Abstract
For pathway analysis of genomic data, the most common methods involve combining p-values from individual statistical tests. However, there are several multivariate statistical methods that can be used to test whether a pathway has changed. Because of the large number of variables and pathway sizes in genomics data, some of these statistics cannot be computed. However, in metabolomics data, the number of variables and pathway sizes are typically much smaller, making such computations feasible. Of particular interest is being able to detect changes in pathways that may not be detected for the individual variables. We compare the performance of both the p-value methods and multivariate statistics for self-contained tests with an extensive simulation study and a human metabolomics study. Permutation tests, rather than asymptotic results are used to assess the statistical significance of the pathways. Furthermore, both one and two-sided alternatives hypotheses are examined. From the human metabolomic study, many pathways were statistically significant, although the majority of the individual variables in the pathway were not. Overall, the p-value methods perform at least as well as the multivariate statistics for these scenarios.
Highlights
In metabolomics, we are interested in changes for individual metabolites, and groups of related metabolites, which may be metabolites in the same class, metabolites in the same pathway, or other groups of bio-signatures
For one-sided alternatives, we propose a simple modification of statistics of the form (2.4)
While all the multivariate statistics require that the covariance matrix is the same for each group, most of the multivariate statistics considered do not require the inversion of the sample covariance matrix, and could be applied for even small sample sizes
Summary
We are interested in changes for individual metabolites, and groups of related metabolites, which may be metabolites in the same class, metabolites in the same pathway, or other groups of bio-signatures. All these categories will be referred to as “pathways.” In particular we are interested in the cases where the individual metabolites miss the cut-off for statistical significance from univariate analyses, but in aggregate are found to be statistically significant. If the pair-wise correlations (unless otherwise stated, “correlation” refers to the Pearson correlation) are 0.99, we expect the aggregate p-value to be similar to an individual p-value. If these are statistically independent, the Fisher meta-analysis [1] p-value = 0.0003. It is desirable to formally test whether a pathway is changed
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