Comparison of co-expression measures: mutual information, correlation, and model based indices

Lin Song,Steve Horvath,Peter Langfelder

doi:10.1186/1471-2105-13-328

Abstract

BackgroundCo-expression measures are often used to define networks among genes. Mutual information (MI) is often used as a generalized correlation measure. It is not clear how much MI adds beyond standard (robust) correlation measures or regression model based association measures. Further, it is important to assess what transformations of these and other co-expression measures lead to biologically meaningful modules (clusters of genes).ResultsWe provide a comprehensive comparison between mutual information and several correlation measures in 8 empirical data sets and in simulations. We also study different approaches for transforming an adjacency matrix, e.g. using the topological overlap measure. Overall, we confirm close relationships between MI and correlation in all data sets which reflects the fact that most gene pairs satisfy linear or monotonic relationships. We discuss rare situations when the two measures disagree. We also compare correlation and MI based approaches when it comes to defining co-expression network modules. We show that a robust measure of correlation (the biweight midcorrelation transformed via the topological overlap transformation) leads to modules that are superior to MI based modules and maximal information coefficient (MIC) based modules in terms of gene ontology enrichment. We present a function that relates correlation to mutual information which can be used to approximate the mutual information from the corresponding correlation coefficient. We propose the use of polynomial or spline regression models as an alternative to MI for capturing non-linear relationships between quantitative variables.ConclusionThe biweight midcorrelation outperforms MI in terms of elucidating gene pairwise relationships. Coupled with the topological overlap matrix transformation, it often leads to more significantly enriched co-expression modules. Spline and polynomial networks form attractive alternatives to MI in case of non-linear relationships. Our results indicate that MI networks can safely be replaced by correlation networks when it comes to measuring co-expression relationships in stationary data.

Highlights

The estimated mutual information depends on parameter choices, e.g. the number of bins used in the equal-width discretization step for defining dx = discretize(x)
It is surprising that a simple approximate relationship holds between the two association measures if x, y are samples from a bivariate normal discretization method is distribution and the used with no.bins =
A second limitation concerns our gene ontology analysis of modules identified in networks based on various association measures in which we found that the correlation based topological overlap measure (TOM) leads to co-expression modules that are more highly enriched with GO terms than those of alternative approaches

Summary

Introduction

Mutual information (MI) is often used as a generalized correlation measure It is not clear how much MI adds beyond standard (robust) correlation measures or regression model based association measures. Most co-expression measures fall into one of two categories: correlation coefficients or mutual information measures. The correlation coefficient and other model based association measures are ideally suited for relating quantitative variables. Researchers trained in statistics often measure gene co-expression by the correlation coefficient. The majority of published articles use the correlation coefficient as co-expression measure [1,2,3,4,5] but hundreds of articles have used the mutual information (MI) measure [6,7,8,9,10,11,12]

Methods

Results

Discussion

Conclusion