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Bayesian optimal design for $$2 \times 2$$ 2 × 2 binary crossover trials using copula

Author

Listed:
  • Satya Prakash Singh

    (Indian Institute of Technology Kanpur)

  • Deepak Prajapati

    (Decision Sciences Area Indian Institute of Management Lucknow)

Abstract

In this article we have considered a $$2\times 2$$ 2 × 2 binary crossover trial. Two main difficulties on designing such trial are: (i) the association of observations measured on the same experimental unit over different time periods; and (ii) the dependency of design selection criterion on the unknown model parameters. Here we present a copula based approach to address (i). Further, a Bayesian approach is adopted to address (ii). Equivalence theorem is provided to verify the optimality of numerically obtained Bayesian design. The proposed methodology is supplemented by thorough numerical studies. Moreover, it is shown that the proposed optimal designs are more efficient than that of based on the generalized estimating equations approach.

Suggested Citation

  • Satya Prakash Singh & Deepak Prajapati, 2025. "Bayesian optimal design for $$2 \times 2$$ 2 × 2 binary crossover trials using copula," Computational Statistics, Springer, vol. 40(9), pages 4875-4900, December.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:9:d:10.1007_s00180-024-01574-2
    DOI: 10.1007/s00180-024-01574-2
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    References listed on IDEAS

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    1. Denman, N.G. & McGree, J.M. & Eccleston, J.A. & Duffull, S.B., 2011. "Design of experiments for bivariate binary responses modelled by Copula functions," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1509-1520, April.
    2. Uttam Bandyopadhyay & Joydeep Basu & Ganesh Dutta, 2015. "Crossover design in clinical trials for binary response," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(10), pages 2100-2114, October.
    3. Huihui Lin & N. Rao Chaganty, 2021. "Multivariate distributions of correlated binary variables generated by pair-copulas," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-14, December.
    4. Uttam Bandyopadhyay & Atanu Biswas & Shirsendu Mukherjee, 2007. "Adaptive two‐treatment two‐period crossover design for binary treatment responses," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(3), pages 329-344, August.
    5. Singh, Satya Prakash & Mukhopadhyay, Siuli, 2016. "Bayesian crossover designs for generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 35-50.
    6. Uttam Bandyopadhyay & Atanu Biswas & Shirsendu Mukherjee, 2009. "Adaptive two-treatment two-period crossover design for binary treatment responses incorporating carry-over effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(1), pages 13-33, March.
    7. Laura Deldossi & Silvia Angela Osmetti & Chiara Tommasi, 2019. "Optimal design to discriminate between rival copula models for a bivariate binary response," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 147-165, March.
    8. S. G. J. Senarathne & C. C. Drovandi & J. M. McGree, 2020. "Bayesian sequential design for Copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 454-478, June.
    9. Elisa Perrone & Andreas Rappold & Werner G. Müller, 2017. "$$D_s$$ D s -optimality in copula models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(3), pages 403-418, August.
    10. Luc Devroye, 1986. "Non-Uniform Random Variate Generation," Springer Books, Springer, number 978-1-4613-8643-8, October.
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