Power Priors for Leveraging Historical Data: Looking Back and Looking Forward✩
Volume 23, Issue 1 (2025), pp. 1–30
Pub. online: 31 December 2024
Type: Data Science Reviews
Open Access
Open Access
✩
Data used in preparation of this article were obtained from the Alzheimer’s Disease Neuroimaging Initiative database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: http://adni.loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf
Received
30 March 2024
30 March 2024
Accepted
17 December 2024
17 December 2024
Published
31 December 2024
31 December 2024
Abstract
Historical data or real-world data are often available in clinical trials, genetics, health care, psychology, environmental health, engineering, economics, and business. The power priors have emerged as a useful class of informative priors for a variety of situations in which historical data are available. In this paper, an overview of the development of the power priors is provided. Various variations of the power priors are derived under a binomial regression model and a normal linear regression model. The development of software on the power priors is also briefly reviewed. Throughout this paper, the data from the Kociba study and the National Toxicology Program study as well as the data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) study are used to demonstrate the derivations of the power priors and their variations. Detailed analyses of the data from these studies are carried out to further demonstrate the usefulness of the power priors and their variations in these real applications. Finally, the directions of future research on the power priors are discussed.
Supplementary material
Supplementary MaterialThe posterior densities in Figure 2 and the posterior estimates reported in Table 5 are computed using SAS while the posterior estimates in Table 6 are obtained either analytically or using R . Additional tables and figures for MCMC convergence checks, which show good convergence and mixing of MCMC samples, are provided in Supplementary Material Sections S.1. Section S.2 contains additional tables and figures for MCMC convergence checks for the ADNI data, which again show good convergence and mixing. Unfortunately, the ADNI data is proprietary. SAS code (Kociba_NTP_example.sas ) for the Kociba and NTP data, R code (analysis_simulated_data.qmd ) for ADNI results, and a simulated dataset (sim_data.csv ) mimicking the ADNI data can be found at https://github.com/MinLinSTAT/PPreview. The posterior estimates of γ for the simulated dataset are given in Section S.3.
References
Alt EM, Chang X, Jiang X, Liu Q, Mo M, Xia HA, et al. (2024). LEAP: The latent exchangeability prior for borrowing information from historical data. Biometrics, 80(3): ujae083. https://doi.org/10.1093/biomtc/ujae083
Bai T, Lan H, Tiwari R (2021). Bayesian approaches to benefit-risk assessment for diagnostic tests. Journal of Biopharmaceutical Statistics, 31(4): 541–558. https://doi.org/10.1080/10543406.2021.1931272
Banbeta A, van Rosmalen J, Dejardin D, Lesaffre E (2019). Modified power prior with multiple historical trials for binary endpoints. Statistics in Medicine, 38(7): 1147–1169. https://doi.org/10.1002/sim.8019
Baron E, Lin M, Zhu J, Tang RS, Chen MH (2024). Enhancing randomized controlled trials: A Bayesian divide-and-conquer approach for borrowing external control data. Statistics in Biosciences. https://doi.org/10.1007/s12561-024-09465-2.
Baron E, Zhu J, Tang RS, Chen MH (2022). Bayesian divide-and-conquer propensity score based approaches for leveraging real world data in single arm clinical trials. Journal of Biopharmaceutical Statistics, 32(1): 75–89. https://doi.org/10.1080/10543406.2021.2011904
Baumann L, Sauer L, Kieser M (2024). A basket trial design based on power priors. Statistics in Biopharmaceutical Research. https://doi.org/10.1080/19466315.2024.2402275
Bennett M, White S, Best N, Mander A (2021). A novel equivalence probability weighted power prior for using historical control data in an adaptive clinical trial design: A comparison to standard methods. Pharmaceutical Statistics, 20(3): 462–484. https://doi.org/10.1002/pst.2088
Berry DA (1991). Bayesian methods in phase III trials. Drug Information Journal, 25(3): 345–368. https://doi.org/10.1177/009286159102500306
Brakenhoff T, Roes K, Nikolakopoulos S (2019). Bayesian sample size re-estimation using power priors. Statistical Methods in Medical Research, 28(6): 1664–1675. https://doi.org/10.1177/0962280218772315
Carvalho LM, Ibrahim JG (2021). On the normalized power prior. Statistics in Medicine, 40(24): 5251–5275. https://doi.org/10.1002/sim.9124
Chao YC, Braun TM, Tamura RN, Kidwell KM (2022). Power prior models for estimating response rates in a small n, sequential, multiple assignment, randomized trial. Statistical Methods in Medical Research, 31(12): 2297–2309. https://doi.org/10.1177/09622802221122795
Chen F (2009). Bayesian modeling using the MCMC procedure. https://support.sas.com/resources/papers/proceedings09/257-2009.pdf. Online, accessed November 10, 2024.
Chen F (2019). Bayesian biopharmaceutical applications using PROC MCMC and PROC BGLIMM. http://www.bayesianscientific.org/wp-content/uploads/2019/03/KOL_FangChen.pdf. Online, accessed November 10, 2024.
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.). Springer, New York.
Chen MH, Ibrahim JG (2006). The relationship between the power prior and hierarchical models. Bayesian Analysis, 1: 551–574. https://doi.org/10.1214/06-BA122B
Chen MH, Ibrahim JG, Lam P, Yu A, Zhang Y (2011). Bayesian design of noninferiority 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, Sinha D (1999a). A new Bayesian model for survival data with a surviving fraction. Journal of the American Statistical Association, 94(447): 909–919. https://doi.org/10.1080/01621459.1999.10474196
Chen MH, Ibrahim JG, Xia HA, Liu T, Hennessey V (2014a). Bayesian sequential meta-analysis design in evaluating cardiovascular risk in a new antidiabetic drug development program. Statistics in Medicine, 33(9): 1600–1618. https://doi.org/10.1002/sim.6067
Chen MH, Ibrahim JG, Yiannoutsos C (1999b). Prior elicitation, variable selection and Bayesian computation for logistic regression models. Journal of the Royal Statistical Society. Series B, 61(1): 223–242. https://doi.org/10.1111/1467-9868.00173
Chen MH, Ibrahim JG, Zeng D, Hu K, Jia C (2014b). 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
Chen MH, Manatunga AK, Williams CJ (1998). Heritability estimates from human twin data by incorporating historical prior information. Biometrics, 54(4): 1348–1362. https://doi.org/10.2307/2533662
Chu C, Yi B (2021). Dynamic historical data borrowing using weighted average. Journal of the Royal Statistical Society Series C: Applied Statistics, 70(5): 846–860. https://doi.org/10.1111/rssc.12512
De Santis F (2006). Power priors and their use in clinical trials. The American Statistician, 60(2): 122–129. https://doi.org/10.1198/000313006X109269
De Santis F (2007). Using historical data for Bayesian sample size determination. Journal of the Royal Statistical Society: Series A (Statistics in Society), 170(1): 95–113. https://doi.org/10.1111/j.1467-985X.2006.00438.x
de Valpine P, Paciorek C, Turek D, Michaud N, Anderson-Bergman C, Obermeyer F, et al. (2024b). NIMBLE user manual. https://doi.org/10.5281/zenodo.1211190
de Valpine P, Turek D, Paciorek C, Anderson-Bergman C, Temple Lang D, Bodik R (2017). Programming with models: writing statistical algorithms for general model structures with NIMBLE. Journal of Computational and Graphical Statistics, 26: 403–417. https://doi.org/10.1080/10618600.2016.1172487
Duan Y, Wang SJ, Ji Y (2021). Hi3 + 3: A model-assisted dose-finding design borrowing historical data. Contemporary Clinical Trials, 109: 106437. https://doi.org/10.1016/j.cct.2021.106437
Duan Y, Ye K, Smith EP (2006). Evaluating water quality using power priors to incorporate historical information. Environmetrics, 17(1): 95–106. https://doi.org/10.1002/env.752
Egbon OA, Nascimento D, Louzada F (2023). Prior elicitation for Gaussian spatial process: An application to TMS brain mapping. Statistics in Medicine, 42(22): 3956–3980. https://doi.org/10.1002/sim.9842
Eggleston BS, Ibrahim JG, McNeil B, Catellier D (2021). BayesCTDesign: An R package for Bayesian trial design using historical control data. Journal of Statistical Software, 100(21): 1–51. https://doi.org/10.18637/jss.v100.i21
Feißt M, Krisam J, Kieser M (2020). Incorporating historical two-arm data in clinical trials with binary outcome: A practical approach. Pharmaceutical Statistics, 19(5): 662–678. https://doi.org/10.1002/pst.2023
Gravestock I, Held L (2019). Power priors based on multiple historical studies for binary outcomes. Biometrical Journal, 61(5): 1201–1218. https://doi.org/10.1002/bimj.201700246
Gravestock I, Held L (Consortium ObotCN) (2017). Adaptive power priors with empirical Bayes for clinical trials. Pharmaceutical Statistics, 16(5): 349–360. https://doi.org/10.1002/pst.1814
Han Z, Ye K, Wang M (2023a). A study on the power parameter in power prior Bayesian analysis. The American Statistician, 77(1): 12–19. https://doi.org/10.1080/00031305.2022.2046160
Han Z, Zhang Q, Wang M, Ye K, Chen MH (2023b). On efficient posterior inference in normalized power prior Bayesian analysis. Biometrical Journal, 65(5): 2200194. https://doi.org/10.1002/bimj.202200194
Hees K, Kieser M (2017). Blinded sample size recalculation in clinical trials incorporating historical data. Contemporary Clinical Trials, 63: 2–7. https://doi.org/10.1016/j.cct.2017.07.013
Hickey GL, Parvu V, Zhang Y, Cooper CK, Wan Y (2023). A pragmatic approach for dynamically incorporating predicate device data in prospective diagnostic test studies. Journal of Biopharmaceutical Statistics, 33(1): 77–89. https://doi.org/10.1080/10543406.2022.2080690
Hirji KF (1992). Computing exact distributions for polytomous response data. Journal of the American Statistical Association, 87: 487–492. https://doi.org/10.1080/01621459.1992.10475230
Hirji KF, Mehta CR, Patel NR (1987). Computing distributions for exact logistic regression. Journal of the American Statistical Association, 82(400): 1110–1117. https://doi.org/10.1080/01621459.1987.10478547
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 L, Su L, Zheng Y, Chen Y, Yan F (2022). Power prior for borrowing the real-world data in bioequivalence test with a parallel design. The International Journal of Biostatistics, 18(1): 73–82. https://doi.org/10.1515/ijb-2020-0119
Hupf B, Bunn V, Lin J, Dong C (2021). Bayesian semiparametric meta-analytic-predictive prior for historical control borrowing in clinical trials. Statistics in Medicine, 40(14): 3385–3399. https://doi.org/10.1002/sim.8970
Ibrahim JG, Chen MH (2000a). Power prior distributions for regression models. Statistical Science, 15(1): 46–60. https://doi.org/10.1214/ss/1009212673
Ibrahim JG, Chen MH, Chu H (2012a). Bayesian methods in clinical trials: A Bayesian analysis of ECOG trials E1684 and E1690. BMC Medical Research Methodology, 12(1): 183. https://doi.org/10.1186/1471-2288-12-183
Ibrahim JG, Chen MH, Gwon Y, Chen F (2015a). The power prior: theory and applications. Statistics in Medicine, 34(28): 3724–3749. https://doi.org/10.1002/sim.6728
Ibrahim JG, Chen MH, Sinha D (2003). On optimality properties of the power prior. Journal of the American Statistical Association, 98(461): 204–213. https://doi.org/10.1198/016214503388619229
Ibrahim JG, Chen MH, Xia HA, Liu T (2012b). Bayesian meta-experimental design: Evaluating cardiovascular risk in new antidiabetic therapies to treat type 2 diabetes. Biometrics, 68(2): 578–586. https://doi.org/10.1111/j.1541-0420.2011.01679.x
Ibrahim JG, Ryan LM, Chen MH (1998). Using historical controls to adjust for covariates in trend tests for binary data. Journal of the American Statistical Association, 93(444): 1282–1293. https://doi.org/10.1080/01621459.1998.10473789
Jiang L, Nie L, Yuan Y (2023). Elastic priors to dynamically borrow information from historical data in clinical trials. Biometrics, 79(1): 49–60. https://doi.org/10.1111/biom.13551
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
Kaplan D, Chen J, Yavuz S, Lyu W (2023). Bayesian dynamic borrowing of historical information with applications to the analysis of large-scale assessments. Psychometrika, 88(1): 1–30. https://doi.org/10.1007/s11336-022-09869-3
Kociba R, Keyes D, Beyer J, Carreon R, Wade C, Dittenber D, et al. (1978). Results of a two-year chronic toxicity and oncogenicity study of 2, 3, 7, 8-tetrachlorodibenzo-p-dioxin in rats. Toxicology and Applied Pharmacology, 46: 279–303. https://doi.org/10.1016/0041-008X(78)90075-3
Kopp-Schneider A, Wiesenfarth M, Held L, Calderazzo S (2023). Simulating and reporting frequentist operating characteristics of clinical trials that borrow external information: Towards a fair comparison in case of one-arm and hybrid control two-arm trials. Pharmaceutical Statistics, 23(1): 4–19. https://doi.org/10.1002/pst.2334
Kopp-Schneider A, Calderazzo S, Wiesenfarth M (2020). Power gains by using external information in clinical trials are typically not possible when requiring strict type I error control. Biometrical Journal, 62(2): 361–374. https://doi.org/10.1002/bimj.201800395
König C (2021). A similarity-weighted informative prior distribution for Bayesian multiple regression models. Frontiers in Psychology, 12: 614236. https://doi.org/10.3389/fpsyg.2021.614236
Li H, Chen WC, Lu N, Song C, Wang C, Tiwari R, et al. (2022a). Mitigating study power loss caused by clinical trial disruptions due to the COVID-19 pandemic: Leveraging external data via propensity score-integrated approaches. Statistics in Biopharmaceutical Research, 14(1): 87–91. https://doi.org/10.1080/19466315.2020.1860813
Li H, Chen WC, Lu N, Wang C, Tiwari R, Xu Y, et al. (2020). Novel statistical approaches and applications in leveraging real-world data in regulatory clinical studies. Health Services and Outcomes Research Methodology, 20(4): 237–246. https://doi.org/10.1007/s10742-020-00218-4
Li H, Chen WC, Wang C, Lu N, Song C, Tiwari R, et al. (2022b). Augmenting both arms of a randomized controlled trial using external data: An application of the propensity score-integrated approaches. Statistics in Biosciences, 14(1): 79–89. https://doi.org/10.1007/s12561-021-09315-5
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
Li Y, Yuan Y (2020). PA-CRM: A continuous reassessment method for pediatric phase I oncology trials with concurrent adult trials. Biometrics, 76(4): 1364–1373. https://doi.org/10.1111/biom.13217
Lin J, Gamalo-Siebers M, Tiwari R (2019). Propensity-score-based priors for Bayesian augmented control design. Pharmaceutical Statistics, 18(2): 223–238. https://doi.org/10.1002/pst.1918
Liu GF (2018). A dynamic power prior for borrowing historical data in noninferiority trials with binary endpoint. Pharmaceutical Statistics, 17(1): 61–73. https://doi.org/10.1002/pst.1836
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
Lorencin I, Pantos M (2017). Evaluating generating unit unavailability using Bayesian power priors. IEEE Transactions on Power Systems, 32(3): 2315–2323. https://doi.org/10.1109/TPWRS.2016.2603469
Lu N, Wang C, Chen WC, Li H, Song C, Tiwari R, et al. (2022). Propensity score-integrated power prior approach for augmenting the control arm of a randomized controlled trial by incorporating multiple external data sources. Journal of Biopharmaceutical Statistics, 32(1): 158–169. https://doi.org/10.1080/10543406.2021.1998098
Mehta CR, Patel NR, Senchaudhuri P (1992). Exact stratified linear rank tests for ordered categorical and binary data. Journal of Computational and Graphical Statistics, 1: 21–40. https://doi.org/10.1080/10618600.1992.10474574
Mezzetti M, Ryan CP, Balestrucci P, Lacquaniti F, Moscatelli A (2023). Bayesian hierarchical models and prior elicitation for fitting psychometric functions. Frontiers in Computational Neuroscience, 17: 1108311. https://doi.org/10.3389/fncom.2023.1108311
Nagase M, Ueda S, Higashimori M, Ichikawa K, Dunyak J, Al-Huniti N (2020). Optimal designs for regional bridging studies using the Bayesian power prior method. Pharmaceutical Statistics, 19(1): 22–30. https://doi.org/10.1002/pst.1967
Neuenschwander B, Branson M, Spiegelhalter DJ (2009). A note on the power prior. Statistics in Medicine, 28(28): 3562–3566. https://doi.org/10.1002/sim.3722
Neuenschwander B, Roychoudhury S, Schmidli H (2016). On the use of co-data in clinical trials. Statistics in Biopharmaceutical Research, 8(3): 345–354. https://doi.org/10.1080/19466315.2016.1174149
Nikolakopoulos S, van der Tweel I, Roes KCB (2018). Dynamic borrowing through empirical power priors that control type I error. Biometrics, 74(3): 874–880. https://doi.org/10.1111/biom.12835
Ohigashi T, Maruo K, Sozu T, Gosho M (2022). Using horseshoe prior for incorporating multiple historical control data in randomized controlled trials. Statistical Methods in Medical Research, 31(7): 1392–1404. https://doi.org/10.1177/09622802221090752
Ollier A, Morita S, Ursino M, Zohar S (2020). An adaptive power prior for sequential clinical trials – application to bridging studies. Statistical Methods in Medical Research, 29(8): 2282–2294. https://doi.org/10.1177/0962280219886609
Pandya SS, Li X, Baron E, Moore TE (2023). Bayesian detection of bias in peremptory challenges using historical strike data. The American Statistician, 78(2): 209–219. https://doi.org/10.1080/00031305.2023.2249967
Pateras K, Nikolakopoulos S, Roes KCB (2021). Combined assessment of early and late-phase outcomes in orphan drug development. Statistics in Medicine, 40(12): 2957–2974. https://doi.org/10.1002/sim.8952
Pawel S, Aust F, Held L, Wagenmakers EJ (2023a). Normalized power priors always discount historical data. Stat, 12(1): e591. https://doi.org/10.1002/sta4.591
Pawel S, Aust F, Held L, Wagenmakers EJ (2023b). Power priors for replication studies. TEST, 33: 127–154. https://doi.org/10.1007/s11749-023-00888-5
Psioda MA, Ibrahim JG (2018). Bayesian design of a survival trial with a cured fraction using historical data. Statistics in Medicine, 37(26): 3814–3831. https://doi.org/10.1002/sim.7846
Psioda MA, Soukup M, Ibrahim JG (2018). A practical Bayesian adaptive design incorporating data from historical controls. Statistics in Medicine, 37(27): 4054–4070. https://doi.org/10.1002/sim.7897
Rosenbaum PR, Rubin DB (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1): 41–55. https://doi.org/10.1093/biomet/70.1.41
SAS Institute Inc (2023). SAS/STAT@ User’s Guide. Cary, NC. https://documentation.sas.com/api/collections/pgmsascdc/v_046/docsets/statug/content/bglimm.pdf?locale=en#nameddest=statug_bglimm_examples10, accessed November 10, 2024.
Sawamoto R, Oba K, Matsuyama Y (2022). Bayesian adaptive randomization design incorporating propensity score-matched historical controls. Pharmaceutical Statistics, 21(5): 1074–1089. https://doi.org/10.1002/pst.2203
Shao K, Small M (2011). Potential uncertainty reduction in model-averaged benchmark dose estimates informed by an additional dose study. Risk Analysis, 31: 1561–1575. https://doi.org/10.1111/j.1539-6924.2011.01595.x
Sheikh MT, Chen MH, Gelfond JA, Ibrahim JG (2022). A power prior approach for leveraging external longitudinal and competing risks survival data within the joint modeling framework. Statistics in Biosciences, 14(2): 318–336. https://doi.org/10.1007/s12561-021-09330-6
Shen Y, Psioda MA, Ibrahim JG (2023). BayesPPD: An R package for Bayesian sample size determination using the power and normalized power prior for generalized linear models. The R Journal, 14(4): 335–351. https://doi.org/10.32614/RJ-2023-016
Shen Y, Psioda MA, Ibrahim JG (2024). BayesPPDSurv: Bayesian power prior design for survival data. https://doi.org/10.32614/CRAN.package.BayesPPDSurv.
Shi D, Chen MH, Kuo L, Lewis PO (2021). New partition based measures for data compatibility and information gain. Statistics in Medicine, 40(15): 3560–3581. https://doi.org/10.1002/sim.8982
Spiegelhalter DJ, Freedman LS, Parmar MKB (1994). Bayesian approaches to randomized trials. Journal of the Royal Statistical Society. Series A (Statistics in Society), 157(3): 357–416. https://doi.org/10.2307/2983527
Thompson L, Chu J, Xu J, Li X, Nair R, Tiwari R (2021). Dynamic borrowing from a single prior data source using the conditional power prior. Journal of Biopharmaceutical Statistics, 31(4): 403–424. https://doi.org/10.1080/10543406.2021.1895190
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 November 10, 2024.
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 November 10, 2024.
US Food and Drug Administration (2018). Framework for FDA’s real-world evidence program. https://www.fda.gov/media/120060/download. Online, accessed November 10, 2024.
US Food and Drug Administration (2021a). 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 November 10, 2024.
US Food and Drug Administration (2021b). 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 November 10, 2024.
US Food and Drug Administration (2023). 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 November 10, 2024.
US Government Publishing Office (2016). 21st Century Cures Act. https://www.govinfo.gov/content/pkg/PLAW-114publ255/html/PLAW-114publ255.htm. Online, accessed November 10, 2024.
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
Wang C, Li H, Chen WC, Lu N, Tiwari R, Xu Y, et al. (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
Wang X, Suttner L, Jemielita T, Li X (2022). Propensity score-integrated Bayesian prior approaches for augmented control designs: a simulation study. Journal of Biopharmaceutical Statistics, 32(1): 170–190. https://doi.org/10.1080/10543406.2021.2011743
Wang YB, Chen MH, Kuo L, Lewis PO (2018). A new Monte Carlo method for estimating marginal likelihoods. Bayesian Analysis, 13(2): 311–333. https://doi.org/10.1214/17-BA1049
Warasi MS, Tebbs JM, McMahan CS, Bilder CR (2016). Estimating the prevalence of multiple diseases from two-stage hierarchical pooling. Statistics in Medicine, 35(21): 3851–3864. https://doi.org/10.1002/sim.6964
Wiesenfarth M, Calderazzo S (2020). Quantification of prior impact in terms of effective current sample size. Biometrics, 76(1): 326–336. https://doi.org/10.1111/biom.13124
Wilson KJ, Williamson SF, Allen AJ, Williams CJ, Hellyer TP, Lendrem BC (2022). Bayesian sample size determination for diagnostic accuracy studies. Statistics in Medicine, 41(15): 2908–2922. https://doi.org/10.1002/sim.9393
Yang P, Zhao Y, Nie L, Vallejo J, Yuan Y (2023). SAM: Self-adapting mixture prior to dynamically borrow information from historical data in clinical trials. Biometrics, 79(4): 2857–2868. https://doi.org/10.1111/biom.13927
Ye K, Han Z, Duan Y, Bai T (2022). Normalized power prior Bayesian analysis. Journal of Statistical Planning and Inference, 216: 29–50. https://doi.org/10.1016/j.jspi.2021.05.005
Yu G, Bian Y, Gamalo M (2022). Power priors with entropy balancing weights in data augmentation of partially controlled randomized trials. Journal of Biopharmaceutical Statistics, 32(1): 4–20. https://doi.org/10.1080/10543406.2021.2021226
Yuan W, Chen MH, Zhong J (2022a). Bayesian design of superiority trials: Methods and applications. Statistics in Biopharmaceutical Research, 14(4): 433–443. https://doi.org/10.1080/19466315.2022.2090429
Yuan W, Chen MH, Zhong J (2022b). 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
Yue LQ (2007). Statistical and regulatory issues with the application of propensity score analysis to nonrandomized medical device clinical studies. Journal of Biopharmaceutical Statistics, 17(1): 1–13. https://doi.org/10.1080/10543400601044691
Zhang H, Shen Y, Li J, Ye H, Chiang AY (2023). Adaptively leveraging external data with robust meta-analytical-predictive prior using empirical Bayes. Pharmaceutical Statistics, 22(5): 846–860. https://doi.org/10.1002/pst.2315
Zhang J, Ko CW, Nie L, Chen Y, Tiwari R (2019). Bayesian hierarchical methods for meta-analysis combining randomized-controlled and single-arm studies. Statistical Methods in Medical Research, 28(5): 1293–1310. https://doi.org/10.1177/0962280218754928
Zhang W, Pan Z, Yuan Y (2021). Elastic meta-analytic-predictive prior for dynamically borrowing information from historical data with application to biosimilar clinical trials. Contemporary Clinical Trials, 110: 106559. https://doi.org/10.1016/j.cct.2021.106559
Zhou T, Ji Y (2021). Incorporating external data into the analysis of clinical trials via Bayesian additive regression trees. Statistics in Medicine, 40(28): 6421–6442. https://doi.org/10.1002/sim.9191
