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

  • Fulvio De Santis and Stefania Gubbiotti EMAIL logo
Published/Copyright: April 27, 2022
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The International Journal of Biostatistics
From the journal The International Journal of Biostatistics Volume 19 Issue 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.

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Received: 2021-11-17
Revised: 2022-02-15
Accepted: 2022-03-28
Published Online: 2022-04-27

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijb-2021-0120
Keywords for this article
Bayesian analysis; dynamic power prior; Hellinger distance; sample size determination; SARS-CoV-2; type-I error

Articles in the same Issue

  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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