High-dimensional varying-coefficient models for genomic studies

Abstract

This thesis is concerned with novel statistical approaches for integrative genomic analysis, particularly methods that incorporate interactions between features from different data types into regression models. Recent technological advancements have enabled the collection of different molecular data types on the same patient. Extensive research efforts have been made towards integrating such comprehensive data set to study the biological mechanisms involved in disease development. While existing integrative approaches mainly focus on accounting for the difference in prognostic power across data types, there are relatively few works engaged in incorporating the interaction effects between different types of biological features on disease prognosis. As many chronic diseases are known to be affected by certain molecular features interacting with clinical factors, it is crucial to identify the relevant risk factors along with their interaction effects. In genomic studies, the major challenges of interaction analysis lie in the high dimensionality of the data and heterogeneity across data types. In order to decipher the association between the molecular interplays and a disease outcome, we propose to use the varying-coefficient models to characterize the interaction effects between the genomic features and a set of effect modifiers. We adopt a class of single-index varying-coefficient models to accommodate the potential interaction effects, and we propose a penalized spline-based estimation method for selecting important features with constant or varying effects. In an ongoing study, we consider a varying-coefficient additive hazards model and propose a kernel-based method to estimate the constant and varying effects.