Multivariate Differential Association Analysis

TL;DR

This paper introduces a kernel-based statistical test to detect differences in dependence relationships between two sets of high-dimensional variables across different conditions, with applications in biological data analysis.

Contribution

It proposes a novel, computationally efficient kernel-based test for differential dependence, including its asymptotic permutation null distribution, suitable for large datasets.

Findings

High power for detecting linear and non-linear dependence differences

Effective in finite samples with good computational efficiency

Implemented in an accessible R package kerDAA

Abstract

Identifying how dependence relationships vary across different conditions plays a significant role in many scientific investigations. For example, it is important for the comparison of biological systems to see if relationships between genomic features differ between cases and controls. In this paper, we seek to evaluate whether the relationships between two sets of variables is different across two conditions. Specifically, we assess: do two sets of high-dimensional variables have similar dependence relationships across two conditions?. We propose a new kernel-based test to capture the differential dependence. Specifically, the new test determines whether two measures that detect dependence relationships are similar or not under two conditions. We introduce the asymptotic permutation null distribution of the test statistic and it is shown to work well under finite samples such that the test is computationally efficient, making it easily applicable to analyze large data sets. We demonstrate through numerical studies that our proposed test has high power for detecting differential linear and non-linear relationships. The proposed method is implemented in an R package kerDAA.