A multivariate statistical test for differential expression analysis

Abstract

Statistical tests of differential expression usually suffer from two problems. Firstly, their statistical power is often limited when applied to small and skewed data sets. Secondly, gene expression data are usually discretized by applying arbitrary criteria to limit the number of false positives. In this work, a new statistical test obtained from a convolution of multivariate hypergeometric distributions, the Hy-test, is proposed to address these issues. Hy-test has been carried out on transcriptomic data from breast and kidney cancer tissues, and it has been compared with other differential expression analysis methods. Hy-test allows implicit discretization of the expression profiles and is more selective in retrieving both differential expressed genes and terms of Gene Ontology. Hy-test can be adopted together with other tests to retrieve information that would remain hidden otherwise, e.g., terms of (1) cell cycle deregulation for breast cancer and (2) "programmed cell death" for kidney cancer.

Figure 1

Venn diagrams of the differentially expressed genes and significant terms found in each of the three analysis steps by the three methods: Hy-test, moderated t-test, and SAM. The upper panels (A, B, C) refer to the breast tissue and the lower panels (D, E, F) to the kidney. The first column (A and D) refers to the DE analysis, the second column (B and E) to the enrichment analysis and the third column (C and F) to the PubMed research. Significance is assessed when a Bonferroni corrected p-value is below the 5% level.

Figure 2

Correlation structure of breast cancer expression genes. Top-left panel refers to all genes, the top-right panel refers to the set of genes selected by moderated t-test, and the bottom panel refers to the set of genes selected by the Hy-test. $\overline{\varrho }$ is the block average correlation.

Figure 3

Correlation structure of kidney cancer expression genes. Top-left panel refers to all genes, the top-right panel refers to the set of genes selected by moderated t-test, and the bottom panel refers to the set of genes selected by the Hy-test. $\overline{\varrho }$ is the block average correlation.