Association Study, Risk Assessment, and Prediction of Children's Growth Trajectories through Methylation Profiles using Functional Mixed Model

This dissertation is motivated by the Newborn Epigenetic STudy (NEST) data. The overall goal is to investigate the relationship between growth trajectories and gene methylation profiles in children. Each child in the NEST data set has up to thirty weight measurements (in kilograms), recorded on days irregularly spaced over a five year time frame. The methylation profiles contain numerous vectors of related, highly correlated, covariates. Although there have been many developments in the functional data literature, standard methods are not suitable to adequately model this type of data, as explained in Chapter 2.;To model this type of data, a functional semiparametric regression modeling framework is introduced, where the response is a function (children growth trajectories measured over time) and the covariates are both vector and scalar (gene methylation profiles and other confounders). The model framework combines standard functional methods, such as functional principal components analysis, with Gaussian process regression and is flexible enough to handle sparse, irregularly spaced data. Using this modeling framework, we first consider the problem of determining if there is an association between the growth trajectories and gene methylation profiles, while accounting for other confounders. A hypothesis testing procedure is developed to test the joint effect of a specific vector of methylation values on the functional response. This is done by modeling the effect of the vector as a random effect and utilizing a linear score test for variance components.;The initial model is then reparameterized and fit as a penalized regression model. By using a different model fitting procedure and making some alterations to the testing procedure, we have a comparable method in terms of Type I error, power, and hypothesis testing results but with significantly reduced computation time. The penalized regression model is expanded to develop a prediction mode. This enables us to determine how the functional response changes based on the vector of related covariates of interest and to predict the full growth trajectory for each individual. Changes in the functional response due to the covariates of interest are captured through what is referred to as individual risk profiles. Using the assumed distribution of the functional random effect and the prediction model, the risk profile and full growth trajectory for a new subject can be predicted using their methylation profiles and other baseline covariate information. The use of prediction variances is introduced to construct prediction bands around the curves, which improves the coverage of the intervals as compared to methods found in current functional data literature.