.
Peng L, Jin J, Chambonneau L, Zhao X, Zhang J (2023). Bayesian borrowing from historical control data in a vaccine efficacy trial. Pharmaceutical Statistics, 22(5): 815–835. https://doi.org/10.1002/pst.2313.
Psioda MA, Bean NW, Wright BA, Lu Y, Mantero A, Majumdar A (2025). Inverse probability weighted Bayesian dynamic borrowing for estimation of marginal treatment effects with application to hybrid control arm oncology studies. Journal of Biopharmaceutical Statistics, 35(6): 1–23. https://doi.org/10.1080/10543406.2025.2489285.
Schmidli H, Gsteiger S, Roychoudhury S, O’Hagan A, Spiegelhalter D, 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.
Schoenfeld DA, Zheng H, Finkelstein DM (2009). Bayesian design using adult data to augment pediatric trials. Clinical Trials, 6(4): 297–304. https://doi.org/10.1177/1740774509339238.
US Food and Drug Administration (2010). Guidance for the use of Bayesian statistics in medical device clinical trials. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/guidance-use-bayesian-statistics-medical-device-clinical-trials. Online. Accessed October 20, 2025.
US Food and Drug Administration (2016). Leveraging existing clinical data for extrapolation to pediatric uses of medical devices. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/leveraging-existing-clinical-data-extrapolation-pediatric-uses-medical-devices. Online. Accessed October 20, 2025.
US Food and Drug Administration (2018). Framework for FDA’s real-world evidence program. https://www.fda.gov/media/120060/download. Online. Accessed October 20, 2025.
US Food and Drug Administration (2021). Advancing the development of pediatric therapeutics complex innovative trial design public workshop. https://www.fda.gov/drugs/news-events-human-drugs/fda-m-cersi-advancing-development-pediatric-therapeutics-complex-innovative-trial-design-public. Online. Accessed October 20, 2025.
US Food and Drug Administration (2023a). Considerations for the use of real-world data and real-world evidence to support regulatory decision-making for drug and biological products. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/considerations-use-real-world-data-and-real-world-evidence-support-regulatory-decision-making-drug. Online. Accessed October 20, 2025.
US Food and Drug Administration (2023b). Pediatric drug development: Regulatory considerations – complying with the pediatric research equity act and qualifying for pediatric exclusivity under the best pharmaceuticals for children act. https://www.fda.gov/media/168201/download. Online. Accessed October 20, 2025.
US Food and Drug Administration (2023c). Real-world data: Assessing registries to support regulatory decision-making for drug and biological products. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/real-world-data-assessing-registries-support-regulatory-decision-making-drug-and-biological-products. Online. Accessed October 20, 2025.
US Food and Drug Administration (2024). Real-world data: Assessing electronic health records and medical claims data to support regulatory decision-making for drug and biological products. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/real-world-data-assessing-electronic-health-records-and-medical-claims-data-support-regulatory. Online. Accessed October 20, 2025.
US Food and Drug Administration (2026). Use of Bayesian methodology in clinical trials of drug and biological products. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/use-bayesian-methodology-clinical-trials-drug-and-biological-products. Online. Accessed March 11, 2026.
US Government Publishing Office (2016). 21st Century Cures Act. https://www.govinfo.gov/content/pkg/PLAW-114publ255/html/PLAW-114publ255.htm. Online. Accessed October 20, 2025.
van Rosmalen J, Dejardin D, van Norden Y, Löwenberg B, Lesaffre E (2018). Including historical data in the analysis of clinical trials: Is it worth the effort? Statistical Methods in Medical Research, 27(10): 3167–3182. https://doi.org/10.1177/0962280217694506.
Viele K, Berry S, Neuenschwander B, Amzal B, Chen F, Enas N, et al. (2014). Use of historical control data for assessing treatment effects in clinical trials. Pharmaceutical Statistics, 13(1): 41–54. https://doi.org/10.1002/pst.1589.
Wang C, Li H, Chen WC, Lu N, Tiwari R, ..., Yue LQ (2019). Propensity score-integrated power prior approach for incorporating real-world evidence in single-arm clinical studies. Journal of Biopharmaceutical Statistics, 29(5): 731–748. https://doi.org/10.1080/10543406.2019.1657133.
Yuan W, Chen MH, Zhong J (2022). Flexible conditional borrowing approaches for leveraging historical data in the Bayesian design of superiority trials. Statistics in Biosciences, 14(2): 197–215. https://doi.org/10.1007/s12561-021-09321-7.
