This research is for the further development of a class of multivariate semi-parametric model building methods, known collectively as Smoothing Spline Analysis of Variance, (SS-ANOVA), which are suitable for the analysis of data from large cohort studies, either epidemiologic or clinical trials, with many qualitatively different variables observed over several time points. Methods in this class provide flexible empirical relationships between multiple complex responses and predictors, but reduce to standard parametric methods when the data suggest that parametric methods are sufficient. Sensitivities of the responses to various predictors can be obtained and the existence of associations between various variables of interest can be tested. SS-ANOVA models have been built and tested for the prediction of multivariate and multi-categorical responses, and methods developed which allow the analysis of large complex data sets. We will continue to extend this work in several directions: Development of methods to prescreen large, complex data sets for patterns of joint relationships that warrant further examination; extension to nonparametric multivariate density estimation for the purpose of uncovering and testing for conditional and time dependent relationships among the variables, nonparametric methods for investigating irregularly clustered data and within cluster relationships, and further development of multi-category nonstandard support vector machines for classification with emphasis on medical decision making. Data from the Wisconsin Epidemiological Study of Diabetic Retinopathy and the Beaver Dam Eye Study will be used to examine the models under study for their reasonableness and for their ability to answer questions meaningful to the study scientists. The results will have broad applicability to other large epidemiological studies as well as to clinical trials. The research software will be developed into a user-friendly form, documented, and made publicly available.
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