Proportionality: a valid alternative to correlation for relative data

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 {varphi} which can be used instead of correlation as the basis of familiar analyses and visualization 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.