Optimal Design for Non-Linear Models, With an Emphasis on Categorical Data

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The investigator identifies optimal and efficient designs for non-linear models. The focus is on (1) generalized linear models (GLMs) for binary data or count data; and (2) non-linear models for Event Related functional Magnetic Resonance Imaging (ER-fMRI) experiments. For the first of these, recent results are mostly restricted to models with a single covariate. The investigator studies common GLMs, such as logistic, probit and loglinear models, with multiple covariates and higher order terms. He develops novel theory and computational tools for identifying locally optimal designs under various optimality criteria as well as for identifying robust designs. For the second problem, the investigator identifies optimal and efficient designs under more realistic non-linear models for the combined objectives of estimation of the hemodynamic response function (HRF) and detection of brain activity. Traditionally, two separate linear models have been used for these disparate objectives. The use of a single non-linear model for modeling the hemodynamic response facilitates the simultaneous pursuit of both objectives. This approach provides not only a more natural formulation of design optimality criteria, but also results in better designs for ER-fMRI experiments.Binary data and count data are very common in many scientific fields, such as drug discovery, clinical trials, social sciences, marketing, etc. While models and methods of analysis for such data are well established, the study of optimal design for the efficient use of available resources lags considerably. For example, when planning a dose-response study, it is important to know which dose levels of a drug should be used in the study, and how many subjects should be assigned to these levels in order to get the most information for questions that are of scientific interest. Recent advances and new tools developed by the investigator and his collaborators make it possible to derive optimal designs for a variety of commonly used models. For a second part of the project, the investigator finds efficient designs for ER-fMRI experiments. These experiments are part of a cutting edge approach for studying brain activity caused by certain simple tasks. A subject in an MRI scanner is presented with a series of tasks, each of them repeated multiple times, and the hemodynamic response is measured. The investigator identifies optimal and efficient orders for presenting the tasks to a subject in order to gain as much information as possible for the scientific goals of the experiment.