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Highly Efficient Designs to Handle the Incorrect Specification of Linear Mixed Models

2008; Taylor & Francis; Volume: 38; Issue: 1 Linguagem: Inglês

10.1080/03610910802379152

1532-4141

S. A. Ortega‐Azurduy, F. E. S. Tan, Martijn P. F. Berger,

Statistical Methods in Clinical Trials

Abstract We apply a maximin criterion to examine the relative efficiency of several D q -optimal designs for a family of linear mixed models. Incorrect specifications of the order of the polynomial, size of the autocorrelation parameter, number of random parameters, and the correlation between random intercept and random slope are investigated. The results of our study allow us to draw the following conclusions: (1) the maximin D q -optimal design encountered appears to be highly efficient; (2) the variation of the minimum relative efficiencies of D q -optimal designs of the family of linear mixed models that were studied decreases as the order of the polynomial increases; (3) the effect of the autocorrelation parameter on the relative efficiencies of D q -optimal designs is the largest for first-degree polynomials; and (4) the relative efficiency of the equidistant design is lower than that of the maximin value and also lower than the reference value 0.85. Keywords: D-optimality D q -optimalityFirst-order autocorrelationLinear mixed modelsMaximin criterionRelative efficiencyRobust designsMathematics Subject Classification: 62K05 (Statistics, Optimal designs)93B51 (Design techniques, Computer aided) Acknowledgments This work is supported by a grant of the Netherlands Organisation for Scientific Research (NWO/MAGW), Grant number: 400-03-100. The authors thank the referees for their suggestions, which improved the presentation of the manuscript.