Optimum design of experiments

• Grant number: 10/08250-8
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: August 08, 2010
• End date: August 20, 2010
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Luzia Aparecida Trinca
• Grantee: Luzia Aparecida Trinca
• Visiting researcher: Steven George Gilmour
• Visiting researcher institution: University of London, England
• Host Institution: Instituto de Biociências (IBB). Universidade Estadual Paulista (UNESP). Campus de Botucatu. Botucatu , SP, Brazil

Abstract

During this visit Dr. Gilmour will collaborate in research topics related to the construction of optimum designs for experiments in two types of problems: 1) multi-stratum designs (involving factors whose levels are hard to change and factors whose levels are easy to change, resulting in restricted randomization) and 2) Pharmacokinetics experiments which, in general, involves correlated responses. In the first case, the underlying model is the linear mixed model. The information matrix then depends on the random variability from each stratum. For only one stratum unbiased estimation of this variability is obtained for the so called pure error. Gilmour and Trinca (2010) propose adjustment to the usual design criteria in order to force the design to include pure error degrees of freedom. For several strata the problem is more complicated since there are the design should include pure error degrees of freedom for each of them. These issues will be considered e adjustments for the design criteria will be proposed. In the second design problem, the experiment involves repeated measures of blood concentration of a drug in the same subject at several time points after the drug administration. The description of the concentration as time function is obtained by fitting, usually, a nonlinear model and measures in the same subject are correlated. The design problem is to specify the time points blood should be collected in order to maximize the information about the parameters to be estimated. The information matrix depend on the true parameter values as well as the correlation structure. Bayesian (pseudo-Bayesian) designs are usually used to overcome the problem by specifying prior probability distributions to the parameters. We propose to evaluate the impact of different correlation structures to the design. (AU)