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Maximin D-optimal designs for binary longitudinal responses

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  • Tekle, Fetene B.
  • Tan, Frans E.S.
  • Berger, Martijn P.F.

Abstract

Optimal design problems for logistic mixed effects models for binary longitudinal responses are considered. A function of the approximate information matrix under the framework of the Penalized Quasi Likelihood (PQL) and a generalized linear mixed model with autocorrelation is optimized. Locally D-optimal designs are computed. Maximin D-optimal designs are considered to overcome the problem of parameter value dependency of the D-optimal designs. The results show that the optimal number of repeated measurements depends on the number of regression parameters in the model. The performance of the maximin D-optimal designs in terms of the maximin efficiency (MME) is high for a range of parameter values that is common in practice. The design locations for mixed-effects logistic models generally shift to the left as compared to the design locations for general linear mixed-effects models known in the literature.

Suggested Citation

  • Tekle, Fetene B. & Tan, Frans E.S. & Berger, Martijn P.F., 2008. "Maximin D-optimal designs for binary longitudinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5253-5262, August.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5253-5262
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    1. Holger Dette, 1997. "Designing Experiments with Respect to ‘Standardized’ Optimality Criteria," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 97-110.
    2. R. R. Sitter & C. F. J. Wu, 1999. "Two-Stage Design of Quanta1 Response Studies," Biometrics, The International Biometric Society, vol. 55(2), pages 396-402, June.
    3. Joy King & Weng-Kee Wong, 2000. "Minimax D-Optimal Designs for the Logistic Model," Biometrics, The International Biometric Society, vol. 56(4), pages 1263-1267, December.
    4. Valery Fedorov & Werner Müller, 1997. "Another view on optimal design for estimating the point of extremum in quadratic regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 46(1), pages 147-157, January.
    5. Cong Han & Kathryn Chaloner, 2004. "Bayesian Experimental Design for Nonlinear Mixed-Effects Models with Application to HIV Dynamics," Biometrics, The International Biometric Society, vol. 60(1), pages 25-33, March.
    6. Viatcheslav Melas & Andrey Pepelyshev & Russell Cheng, 2003. "Designs for estimating an extremal point of quadratic regression models in a hyperball," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(2), pages 193-208, September.
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    Cited by:

    1. Fetene B. Tekle & Dereje W. Gudicha & Jeroen K. Vermunt, 2016. "Power analysis for the bootstrap likelihood ratio test for the number of classes in latent class models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 10(2), pages 209-224, June.
    2. Sheng Wu & Weng Kee Wong & Catherine M. Crespi, 2017. "Maximin optimal designs for cluster randomized trials," Biometrics, The International Biometric Society, vol. 73(3), pages 916-926, September.
    3. Jóźwiak, Katarzyna & Moerbeek, Mirjam, 2012. "Cost-effective designs for trials with discrete-time survival endpoints," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2086-2096.
    4. Ueckert, Sebastian & Mentré, France, 2017. "A new method for evaluation of the Fisher information matrix for discrete mixed effect models using Monte Carlo sampling and adaptive Gaussian quadrature," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 203-219.
    5. H. Abebe & F. Tan & G. Breukelen & M. Berger, 2014. "Robustness of Bayesian D-optimal design for the logistic mixed model against misspecification of autocorrelation," Computational Statistics, Springer, vol. 29(6), pages 1667-1690, December.
    6. Candel, Math J.J.M. & Van Breukelen, Gerard J.P., 2010. "D-optimality of unequal versus equal cluster sizes for mixed effects linear regression analysis of randomized trials with clusters in one treatment arm," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1906-1920, August.
    7. 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.
    8. 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.
    9. 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.
    10. Maryam Safarkhani & Mirjam Moerbeek, 2016. "D-optimal designs for a continuous predictor in longitudinal trials with discrete-time survival endpoints," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(2), pages 146-171, May.
    11. Karvanen, Juha, 2009. "Approximate cost-efficient sequential designs for binary response models with application to switching measurements," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1167-1176, February.
    12. Wiens, Douglas P., 2010. "Robustness of design for the testing of lack of fit and for estimation in binary response models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3371-3378, December.

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