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Borrowing historical information for non-inferiority trials on Covid-19 vaccines

  • Fulvio De Santis und Stefania Gubbiotti EMAIL logo
Veröffentlicht/Copyright: 27. April 2022
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The International Journal of Biostatistics
Aus der Zeitschrift The International Journal of Biostatistics Band 19 Heft 1

Abstract

Non-inferiority vaccine trials compare new candidates to active controls that provide clinically significant protection against a disease. Bayesian statistics allows to exploit pre-experimental information available from previous studies to increase precision and reduce costs. Here, historical knowledge is incorporated into the analysis through a power prior that dynamically regulates the degree of information-borrowing. We examine non-inferiority tests based on credible intervals for the unknown effects-difference between two vaccines on the log odds ratio scale, with an application to new Covid-19 vaccines. We explore the frequentist properties of the method and we address the sample size determination problem.

Keywords: Bayesian analysis; dynamic power prior; Hellinger distance; sample size determination; SARS-CoV-2; type-I error
Corresponding author: Stefania Gubbiotti, Dipartimento di Scienze Statistiche, Sapienza University of Rome, Piazzale Aldo Moro n. 5, 00185 Roma, Italy, E-mail:

Ackwowledgements

The Authors would like to thank two anonymous reviewers for their helpful comments.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Appendix A

To determine the values of the power function η(ζ) defined in Eq. (4) we proceed as follows.

  1. Specify x h, n h, n e, n c, κ, δ, 1 − γ.

  2. Fix a design value θ c ⋆ for θ c and find ξ c ⋆ = log θ c ⋆ 1 − θ c ⋆ .

  3. Set ξ e ⋆ = ξ c ⋆ − δ − ζ , with ζ = 0 under H 0 and ζ > 0 under H 1.

  4. Find θ e ⋆ = e ξ e ⋆ / 1 + e ξ e ⋆ .

  5. Generate M values x c ( j ) from Binom n c , θ c ⋆ and M values x e ( j ) from Binom n e , θ e ⋆ .

  6. Compute ξ ̂ h = log x ̄ h 1 − x ̄ h , ξ ̂ c ( j ) = log x ̄ c ( j ) 1 − x ̄ c ( j ) , ξ ̂ e ( j ) = log x ̄ e ( j ) 1 − x ̄ e ( j ) , j = 1, …, M.

  7. For each ξ ̂ c ( j ) , set a = 1 for full borrowing, a = 0 for null borrowing or compute a as a function of ξ ̂ c ( j ) and ξ ̂ h for dynamic borrowing (see Section 2.1).

  8. For each j = 1, …, M compute L ( j ) = θ ̂ ( j ) − z 1 − γ 2 / τ ̂ ( j ) (see step 7 of Section 2) where θ ̂ ( j ) and τ ̂ ( j ) are determined following steps 5 and 6 of Section 2.

  9. Compute the fraction of L (j) > δ and obtain the empirical type-I error (if ζ = 0) or the empirical power (if ζ > 0).

This scheme, used for Tables 1 and 2 and for Figures 2 and 3, is implemented with R [44]. Code is available upon request.

References

1. Polack, FP, Thomas, SJ, Kitchin, N, Absalon, J, Gurtman, A, Lockhart, S, et al.. Safety and efficacy of the BNT162b2 mRNA Covid-19 vaccine. N Engl J Med 2020;383:2603–15. https://doi.org/10.1056/nejmoa2034577.Suche in Google Scholar

2. Baden, LR, El Sahly, HM, Essink, B, Kotloff, K, Frey, S, Novak, R, et al.. Efficacy and safety of the mRNA-1273 SARS-CoV-2 vaccine. N Engl J Med 2021;384:403–16. https://doi.org/10.1056/NEJMoa2035389.Suche in Google Scholar PubMed PubMed Central

3. Voysey, M, Costa Clemens, SA, Madhi, SA, Weckx, LY, Folegatti, PM, Aley, PK, et al.. Safety and efficacy of the ChAdOx1 nCoV-19 vaccine (AZD1222) against SARS-CoV-2: an interim analysis of four randomised controlled trials in Brazil, South Africa, and the UK. Lancet 2021;397:99–111. https://doi.org/10.1016/s0140-6736(21)00976-4.Suche in Google Scholar PubMed

4. Sadoff, J, Gray, G, Vandebosch, A, Cárdenas, V, Shukarev, G, Grinsztejn, B, et al.. Safety and efficacy of single-dose Ad26.COV2.S vaccine against Covid-19. N Engl J Med 2021;384:2187–201. https://doi.org/10.1056/NEJMoa2101544.Suche in Google Scholar PubMed PubMed Central

5. FDA. CDHR/FDA. Guidance for the use of bayesian statistics in medical device clinical trials. Rockville, MD: Guidance for industry and FDA staff; 2010.Suche in Google Scholar

6. Fleming, TR, Krause, PR, Nason, M, Longini, IM, Henao-Restrepo A-MN. COVID-19 vaccine trials: the use of active controls and non-inferiority studies. Clin Trials 2021;18:335–42.10.1177/1740774520988244Suche in Google Scholar PubMed PubMed Central

7. FDA. CDER-CDBR/FDA. Non-inferiority clinical trials to establish effectiveness. Silver Spring, MD: Guidance for industry; 2016.Suche in Google Scholar

8. Durrleman, S, Chaikin, P. The use of putative placebo in active control trials:two applications in a regulatory setting. Stat Med 2003;22:941–52. https://doi.org/10.1002/sim.1454.Suche in Google Scholar PubMed

9. FDA. CDER-CDBR/FDA. E 10 choice of control group and related issues in clinical trials. Rockville, MD: Guidance for Industry; 2001.Suche in Google Scholar

10. EMA. Guideline on the choice of non-inferiority margin. EMEA/CPMP/EWP/2158/99; 2005.Suche in Google Scholar

11. Liu, M, Li, Q, Lin, J, Lin, Y, Hoffman, E. Innovative trial designs and analyses for vaccine clinical development. Contemp Clin Trials 2021;100:106225. https://doi.org/10.1016/j.cct.2020.106225.Suche in Google Scholar PubMed PubMed Central

12. Jin, M, Feng, D, Liu, G. Bayesian approaches on borrowing historical data for vaccine efficacy trials. Stat Biopharm Res 2020;12:284–92. https://doi.org/10.1080/19466315.2020.1736617.Suche in Google Scholar

13. Wang, WWB, Mehrotra, DV, Chan, ISF, Heyse, JF. Statistical considerations for NonInferiority/equivalence trials in vaccine development. J Biopharm Stat 2006;16:429–41. https://doi.org/10.1080/10543400600719251.Suche in Google Scholar PubMed

14. Chen, MH, Ibrahim, JG, Lam, P, Yu, A, Zhang, Y. Bayesian design of noninferiority trials for medical devices using historical data. Biometrics 2011;67:1163–70. https://doi.org/10.1111/j.1541-0420.2011.01561.x.Suche in Google Scholar PubMed PubMed Central

15. Gamalo, MA, Wu, R, Tiwari, RC. Bayesian approach to noninferiority trials for proportions. J Biopharm Stat 2011;21:902–19. https://doi.org/10.1080/10543406.2011.589646.Suche in Google Scholar PubMed

16. Gamalo, MA, Wu, R, Tiwari, RC. Bayesian approach to non-inferiority trials for normal means. Stat Methods Med Res 2016;25:221–40. https://doi.org/10.1177/0962280212448723.Suche in Google Scholar PubMed

17. Gamalo-Siebers, M, Gao, A, Lakshminarayanan, M, Liu, G, Natanegara, F, Railkar, R, et al.. Bayesian methods for the design and analysis of noninferiority trials. J Biopharm Stat 2016;26:823–41. https://doi.org/10.1080/10543406.2015.1074920.Suche in Google Scholar PubMed

18. Gamalo, MA, Tiwari, RC, LaVange, LM. Bayesian approach to the design and analysis of non-inferiority trials for anti-infective products. Pharmaceut Stat 2014;13:25–40. https://doi.org/10.1002/pst.1588.Suche in Google Scholar PubMed

19. Li, W, Chen, MH, Wang, X, Dey, DK. Bayesian design of non-inferiority clinical trials via the Bayes factor. Stat. Biosci. 2018;10:439–59. https://doi.org/10.1007/s12561-017-9200-5.Suche in Google Scholar PubMed PubMed Central

20. Liu, GF. A dynamic power prior for borrowing historical data in noninferiority trials with binary endpoint. Pharmaceut Stat 2018;17:61–73. https://doi.org/10.1002/pst.1836.Suche in Google Scholar PubMed

21. Osman, M, Ghosh, SK. Semiparametric bayesian testing procedure for noninferiority trials with binary endpoints. J Biopharm Stat 2011;21:920–37. https://doi.org/10.1080/10543406.2010.544526.Suche in Google Scholar PubMed

22. Fleming, TR. Current issues in non-inferiority trials. Stat Med 2008;27:317–32. https://doi.org/10.1002/sim.2855.Suche in Google Scholar PubMed

23. Fleming, TR, Odem-Davis, K, Rothmann, MD, Shen, YL. Some essential considerations in the design and conduct of non-inferiority trials. Clin Trials 2011;8:432–9. https://doi.org/10.1177/1740774511410994.Suche in Google Scholar PubMed PubMed Central

24. Hobbs, BP, Carlin, BP, Mandrekar, SJ, Sargent, DJ. Hierarchical commensurate and power prior models for adaptive incorporation of historical information in clinical trials. Biometrics 2011;67:1047–56. https://doi.org/10.1111/j.1541-0420.2011.01564.x.Suche in Google Scholar PubMed PubMed Central

25. Hobbs, BP, Sargent, DJ, Carlin, BP. Commensurate priors for incorporating historical information in clinical trials using general and generalized linear models. Bayesian Anal 2014;7:639–74. https://doi.org/10.1214/12-BA722.Suche in Google Scholar PubMed PubMed Central

26. Harun, N, Liu, C, Kim, M-O. Critical appraisal of Bayesian dynamic borrowing from an imperfectly commensurate historical control. Pharmaceut Stat 2020;19:613–25. https://doi.org/10.1002/pst.2018.Suche in Google Scholar PubMed

27. Neuenschwander, B, Capkun-Niggli, G, Branson, M, Spiegelhalter, DJ. Summarizing historical information on controls in clinical trials. Clin Trials 2010;7:5–18. https://doi.org/10.1177/1740774509356002.Suche in Google Scholar PubMed

28. Viele, K, Berry, S, Neuenschwander, B, Amzal, B, Chen, F, Enas, N, et al.. Use of historical control data for assessing treatment effects in clinical trials. Pharmaceut Stat 2014;13:41–54. https://doi.org/10.1002/pst.1589.Suche in Google Scholar PubMed PubMed Central

29. Ibrahim, JG, Chen, MH. Power prior distributions for regression models. Stat Sci 2000;15:46–60.10.1214/ss/1009212673Suche in Google Scholar

30. Gravestock, I, Held, L. Adaptive power priors with empirical Bayes for clinical trials. Pharmaceut Stat 2017;16:349–60. https://doi.org/10.1002/pst.1814.Suche in Google Scholar PubMed

31. Gravestock, I, Held, L. Power priors based on multiple historical studies for binary outcomes. Biom J 2019;61:1201–18. https://doi.org/10.1002/bimj.201700246.Suche in Google Scholar PubMed

32. Nikolakopoulos, S, van der Tweel, I, Roes, KCB. Dynamic borrowing through empirical power priors that control type I error. Biometrics 2018;74:874–80. https://doi.org/10.1111/biom.12835.Suche in Google Scholar PubMed

33. Pan, H, Yuan, Y, Xia, J. A calibrated power prior approach to borrow information from historical data with application to biosimilar clinical trials. Appl Stat 2017;66:979–96. https://doi.org/10.1111/rssc.12204.Suche in Google Scholar PubMed PubMed Central

34. Ollier, A, Morita, S, Ursino, M, Zohar, S. An adaptive power prior for sequential clinical trials - application to bridging studies. Stat Methods Med Res 2020;29:2282–94. https://doi.org/10.1177/0962280219886609.Suche in Google Scholar PubMed PubMed Central

35. Spiegelhalter, DJ, Abrams, KR, Myles, JP. Bayesian approaches to clinical trials and health-care evaluation. New York: Wiley; 2004.10.1002/0470092602Suche in Google Scholar

36. Brutti, P, De Santis, F, Gubbiotti, S. Bayesian-frequentist sample size determination: a game of two priors. METRON 2014;72:133–51. https://doi.org/10.1007/s40300-014-0043-2.Suche in Google Scholar

37. De Santis, F. Power priors and their use in clinical trials. Am Statistician 2006;60:122–9. https://doi.org/10.1198/000313006x109269.Suche in Google Scholar

38. De Santis, F. Using historical data for Bayesian sample size determination. J Roy Stat Soc 2007;170:95–113. https://doi.org/10.1111/j.1467-985x.2006.00438.x.Suche in Google Scholar

39. Psioda, MA, Ibrahim, JG. Bayesian clinical trial design using historical data that inform the treatment effect. Biostatistics 2019;20:400–15. https://doi.org/10.1093/biostatistics/kxy009.Suche in Google Scholar PubMed PubMed Central

40. Ventz, S, Trippa, L. Bayesian designs and the control of frequentist characteristics: a practical solution. Biometrics 2015;71:218–26. https://doi.org/10.1111/biom.12226.Suche in Google Scholar PubMed

41. Wang, F, Gelfand, AE. A simulation-based approach to Bayesian sample size determination for performance under a given model and for separating models. Stat Sci 2002;17:193–208.10.1214/ss/1030550861Suche in Google Scholar

42. Chang, W, Cheng, J, Allaire, JJ, Sievert, C, Schloerke, B, Xie, Y, et al.. shiny: Web application framework for R. R package version 1.6.0; 2021. Available from: https://CRAN.R-project.org/package=shiny.Suche in Google Scholar

43. Krause, P, Fleming, TR, Longini, I, Henao-Restrepo, A-M, Peto, R. COVID-19 vaccine trials should seek worthwhile efficacy. Lancet 2020;396:741–3.10.1016/S0140-6736(20)31821-3Suche in Google Scholar PubMed PubMed Central

44. R Core Team. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing; 2021. Available from: https://www.R-project.org/.Suche in Google Scholar
Received: 2021-11-17
Revised: 2022-02-15
Accepted: 2022-03-28
Published Online: 2022-04-27

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Research Articles
  3. Two-sample t α -test for testing hypotheses in small-sample experiments
  4. Estimating risk and rate ratio in rare events meta-analysis with the Mantel–Haenszel estimator and assessing heterogeneity
  5. Estimating population-averaged hazard ratios in the presence of unmeasured confounding
  6. Commentary
  7. Comments on ‘A weighting analogue to pair matching in propensity score analysis’ by L. Li and T. Greene
  8. Research Articles
  9. Variable selection for bivariate interval-censored failure time data under linear transformation models
  10. A quantile regression estimator for interval-censored data
  11. Modeling sign concordance of quantile regression residuals with multiple outcomes
  12. Robust statistical boosting with quantile-based adaptive loss functions
  13. A varying-coefficient partially linear transformation model for length-biased data with an application to HIV vaccine studies
  14. Application of the patient-reported outcomes continual reassessment method to a phase I study of radiotherapy in endometrial cancer
  15. Borrowing historical information for non-inferiority trials on Covid-19 vaccines
  16. Multivariate small area modelling of undernutrition prevalence among under-five children in Bangladesh
  17. The optimal dynamic treatment rule superlearner: considerations, performance, and application to criminal justice interventions
  18. Estimators for the value of the optimal dynamic treatment rule with application to criminal justice interventions
  19. Efficient estimation of pathwise differentiable target parameters with the undersmoothed highly adaptive lasso
https://doi.org/10.1515/ijb-2021-0120
Schlagwörter für diesen Artikel
Bayesian analysis; dynamic power prior; Hellinger distance; sample size determination; SARS-CoV-2; type-I error

Artikel in diesem Heft

  1. Frontmatter
  2. Research Articles
  3. Two-sample t α -test for testing hypotheses in small-sample experiments
  4. Estimating risk and rate ratio in rare events meta-analysis with the Mantel–Haenszel estimator and assessing heterogeneity
  5. Estimating population-averaged hazard ratios in the presence of unmeasured confounding
  6. Commentary
  7. Comments on ‘A weighting analogue to pair matching in propensity score analysis’ by L. Li and T. Greene
  8. Research Articles
  9. Variable selection for bivariate interval-censored failure time data under linear transformation models
  10. A quantile regression estimator for interval-censored data
  11. Modeling sign concordance of quantile regression residuals with multiple outcomes
  12. Robust statistical boosting with quantile-based adaptive loss functions
  13. A varying-coefficient partially linear transformation model for length-biased data with an application to HIV vaccine studies
  14. Application of the patient-reported outcomes continual reassessment method to a phase I study of radiotherapy in endometrial cancer
  15. Borrowing historical information for non-inferiority trials on Covid-19 vaccines
  16. Multivariate small area modelling of undernutrition prevalence among under-five children in Bangladesh
  17. The optimal dynamic treatment rule superlearner: considerations, performance, and application to criminal justice interventions
  18. Estimators for the value of the optimal dynamic treatment rule with application to criminal justice interventions
  19. Efficient estimation of pathwise differentiable target parameters with the undersmoothed highly adaptive lasso
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