Distance-based analysis of variance: approximate inference and an application to genome-wide association studies

TL;DR

This paper introduces a distance-based MANOVA-like test, the DBF test, which enables group comparisons across complex data types like graphs and functions, with an approximate null distribution for efficient inference, demonstrated on genetic data.

Contribution

The paper proposes the DBF test, a novel distance-based method for multivariate group comparison that extends MANOVA to complex data types with an approximate null distribution for inference.

Findings

The DBF test performs well across various data types and distances.

It provides accurate group difference detection without permutation testing.

Applied successfully to genome-wide association data for Alzheimer's disease.

Abstract

In several modern applications, ranging from genetics to genomics and neuroimaging, there is a need to compare observations across different populations, such as groups of healthy and diseased individuals. The interest is in detecting a group effect. When the observations are vectorial, real-valued and follow a multivariate Normal distribution, multivariate analysis of variance (MANOVA) tests are routinely applied. However, such traditional procedures are not suitable when dealing with more complex data structures such as functional (e.g. curves) or graph-structured (e.g. trees and networks) objects, where the required distributional assumptions may be violated. In this paper we discuss a distance-based MANOVA-like approach, the DBF test, for detecting differences between groups for a wider range of data types. The test statistic, analogously to other distance-based statistics, only relies on a suitably chosen distance measure that captures the pairwise dissimilarity among all available samples. An approximate null probability distribution of the DBF statistic is proposed thus allowing inferences to be drawn without the need for costly permutation procedures. Through extensive simulations we provide evidence that the proposed methodology works well for a range of data types and distances, and generalizes the traditional MANOVA tests. We also report on an application of the proposed methodology for the analysis of a multi-locus genome-wide association study of Alzheimer's disease, which has been carried out using several genetic distance measures.