High-dimensional data analysis with applications to diabetes prevention and physical activity data

This dissertation presents two important approaches to diabetes prevention research. The first is a classic epidemiological approach to studying depressive symptoms as a risk for developing type 2 diabetes mellitus. The second, and most prominent theme of the dissertation, focuses on the statistical issues relevant to the prevention of diabetes. In particular, emphasis is placed on a very important risk factor of type 2 diabetes—physical inactivity.; Chapter 1 is a longitudinal analysis of whether the presence of depressive symptoms increases the risk of developing type 2 diabetes in women. Pooled logistic regression with 2-year intervals was used to estimate the multivariate relative risk of developing type 2 diabetes in the presence of depressive symptoms. Our results suggest a potential need for closer screening of patients with depressive symptoms and the need for similar studies to be conducted within ethnically diverse populations.; Chapter 2 presents a functional data analysis case study based on TriTrac R3D accelerometer data taken from the Planet Health study. We propose the use of wavelets as an appropriate framework within which to characterize the general features of the accelerometer data and provide a discussion of the issues that arise when existing methods are considered for analyzing the data. In Chapter 3, we investigate an approach to incorporating the accelerometer data into an analysis of data on all subjects. A scaled latent variable model for bivariate longitudinal data is proposed to incorporate the accelerometer information, which is not available on all subjects. A moment-based iterative algorithm for estimating the scaling coefficients is offered as a precursor to the maximum likelihood estimation of the covariate effects. Chapter 4 is a discussion of optimal design for studies where resources do not allow for one of the bivariate outcomes to be measured on all subjects in the study. We use the unsealed version of the latent variable model presented in Chapter 3 to set the stage for the optimal design discussion. Some general guidelines and suggestions for design are provided.