A graph theoretic approach to testing associations between disparate sources of functional genomic data

The last few years have seen the advent of high-throughput technologies to analyze various properties of the transcriptome and proteome of several organisms. The congruency of these different data sources, or lack thereof, can shed light on the mechanisms that govern cellular function. A central challenge for bioinformatics research is to develop a unified framework for combining the multiple sources of functional genomics information and testing associations between them, thus obtaining a robust and integrated view of the underlying biology. We present a graph theoretic approach to test the significance of the association between multiple disparate sources of functional genomics data by proposing two statistical tests, namely edge permutation and node label permutation tests. We demonstrate the use of the proposed tests by finding significant association between a Gene Ontology-derived "predictome" and data obtained from mRNA expression and phenotypic experiments for Saccharomyces cerevisiae. Moreover, we employ the graph theoretic framework to recast a surprising discrepancy presented in Giaever et al. (2002) between gene expression and knockout phenotype, using expression data from a different set of experiments.

FUNCTIONAL PRINCIPAL COMPONENTS MODEL FOR HIGH-DIMENSIONAL BRAIN IMAGING

We establish a fundamental equivalence between singular value decomposition (SVD) and functional principal components analysis (FPCA) models. The constructive relationship allows to deploy the numerical efficiency of SVD to fully estimate the components of FPCA, even for extremely high-dimensional functional objects, such as brain images. As an example, a functional mixed effect model is fitted to high-resolution morphometric (RAVENS) images. The main directions of morphometric variation in brain volumes are identified and discussed.

PENALIZED FUNCTIONAL REGRESSION

We develop fast fitting methods for generalized functional linear models. An undersmooth of the functional predictor is obtained by projecting on a large number of smooth eigenvectors and the coefficient function is estimated using penalized spline regression. Our method can be applied to many functional data designs including functions measured with and without error, sparsely or densely sampled. The methods also extend to the case of multiple functional predictors or functional predictors with a natural multilevel structure. Our approach can be implemented using standard mixed effects software and is computationally fast. Our methodology is motivated by a diffusion tensor imaging (DTI) study. The aim of this study is to analyze differences between various cerebral white matter tract property measurements of multiple sclerosis (MS) patients and controls. While the statistical developments proposed here were motivated by the DTI study, the methodology is designed and presented in generality and is applicable to many other areas of scientific research. An online appendix provides R implementations of all simulations.