Distance-based methods for detecting associations in structured data with applications in bioinformatics

摘要

In bioinformatics applications samples of biological variables of interest can take a varietyudof structures. For instance, in this thesis we consider vector-valued observationsudof multiple gene expression and genetic markers, curve-valued gene expression timeudcourses, and graph-valued functional connectivity networks within the brain. Thisudthesis considers three problems routinely encountered when dealing with such variables:uddetecting differences between populations, detecting predictive relationshipsudbetween variables, and detecting association between variables.udDistance-based approaches to these problems are considered, offering great flexibilityudover alternative approaches, such as traditional multivariate approaches whichudmay be inappropriate. The notion of distance has been widely adopted in recent yearsudto quantify the dissimilarity between samples, and suitable distance measures can beudapplied depending on the nature of the data and on the specific objectives of the study.udFor instance, for gene expression time courses modeled as time-dependent curves, distanceudmeasures can be specified to capture biologically meaningful aspects of theseudcurves which may differ. On obtaining a distance matrix containing all pairwise distancesudbetween the samples of a given variable, many distance-based testing proceduresudcan then be applied. The main inhibitor of their effective use in bioinformatics is thatudp-values are typically estimated by using Monte Carlo permutations. Thousands orudeven millions of tests need to be performed simultaneously, and time/computationaludconstraints lead to a low number of permutations being enumerated for each test.udThe contributions of this thesis include the proposal of two new distance-basedudstatistics, the DBF statistic for the problem of detecting differences between populations,udand the GRV coefficient for the problem of detecting association betweenudvariables. In each case approximate null distributions are derived, allowing estimationudof p-values with reduced computational cost, and through simulation these are shown to work well for a range of distances and data types. The tests are also demonstratedudto be competitive with existing approaches. For the problem of detecting predictiveudrelationships between variables, the approximate null distribution is derived for theudroutinely used distance-based pseudo F test, and through simulation this is shown toudwork well for a range of distances and data types. All tests are applied to real datasets,udincluding a longitudinal human immune cell M. tuberculosis dataset, an Alzheimer’suddisease dataset, and an ovarian cancer dataset.