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FUNCTIONAL DATA ANALYSIS METHODS FOR PREDICTING DISEASE STATUS Sarah Kendrick November 20, 2017 Introduction: Differential scanning calorimetry (DSC) is used to determine thermally-induced conformational changes of biomolecules within a blood plasma sample. Recent research has indicated that DSC curves (or thermograms) may have different characteristics based on disease status and, thus, may be useful as a monitoring and diagnostic tool for some diseases. Since thermograms are curves measured over a range of temperature values, they are often considered as functional data. In this dissertation we propose and apply functional data analysis (FDA) techniques to analyze DSC data from the Lupus Family Registry and Repository (LFRR). The aim is to develop FDA methods to create models for classifying lupus vs. control patients on the basis of the thermogram curves. Methods: In project 1 we examine how well standard functional regression is able to capture the differences in curves for cases and controls and compare this to a multivariate approach. In project 2 we develop a semiparametric model; the Generalized Functional Partially Linear Single-Index Model (GFPL). This model is useful when there exists some curvature or non-linearity in the logit, which cannot be modeled by the standard Functional Generalized Linear Model (FGLM). It also mitigates the curse of dimensionality, is a more flexible model, and yields interpretable

Functional data analysis methods for predicting disease status.