This research is for the extension and further development of a new class of multivariate semi-parametric model building methods, known collectively as Smoothing Spline Analysis of Variance, which are suitable for the analysis of response data from large cohort studies, either epidemiologic or clinical trials, with many predictor variables, or covariates. These methods represent an attempt to obtain flexible empirical relationships between a response and many predictors considered simultaneously. If such a model can be fitted to the data, then the estimated sensitivities of the responses to various predictors and groups of predictors can be obtained by examining the models. Semiparametric models of interaction effects among the predictors are specifically included, as are continuous as well as certain kinds of ordinal responses. The models reduce to various standard parametric models if the data suggest that nonparametric terms in the model are not present. There are a number of developmental issues, including establishing the validity of certain model selection techniques, evaluating certain techniques for making confidence statements, and development of efficient numerical methods, which we propose to solve in order that the methods can be profitably applied in the multi-predictor demographic studies context. Data from the Wisconsin Epidemiological Study of Diabetic Retinopathy, a large ongoing prospective follow-up study of diabetic complications and their risk factors, will be used to examine the different 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 epidemiologic studies as well as clinical trials. The research software will be further developed into a user friendly form, documented, and made publicly available.
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