This step is links distal probes with methylation changes to target genes with expression changes and report the putative target gene for selected probes. This is carried out by function get.pair.
For each differentially methylated distal probe (DMC), the closest 10 upstream genes and the closest 10 downstream genes are tested for inverse correlation between methylation of the probe and expression of the gene, which is the same basic strategy employed in ELMER version 1. However, we now import all gene annotations programmatically using the Biomart (Durinck and others 2005) package. This allows easy extensibility to use any annotations desired (our default uses Ensembl annotations).
This step also differs between the Supervised and Unsupervised modes. In the Unsupervised mode, as in ELMER 1.0, for each probe-gene pair, the samples (all samples from both groups) are divided into two groups: the M group, which consist of the upper methylation quintile (the 20%of samples with the highest methylation at the enhancer probe), and the U group, which consists of the lowest methylation quintile (the 20% of samples with the lowest methylation). In the new Supervised mode, the U and M groups are defined strictly by sample group labels, and all samples in each group are used. For each differentially methylated distal probe (DMC), the closest 10 upstream genes and the closest 10 downstream genes are tested for inverse correlation between methylation of the probe and expression of the gene (the number 10 can be changed using the numFlankingGenes parameter). To select these genes, the probe-gene distance is defined as the distance from the probe to the transcription start site specified by the ENSEMBL gene level annotations (Yates and others 2015) accessed via the R/Bioconductor package biomaRt (Durinck and others 2009,Durinck and others (2005)). By choosing a constant number of genes to test for each probe, our goal is to avoid systematic false positives for probes in gene rich regions. This is especially important given the highly non-uniform gene density of mammalian genomes.
Thus, exactly 20 statistical tests were performed for each probe, as follows.
For each candidate probe-gene pair, the Mann-Whitney U test is used to test the null hypothesis that overall gene expression in group M is greater than or equal than that in group U. This non-parametric test was used in order to minimize the effects of expression outliers, which can occur across a very wide dynamic range. In the unsupervised mode for each probe-gene pair tested, the raw p-value Pr is corrected for multiple hypothesis using a permutation approach as follows. The gene in the pair is held constant, and x random methylation probes are chosen to perform the same one-tailed U test, generating a set of x permutation p-values Pp. We chose the x random probes only from among those that were “distal” (farther than 2kb from an annotated transcription start site), in order to draw these null-model probes from the same set as the probe being tested (Sham and Purcell 2014). An empirical p-value Pe value was calculated using the following formula (which introduces a pseudo-count of 1):
In the unsupervised mode for each probe-gene pair tested, the raw p-value Pr is corrected for multiple hypothesis using Benjamini-Hochberg Procedure.
Notice that in the Supervised mode, no additional filtering is necessary to ensure that the M and U group segregate by sample group labels. The two sample groups are segregated by definition, since these probes were selected for their differential methylation, with the same directionality, between the two groups.