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Bayesian D-optimal designs for the two parameter logistic mixed effects model

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  • Abebe, Haftom T.
  • Tan, Frans E.S.
  • Van Breukelen, Gerard J.P.
  • Berger, Martijn P.F.

Abstract

Bayesian optimal designs for binary longitudinal responses analyzed with mixed logistic regression describing a linear time effect are considered. In order to find the optimal number and allocations of time points, for different priors, cost constraints and covariance structures of the random effects, a scalar function of the approximate information matrix based on the first order penalized quasi likelihood (PQL1) is optimized. To overcome the problem of dependence of Bayesian designs on the choice of prior distributions, maximin Bayesian D-optimal designs are proposed. The results show that the optimal number of time points depends on the subject-to-measurement cost ratio and increases with the cost ratio. Furthermore, maximin Bayesian D-optimal designs are highly efficient and robust under changes in priors. Locally D-optimal designs are also investigated and maximin locally D-optimal designs are found to have much lower minimum relative efficiency and fewer time points than maximin Bayesian D-optimal designs. When comparing the efficiencies of designs with equidistant time points with the Bayesian D-optimal designs, it was found that three or four equidistant time points are advisable for small cost ratios and five or six equidistant time points for large cost ratios.

Suggested Citation

  • Abebe, Haftom T. & Tan, Frans E.S. & Van Breukelen, Gerard J.P. & Berger, Martijn P.F., 2014. "Bayesian D-optimal designs for the two parameter logistic mixed effects model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1066-1076.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:1066-1076
    DOI: 10.1016/j.csda.2013.07.040
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    References listed on IDEAS

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    1. Martijn P. F. Berger & Frans E. S. Tan, 2004. "Robust designs for linear mixed effects models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(4), pages 569-581, November.
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    Cited by:

    1. Nguyen, Thu Thuy & Mentré, France, 2014. "Evaluation of the Fisher information matrix in nonlinear mixed effect models using adaptive Gaussian quadrature," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 57-69.
    2. Hong-Yan Jiang & Rong-Xian Yue, 2019. "Pseudo-Bayesian D-optimal designs for longitudinal Poisson mixed models with correlated errors," Computational Statistics, Springer, vol. 34(1), pages 71-87, March.
    3. Xiao-Dong Zhou & Yun-Juan Wang & Rong-Xian Yue, 2021. "Optimal designs for discrete-time survival models with random effects," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(2), pages 300-332, April.

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