Gene Set Analysis Using Spatial Statistics

Gene differential expression consists of the study of the possible association between the gene expression, evaluated using different types of data as DNA microarray or RNA-Seq technologies, and the phenotype. This can be performed marginally for each gene (differential gene expression) or using a gene set collection (gene set analysis). A previous (marginal) per-gene analysis of differential expression is usually performed in order to obtain a set of significant genes or marginal p-values used later in the study of association between phenotype and gene expression. This paper proposes the use of methods of spatial statistics for testing gene set differential expression analysis using paired samples of RNA-Seq counts. This approach is not based on a previous per-gene differential expression analysis. Instead, we compare the paired counts within each sample/control using a binomial test. Each pair per gene will produce a p-value so gene expression profile is transformed into a vector of p-values which will be considered as an event belonging to a point pattern. This would be the first component of a bivariate point pattern. The second component is generated by applying two different randomization distributions to the correspondence between samples and treatment. The self-contained null hypothesis considered in gene set analysis can be formulated in terms of the associated point pattern as a random labeling of the considered bivariate point pattern. The gene sets were defined by the Gene Ontology (GO) terms and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways. The proposed methodology was tested in four RNA-Seq datasets of colorectal cancer (CRC) patients and the results were contrasted with those obtained using the edgeR-GOseq pipeline. The proposed methodology has proved to be consistent at the biological and statistical level, in particular using Cuzick and Edwards test with one realization of the second component and between-pair distribution.