Proportionality: A Valid Alternative to Correlation for Relative Data

TLDR

In life sciences, many assays yield only relative abundances, making differential expression analysis challenging and rendering correlation an inappropriate measure of association for compositional data. The study aims to demonstrate that correlation is misleading for relative data and to introduce proportionality, using yeast gene expression data, as a valid alternative for analyzing such data while also prompting investigation into the mechanisms of proportional regulation. The authors define a new statistic, φ, that quantifies the strength of proportionality between variables and can replace correlation in standard analyses and visualisations such as co‑expression networks and clustered heatmaps. They show that correlation can mislead interpretation, whereas proportionality measured by φ provides a meaningful, interpretable metric that can be applied to familiar analytical workflows.

Abstract

In the life sciences, many measurement methods yield only the relative abundances of different components in a sample. With such relative—or compositional—data, differential expression needs careful interpretation, and correlation—a statistical workhorse for analyzing pairwise relationships—is an inappropriate measure of association. Using yeast gene expression data we show how correlation can be misleading and present proportionality as a valid alternative for relative data. We show how the strength of proportionality between two variables can be meaningfully and interpretably described by a new statistic ϕ which can be used instead of correlation as the basis of familiar analyses and visualisation methods, including co-expression networks and clustered heatmaps. While the main aim of this study is to present proportionality as a means to analyse relative data, it also raises intriguing questions about the molecular mechanisms underlying the proportional regulation of a range of yeast genes.