A Statistical Framework for Incorporating Multi-Omics Technologies for Precision Medicine

This thesis addresses important statistical challenges in precision medicine, the clinical practice to customise treatment plans for individual patients using genetic information. We propose methods, frameworks and procedures that tackle the discovery, translation and implementation of precision medicine through the use of omics data. In Chapter 1, we provide a brief overview of precision medicine with a special focus on targeted assays as a potential instrument for large-scale implementation. We present an overview of the statistical challenges that must be overcome in three phases of precision medicine in order to facilitate the final implementation. Chapter 2 of this thesis focuses on adapting the classical gene-set tests for targeted assays by proposing a new method, bcGST (bias-corrected Gene Set Test). We will show how bcGST makes an improvement in cases where the gene-set selection bias is ignored. In Chapter 3 we propose a novel variable selection method, APES (APproximated Exhaustive Search), for generalised linear models (GLMs). APES is capable in approximating a genuine exhaustive search with a dramatically improved speed. We devise a comprehensive set of simulations to test APES's performance and apply it to a real targeted assay with hundreds of variables. In Chapter 4 we propose the Cross-Platform Omics Prediction (CPOP) procedure that constructs "transferable" models which possess high predictive power across multiple omics datasets with no additional manipulations on the model. CPOP models have biologically relevant features that are statistically stable with respect to between-data noise and thus improve the reproducibility of the predictions. We curate four melanoma datasets and a prospective targeted assay experiment to illustrate the novelty of CPOP. This thesis contributes to precision medicine research by developing relevant, interpretable and implementable statistical methods