Proportionality: A Valid Alternative to Correlation for Relative Data

David Lovell
Queensland University of Technology, Brisbane, Australia
Vera Pawlowsky-Glahn
Dept. d’Informàtica, Matemàtica Aplicada i Estadística. U. de Girona, España
Juan José Egozcue
Dept. Applied Mathematics III, U. Politécnica de Catalunya, Barcelona, Spain
Samuel Marguerat
MRC Clinical Sciences Centre, Imperial College London, United Kingdom
Jürg Bähler
Research Department of Genetics, Evolution and Environment, University College London, United Kingdom

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.