Binary Expansion Testing and Gait Force Analysis

The Cancer Genome Atlas (TCGA) gene expression data are very complex, reflecting many types of relationships between genes. Here we study pairs of genes and investigate potentially interesting nonlinear dependencies some of which classical correlation-related methods fail to find. One part of this dissertation studies such nonlinear relationships using a powerful tool called Binary Expansion Testing (BET). We find many nonlinear patterns, some of which are driven by known cancer subtypes, some of which are novel. The Bonferroni adjusted p-values in this exploratory data analysis of TCGA could be overly conservative when used to determine the significant gene pairs. A novel contribution of this dissertation is an improvement of the power of BET. This is done by studying the distribution of the maximal BET z-statistics when doing pairwise testing in a large-scale data set. We use extreme value theory to propose a selection method of significant dependence pairs based on BET z-scores using this distribution.

Another important part of this dissertation is a deep analysis of gait force curve data in arthritis from the viewpoint of Object Oriented Data Analysis (OODA). Our goal is to detect useful patterns and biomechanical phenotypes of knee forces among people with knee osteoarthritis. We find many interesting modes of variation from original force curves, amplitude, and phase data objects. Moreover, an important part of this study is to understand the relationships between movement phenotypes and clinical covariates. Therefore, the dissertation investigates which clinical covariates are correlated to those modes of variation by using a data integration method Angle-based Joint and Individual Variation Explained (AJIVE). We find four joint components which illustrate interesting modes of variation of the force curves explained by the corresponding clinical covariates.

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