# Function to conduct enrichment analysis given the input data and the ontology and its annotation

### Description

`xEnricher`

is supposed to conduct enrichment analysis given the
input data and the ontology direct acyclic graph (DAG) and its
annotation. It returns an object of class "eTerm". Enrichment analysis
is based on either Fisher's exact test or Hypergeometric test. The test
can respect the hierarchy of the ontology.

### Usage

1 2 3 4 5 6 7 8 9 | ```
xEnricher(data, annotation, g, background = NULL, size.range = c(10,
2000),
min.overlap = 3, which.distance = NULL, test = c("hypergeo", "fisher",
"binomial"), p.adjust.method = c("BH", "BY", "bonferroni", "holm",
"hochberg", "hommel"), ontology.algorithm = c("none", "pc", "elim",
"lea"),
elim.pvalue = 0.01, lea.depth = 2, path.mode = c("all_paths",
"shortest_paths", "all_shortest_paths"), true.path.rule = TRUE,
verbose = T)
``` |

### Arguments

`data` |
an input vector containing a list of genes or SNPs of interest |

`annotation` |
the vertices/nodes for which annotation data are provided. It can be a sparse Matrix of class "dgCMatrix" (with variants/genes as rows and terms as columns), or a list of nodes/terms each containing annotation data, or an object of class 'GS' (basically a list for each node/term with annotation data) |

`g` |
an object of class "igraph" to represent DAG. It must have node/vertice attributes: "name" (i.e. "Term ID"), "term_id" (i.e. "Term ID"), "term_name" (i.e "Term Name") and "term_distance" (i.e. Term Distance: the distance to the root; always 0 for the root itself) |

`background` |
a background vector. It contains a list of genes or SNPs as the test background. If NULL, by default all annotatable are used as background |

`size.range` |
the minimum and maximum size of members of each term in consideration. By default, it sets to a minimum of 10 but no more than 2000 |

`min.overlap` |
the minimum number of overlaps. Only those terms with members that overlap with input data at least min.overlap (3 by default) will be processed |

`which.distance` |
which terms with the distance away from the ontology root (if any) is used to restrict terms in consideration. By default, it sets to 'NULL' to consider all distances |

`test` |
the test statistic used. It can be "fisher" for using fisher's exact test, "hypergeo" for using hypergeometric test, or "binomial" for using binomial test. Fisher's exact test is to test the independence between gene group (genes belonging to a group or not) and gene annotation (genes annotated by a term or not), and thus compare sampling to the left part of background (after sampling without replacement). Hypergeometric test is to sample at random (without replacement) from the background containing annotated and non-annotated genes, and thus compare sampling to background. Unlike hypergeometric test, binomial test is to sample at random (with replacement) from the background with the constant probability. In terms of the ease of finding the significance, they are in order: hypergeometric test > fisher's exact test > binomial test. In other words, in terms of the calculated p-value, hypergeometric test < fisher's exact test < binomial test |

`p.adjust.method` |
the method used to adjust p-values. It can be one of "BH", "BY", "bonferroni", "holm", "hochberg" and "hommel". The first two methods "BH" (widely used) and "BY" control the false discovery rate (FDR: the expected proportion of false discoveries amongst the rejected hypotheses); the last four methods "bonferroni", "holm", "hochberg" and "hommel" are designed to give strong control of the family-wise error rate (FWER). Notes: FDR is a less stringent condition than FWER |

`ontology.algorithm` |
the algorithm used to account for the hierarchy of the ontology. It can be one of "none", "pc", "elim" and "lea". For details, please see 'Note' below |

`elim.pvalue` |
the parameter only used when "ontology.algorithm" is "elim". It is used to control how to declare a signficantly enriched term (and subsequently all genes in this term are eliminated from all its ancestors) |

`lea.depth` |
the parameter only used when "ontology.algorithm" is "lea". It is used to control how many maximum depth is used to consider the children of a term (and subsequently all genes in these children term are eliminated from the use for the recalculation of the signifance at this term) |

`path.mode` |
the mode of paths induced by vertices/nodes with input annotation data. It can be "all_paths" for all possible paths to the root, "shortest_paths" for only one path to the root (for each node in query), "all_shortest_paths" for all shortest paths to the root (i.e. for each node, find all shortest paths with the equal lengths) |

`true.path.rule` |
logical to indicate whether the true-path rule should be applied to propagate annotations. By default, it sets to true |

`verbose` |
logical to indicate whether the messages will be displayed in the screen. By default, it sets to true for display |

### Value

an object of class "eTerm", a list with following components:

`term_info`

: a matrix of nTerm X 4 containing snp/gene set information, where nTerm is the number of terms, and the 4 columns are "id" (i.e. "Term ID"), "name" (i.e. "Term Name"), "namespace" and "distance"`annotation`

: a list of terms containing annotations, each term storing its annotations. Always, terms are identified by "id"`g`

: an igraph object to represent DAG`data`

: a vector containing input data in consideration. It is not always the same as the input data as only those mappable are retained`background`

: a vector containing the background data. It is not always the same as the input data as only those mappable are retained`overlap`

: a list of overlapped snp/gene sets, each storing snps/genes overlapped between a snp/gene set and the given input data (i.e. the snps/genes of interest). Always, gene sets are identified by "id"`fc`

: a vector containing fold changes`zscore`

: a vector containing z-scores`pvalue`

: a vector containing p-values`adjp`

: a vector containing adjusted p-values. It is the p value but after being adjusted for multiple comparisons`cross`

: a matrix of nTerm X nTerm, with an on-diagnal cell for the overlapped-members observed in an individaul term, and off-diagnal cell for the overlapped-members shared between two terms`call`

: the call that produced this result

### Note

The interpretation of the algorithms used to account for the hierarchy of the ontology is:

"none": does not consider the ontology hierarchy at all.

"lea": estimates the significance of a term in terms of the significance of its children at the maximum depth (e.g. 2). Precisely, once snps/genes are already annotated to any children terms with a more signficance than itself, then all these snps/genes are eliminated from the use for the recalculation of the signifance at that term. The final p-values takes the maximum of the original p-value and the recalculated p-value.

"elim": estimates the significance of a term in terms of the significance of its all children. Precisely, once snps/genes are already annotated to a signficantly enriched term under the cutoff of e.g. pvalue<1e-2, all these snps/genes are eliminated from the ancestors of that term).

"pc": requires the significance of a term not only using the whole snps/genes as background but also using snps/genes annotated to all its direct parents/ancestors as background. The final p-value takes the maximum of both p-values in these two calculations.

"Notes": the order of the number of significant terms is: "none" > "lea" > "elim" > "pc".

### See Also

`xDAGanno`

, `xEnricherGenes`

,
`xEnricherSNPs`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | ```
## Not run:
# 1) SNP-based enrichment analysis using GWAS Catalog traits (mapped to EF)
# 1a) ig.EF (an object of class "igraph" storing as a directed graph)
g <- xRDataLoader('ig.EF')
# 1b) load GWAS SNPs annotated by EF (an object of class "dgCMatrix" storing a spare matrix)
anno <- xRDataLoader(RData='GWAS2EF')
# 1c) optionally, provide the test background (if not provided, all annotatable SNPs)
background <- rownames(anno)
# 1d) provide the input SNPs of interest (eg 'EFO:0002690' for 'systemic lupus erythematosus')
ind <- which(colnames(anno)=='EFO:0002690')
data <- rownames(anno)[anno[,ind]==1]
data
# 1e) perform enrichment analysis
eTerm <- xEnricher(data=data, annotation=anno, background=background,
g=g, path.mode=c("all_paths"))
# 1f) view enrichment results for the top significant terms
xEnrichViewer(eTerm)
# 1f') save enrichment results to the file called 'EF_enrichments.txt'
res <- xEnrichViewer(eTerm, top_num=length(eTerm$adjp), sortBy="adjp",
details=TRUE)
output <- data.frame(term=rownames(res), res)
utils::write.table(output, file="EF_enrichments.txt", sep="\t",
row.names=FALSE)
# 1g) barplot of significant enrichment results
bp <- xEnrichBarplot(eTerm, top_num="auto", displayBy="adjp")
print(bp)
# 1h) visualise the top 10 significant terms in the ontology hierarchy
# color-code terms according to the adjust p-values (taking the form of 10-based negative logarithm)
xEnrichDAGplot(eTerm, top_num=10, displayBy="adjp",
node.info=c("full_term_name"))
# color-code terms according to the z-scores
xEnrichDAGplot(eTerm, top_num=10, displayBy="zscore",
node.info=c("full_term_name"))
## End(Not run)
``` |