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Bayesian crossover designs for generalized linear models

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  • Singh, Satya Prakash
  • Mukhopadhyay, Siuli

Abstract

This article discusses optimal Bayesian crossover designs for generalized linear models. Crossover trials with t treatments and p periods, for t<=p, are considered. The designs proposed in this paper minimize the log determinant of the variance of the estimated treatment effects over all possible allocation of the n subjects to the treatment sequences. It is assumed that the p observations from each subject are mutually correlated while the observations from different subjects are uncorrelated. Since main interest is in estimating the treatment effects, the subject effect is assumed to be nuisance, and generalized estimating equations are used to estimate the marginal means. To address the issue of parameter dependence a Bayesian approach is employed. Prior distributions are assumed on the model parameters which are then incorporated into the DA-optimal design criterion by integrating it over the prior distribution. Three case studies, one with binary outcomes in a 4×4 crossover trial, second one based on count data for a 2×2 trial and a third one with Gamma responses in a 3×2 crossover trial are used to illustrate the proposed method. The effect of the choice of prior distributions on the designs is also studied. A general equivalence theorem is stated to verify the optimality of designs obtained.

Suggested Citation

  • Singh, Satya Prakash & Mukhopadhyay, Siuli, 2016. "Bayesian crossover designs for generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 35-50.
    • Handle: RePEc:eee:csdana:v:104:y:2016:i:c:p:35-50
    DOI: 10.1016/j.csda.2016.06.002
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    References listed on IDEAS

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    1. Hans Pettersson, 2005. "Optimal design in average for inference in generalized linear models," Statistical Papers, Springer, vol. 46(1), pages 79-99, January.
    2. R. A. Bailey & J. Kunert, 2006. "On optimal crossover designs when carryover effects are proportional to direct effects," Biometrika, Biometrika Trust, vol. 93(3), pages 613-625, September.
    3. 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.
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    Cited by:

    1. Singh, Rakhi & Mukhopadhyay, Siuli, 2019. "Exact Bayesian designs for count time series," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 157-170.

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