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Robust designs for multivariate logistic regression

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  • Sanjoy Sinha

Abstract

In this paper, the author investigates optimal designs for multivariate binary regression models used in many clinical experiments. As the computation of a joint likelihood for multiple binary outcomes is often tedious, the author proposes and explores a pseudo-likelihood approach for choosing an optimal design under minimal parametric assumptions. The proposed design is considered robust in the sense that it provides estimators that are almost as efficient as those obtained from D-optimal designs under correctly specified likelihood functions and it can provide more efficient estimators as compared to D-optimal designs under misspecified likelihood functions. The asymptotic relative efficiencies of the maximum pseudo-likelihood estimators with respect to the exact maximum likelihood estimators are investigated. Monte Carlo simulations are carried out to explore the finite-sample properties of the maximum pseudo-likelihood estimators obtained under the proposed design scheme. The method is also illustrated in an example using actual data from a clinical study. Copyright Sapienza Università di Roma 2013

Suggested Citation

  • Sanjoy Sinha, 2013. "Robust designs for multivariate logistic regression," METRON, Springer;Sapienza Università di Roma, vol. 71(2), pages 157-173, September.
    • Handle: RePEc:spr:metron:v:71:y:2013:i:2:p:157-173
    DOI: 10.1007/s40300-013-0010-3
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    References listed on IDEAS

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    1. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    2. 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.
    3. Thomas Schmelter, 2007. "The Optimality of Single-group Designs for Certain Mixed Models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(2), pages 183-193, February.
    4. Adewale, Adeniyi J. & Xu, Xiaojian, 2010. "Robust designs for generalized linear models with possible overdispersion and misspecified link functions," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 875-890, April.
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