IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v39y2024i4d10.1007_s00180-023-01384-y.html
   My bibliography  Save this article

Semiparametric Bayesian approach to assess non-inferiority with assay sensitivity in a three-arm trial with normally distributed endpoints

Author

Listed:
  • Niansheng Tang

    (Yunnan University)

  • Fan Liang

    (Yunnan University)

  • Depeng Jiang

    (University of Manitoba)

Abstract

The non-inferiority (NI) trial is designed to show that an experimental treatment is not worse than an active reference by more than a pre-specified margin. Traditional NI trials do not include a placebo for ethical reasons; however, three-arm NI trials consisting of placebo, reference, and experimental treatment, can test the NI of experimental treatment to the reference while assessing the superiority of the reference over placebo. Assay sensitivity (AS) of a clinical trial is defined as its ability to distinguish between an effective and ineffective treatment and has been used to assess the superiority of the reference over placebo. Bayesian approaches have been predominantly used in clinical trials, particularly in NI trials. Most previous Bayesian approaches have focused on parametric priors of treatment effects. Restriction to parametric priors can mislead investigators into an inappropriate illusion of posterior certainty, leading to misleading decisions and inference. In this paper, we develop a novel semiparametric Bayesian approach to simultaneously assess NI of experimental treatment over the reference and AS of the reference over placebo in a three-arm trial with normally distributed endpoints. We use Dirichlet process priors to specify the priors of treatment effects. A Markov chain Monte Carlo algorithm is developed to calculate the posterior probability for assessing NI and AS. Simulation studies show that our proposed method is comparable to, or better than, the frequentist approach and parametric Bayesian methods in terms of the ability of controlling the type I errors and empirical statistical powers for testing NI. Data from two real trials are illustrated by the proposed methods. We recommend the usage of the proposed method in a three-arm trial.

Suggested Citation

  • Niansheng Tang & Fan Liang & Depeng Jiang, 2024. "Semiparametric Bayesian approach to assess non-inferiority with assay sensitivity in a three-arm trial with normally distributed endpoints," Computational Statistics, Springer, vol. 39(4), pages 2157-2181, June.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:4:d:10.1007_s00180-023-01384-y
    DOI: 10.1007/s00180-023-01384-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-023-01384-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-023-01384-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ming-Hui Chen & Joseph G. Ibrahim & Peter Lam & Alan Yu & Yuanye Zhang, 2011. "Bayesian Design of Noninferiority Trials for Medical Devices Using Historical Data," Biometrics, The International Biometric Society, vol. 67(3), pages 1163-1170, September.
    2. Tang, Nian-Sheng & Tang, An-Min & Pan, Dong-Dong, 2014. "Semiparametric Bayesian joint models of multivariate longitudinal and survival data," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 113-129.
    3. Barry Arnold & Robert Beaver & Richard Groeneveld & William Meeker, 1993. "The nontruncated marginal of a truncated bivariate normal distribution," Psychometrika, Springer;The Psychometric Society, vol. 58(3), pages 471-488, September.
    4. Gary L. Rosner, 2005. "Bayesian Monitoring of Clinical Trials with Failure-Time Endpoints," Biometrics, The International Biometric Society, vol. 61(1), pages 239-245, March.
    5. Wenqing Li & Ming-Hui Chen & Xiaojing Wang & Dipak K. Dey, 2018. "Bayesian Design of Non-inferiority Clinical Trials Via the Bayes Factor," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(2), pages 439-459, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chabé-Ferret, Sylvain, 2015. "Analysis of the bias of Matching and Difference-in-Difference under alternative earnings and selection processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 110-123.
    2. Metzler A., 2020. "State dependent correlations in the Vasicek default model," Dependence Modeling, De Gruyter, vol. 8(1), pages 298-329, January.
    3. Denisa Banulescu-Radu & Christophe Hurlin & Jérémy Leymarie & Olivier Scaillet, 2021. "Backtesting Marginal Expected Shortfall and Related Systemic Risk Measures," Management Science, INFORMS, vol. 67(9), pages 5730-5754, September.
    4. George J Borjas & Ilpo Kauppinen & Panu Poutvaara, 2019. "Self-selection of Emigrants: Theory and Evidence on Stochastic Dominance in Observable and Unobservable Characteristics," The Economic Journal, Royal Economic Society, vol. 129(617), pages 143-171.
    5. Melkamu Molla Ferede & Samuel Mwalili & Getachew Dagne & Simon Karanja & Workagegnehu Hailu & Mahmoud El-Morshedy & Afrah Al-Bossly, 2022. "A Semiparametric Bayesian Joint Modelling of Skewed Longitudinal and Competing Risks Failure Time Data: With Application to Chronic Kidney Disease," Mathematics, MDPI, vol. 10(24), pages 1-21, December.
    6. Chen, Nan & Carlin, Bradley P. & Hobbs, Brian P., 2018. "Web-based statistical tools for the analysis and design of clinical trials that incorporate historical controls," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 50-68.
    7. Yael Grushka-Cockayne & Victor Richmond R. Jose & Kenneth C. Lichtendahl Jr., 2017. "Ensembles of Overfit and Overconfident Forecasts," Management Science, INFORMS, vol. 63(4), pages 1110-1130, April.
    8. Rachid Belhachemi, 2024. "Option Valuation with Conditional Heteroskedastic Hidden Truncation Models," Computational Economics, Springer;Society for Computational Economics, vol. 63(6), pages 2585-2601, June.
    9. Arthur Pewsey & Héctor Gómez & Heleno Bolfarine, 2012. "Likelihood-based inference for power distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 775-789, December.
    10. Wenlin Yuan & Ming-Hui Chen & John Zhong, 2022. "Flexible Conditional Borrowing Approaches for Leveraging Historical Data in the Bayesian Design of Superiority Trials," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(2), pages 197-215, July.
    11. Wenhao Gui & Lei Guo, 2018. "Statistical Inference for the Location and Scale Parameters of the Skew Normal Distribution," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(4), pages 633-650, December.
    12. Wenqing Li & Ming-Hui Chen & Xiaojing Wang & Dipak K. Dey, 2018. "Bayesian Design of Non-inferiority Clinical Trials Via the Bayes Factor," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(2), pages 439-459, August.
    13. Lei Liu & Zhihua Sun, 2017. "Kernel-based global MLE of partial linear random effects models for longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(3), pages 615-635, July.
    14. Arismendi, J.C., 2013. "Multivariate truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 41-75.
    15. Bhat, Chandra R., 2018. "New matrix-based methods for the analytic evaluation of the multivariate cumulative normal distribution function," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 238-256.
    16. Ming-Hui Chen & Joseph G. Ibrahim & Donglin Zeng & Kuolung Hu & Catherine Jia, 2014. "Bayesian design of superiority clinical trials for recurrent events data with applications to bleeding and transfusion events in myelodyplastic syndrome," Biometrics, The International Biometric Society, vol. 70(4), pages 1003-1013, December.
    17. Chabé-Ferret, Sylvain, 2012. "Matching vs Differencing when Estimating Treatment Effects with Panel Data: the Example of the Effect of Job Training Programs on Earnings," LERNA Working Papers 12.24.381, LERNA, University of Toulouse.
    18. Kampkötter, Patrick & Sliwka, Dirk, 2014. "Wage premia for newly hired employees," Labour Economics, Elsevier, vol. 31(C), pages 45-60.
    19. L.M. LaVange & E.M. Alt & J.G. Ibrahim, 2023. "Discussion of “Optimal test procedures for multiple hypotheses controlling the familywise expected loss” by Willi Maurer, Frank Bretz, and Xiaolei Xun," Biometrics, The International Biometric Society, vol. 79(4), pages 2802-2805, December.
    20. Jörg Martin & Clemens Elster, 2021. "The variation of the posterior variance and Bayesian sample size determination," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1135-1155, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:39:y:2024:i:4:d:10.1007_s00180-023-01384-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.