Mantel statistics to correlate gene expression levels from microarrays with clinical covariates

Mantel statistics provide an additional step to standard approaches in the analysis of gene expression and covariate data, allow the calculation of standard statistics such as correlation, partial correlation, and regression coefficients, and, with permutation tests, provide P values for these statistics to relate the sample covariates to the expression levels. In this article we describe the Mantel statistics and illustrate their use and interpretation with data from a study of seven human oligodendrogliomas (brain tumors) where expression levels of 1013 genes and five covariates were previously analyzed using standard approaches. In the previous analysis of these data, qualitative relationships were found between gene expressions and two of the clinical covariates. We show in this article how the Mantel statistics are able to formally quantify and provide P values to determine statistical significance of these relationships. We also show how the Mantel statistics can be used to rank subsets of genes, found using standard clustering methods, in terms of differential expression across samples.