Optimal and efficient designs for 2-parameter nonlinear models |
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| Institution: | 1. Department of Mathematics, University of Illinois at Chicago, Chicago, IL 60607, USA;2. Merck Research Laboratories, West Point, PA 19486, USA;3. University of Maryland at Baltimore County, Baltimore, MD 20250, USA;1. Imperial College, Department of Paediatrics, London, United Kingdom;2. Division of Allergy and Immunology, Icahn School of Medicine at Mount Sinai, New York, NY;3. Section of Allergy and Immunology, Children''s Hospital Colorado, University of Colorado, Denver, Colo;1. EuroQol Research Foundation, Rotterdam, The Netherlands;2. Health Economics and Health Care Management, Bielefeld University, Bielefeld, Germany;3. Department of Health Management and Health Economics, University of Oslo, Oslo, Norway;4. Health Services Research Centre, Akershus University Hospital, Lørenskog, Norway;5. School of Health and Related Research, University of Sheffield, Sheffield, UK;1. University of Sheffield;2. Bristol Meyers Squibb, Princeton Pike, Lawrenceville, NJ |
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| Abstract: | By Carathéodory's theorem, for a k-parameter nonlinear model, the minimum number of support points for any D-optimal design is between k and k(k+1)/2. Characterizing classes of models for which a D-optimal design sits on exactly k support points is of great theoretical interest. By utilizing the equivalence theorem, we identify classes of 2-parameter nonlinear models for which a D-optimal design is precisely supported on 2 points. We also introduce the theory of maximum principle from differential equations into the design area and obtain some results on characterizing the minimally supported nonlinear designs. Examples are given to demonstrate our results. Designs with minimum number of support points may not always be suitable in practice. To alleviate this problem, we utilize some geometric and analytical methods to obtain some efficient designs which provide more opportunity for the model checking and prevent biases due to mis-specified initial parameters. |
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