3.1 Handling GEO (Gene Expression Omnibus) metadata

First, it is necessary to obtain a connection to the GEOmetadb SQLite database. If this were already downloaded, connectToGEODB returns a connection to the database given the full path to the SQLite database file. Alternatively, by setting download to TRUE the database is downloaded. The getGEOmetadata function can be used to retrieve the metadata related to specific GEO samples, taking as minimal parameters the connection to the database and one of the experiment types available. Optionally it is possible to specify the organism and the platform. The following code illustrates how to download the metadata corresponding to expression arrays, or DNA methylation sequencing experiments. The meth_metadata object, containing the results for the latter, was stored within Onassis. Therefore, the queries illustrated here can be skipped.

require('GEOmetadb')

## Running this function might take some time if the database (6.8GB) has to be downloaded.
geo_con <- connectToGEODB(download=TRUE)

#Showing the experiment types available in GEO
experiments <- experiment_types(geo_con)

#Showing the organism types available in GEO
species <- organism_types(geo_con)

#Retrieving Human gene expression metadata, knowing the GEO platform identifier, e.g. the Affymetrix Human Genome U133 Plus 2.0 Array
expression <- getGEOMetadata(geo_con, experiment_type='Expression profiling by array', gpl='GPL570')

#Retrieving the metadata associated to experiment type "Methylation profiling by high througput sequencing"
meth_metadata <- getGEOMetadata(geo_con, experiment_type='Methylation profiling by high throughput sequencing', organism = 'Homo sapiens')

Some of the experiment types available are the following:

Some of the organisms available are the following:

As specified above, meth_metadata was previously saved and can be loaded from the Onassis package external data (hover on the table to view additional rows and columns):

meth_metadata <- readRDS(system.file('extdata', 'vignette_data', 'GEOmethylation.rds', package='Onassis'))

3.2 Handling SRA (Sequence Read Archive) metadata

In this section we provide an example showing how it is possible to retrieve metadata from other sources such as SRA. This database is not directly supported by Onassis, since it is not available for Windows platforms. Hence, the code reported below is slightly more complicated, and exemplifies how to query the SRA database provided by the SRAdb package and store metadata of human ChIP-seq experiments within a data frame. Due to the size of the SRA database (2.4 GB for the compressed file, 36 GB for the .sqlite file), a sample of the results of the query is available within Onassis as external data (see below), and the example code illustrated here can be skipped.

# Optional download of SRAdb and connection to the corresponding sqlite file
require(SRAdb)
sqliteFileName <- '/pathto/SRAdb.sqlite'
sra_con <- dbConnect(SQLite(), sqliteFileName)

# Query for the ChIP-Seq experiments contained in GEO for human samples 
library_strategy <- 'ChIP-Seq' #ChIP-Seq data
library_source='GENOMIC' 
taxon_id=9606 #Human samples
center_name='GEO' #Data from GEO
 
# Query to the sample table 
samples_query <- paste0("select sample_accession, description, sample_attribute, sample_url_link from sample where taxon_id='", taxon_id, "' and sample_accession IS NOT NULL", " and center_name='", center_name, "'"  )

samples_df <- dbGetQuery(sra_con, samples_query)
samples <- unique(as.character(as.vector(samples_df[, 1])))

experiment_query <- paste0("select experiment_accession, center_name, title, sample_accession, sample_name, experiment_alias, library_strategy, library_layout, experiment_url_link, experiment_attribute from experiment where library_strategy='", library_strategy, "'" , " and library_source ='", library_source,"' ", " and center_name='", center_name, "'" )
experiment_df <- dbGetQuery(sra_con, experiment_query)

#Merging the columns from the sample and the experiment table
experiment_df <- merge(experiment_df, samples_df, by = "sample_accession")

# Replacing the '_' character with white spaces
experiment_df$sample_name <- sapply(experiment_df$sample_name, function(value) {gsub("_", " ", value)})
experiment_df$experiment_alias <- sapply(experiment_df$experiment_alias, function(value) {gsub("_", " ", value)})

sra_chip_seq <- experiment_df

The query returns a table with thousands of samples. Alternatively, as described above, a sample of this table useful for the subsequent examples can be retrieved in Onassis:

sra_chip_seq <- readRDS(system.file('extdata', 'vignette_data', 'GEO_human_chip.rds',  package='Onassis'))

4.1 Data preparation

The findEntities method supports input text in the form of:

• The path of a directory containing named documents.
  • The path of a single file containing multiple documents. In this case each row contains the name/identifier of the document followed by a ‘|’ separator and the text to annotate.

Alternatively, the annotateDF method supports input text in the form of a data frame. In this case each row represents a document; the first column has to be the document identifier; the remaining columns will be combined and contain the text to analyze. This option can be conveniently used with the metadata retrieved from GEOmetadb and SRAdb, possibly selecting a subset of the available columns.

4.2 Creation of a Conceptmapper Dictionary

Onassis handles the convertion of OBO dictionaries into a format suitable to Conceptmapper: XML files with a set of entries specified by the xml tag <token> with a canonical name (the name of the entry) and one or more variants (synonyms).

The constructor CMdictionary creates an instance of the class CMdictionary.

• If an XML file containing the Conceptmapper dictionary is already available, it can be uploaded into Onassis indicating its path and setting the dictType option to “CMDICT”.
  • If the dictionary has to be built from an OBO ontology (OBO or OWL formats are supported), the path or URL to the corresponding file has to be provided and dictType has to be set to “OBO”. The synonymType argument can be set to EXACT_ONLY or ALL to consider only canonical concept names or also to include any synonym. The resulting XML file is written in the indicated outputdir.
  • Additionally, to facilitate the named entity recognition of specific targets, such in the case of ChIP-seq experiments, these can be included within a specific dictionary, and dictType has to be set to ENTREZ. If a specific Org.xx.eg.db Bioconductor library is installed and loaded, it can be indicated in the inputFileOrDb parameter as a character string, and gene names will be derived from it. Instead, if inputFileOrDb is empty and a specific species is indicated in the taxID parameter, gene names will be derived from the corresponding gene_info.gz file downloaded from NCBI (300MB). Finally, if dictType is set to TARGET, known histone post-translational modifications and epigenetic marks are also included, in addition to gene names.

# If a Conceptmapper dictionary is already available the dictType CMDICT can be specified and the corresponding file loaded
sample_dict <- CMdictionary(inputFileOrDb=system.file('extdata', 'cmDict-sample.cs.xml', package = 'Onassis'), dictType = 'CMDICT')

#Creation of a dictionary from the file sample.cs.obo available in OnassisJavaLibs
obo <- system.file('extdata', 'sample.cs.obo', package='OnassisJavaLibs')

sample_dict <- CMdictionary(inputFileOrDb=obo, outputDir=getwd(), synonymType='ALL')

# Creation of a dictionary for human genes/proteins. This requires org.Hs.eg.db to be installed
require(org.Hs.eg.db)
targets <- CMdictionary(dictType='TARGET', inputFileOrDb = 'org.Hs.eg.db', synonymType='EXACT')

The following XML markup code illustrates a sample of the Conceptmapper dictionary corresponding to the Brenda tissue ontology.

   <?xml version="1.0" encoding="UTF-8" ?>
   <synonym>
      <token id="http://purl.obolibrary.org/obo/BTO_0005205" canonical="cerebral artery">
        <variant base="cerebral artery"/>
      </token>
      <token id="http://purl.obolibrary.org/obo/BTO_0002179" canonical="184A1N4 cell">
        <variant base="184A1N4 cell"/>
        <variant base="A1N4 cell"/>
      </token>
      <token id="http://purl.obolibrary.org/obo/BTO_0003871" canonical="uterine endometrial cancer cell">
        <variant base="uterine endometrial cancer cell"/>
        <variant base="endometrial cancer cell"/>
        <variant base="uterine endometrial carcinoma cell"/>
        <variant base="endometrial carcinoma cell"/>
      </token>
  </synonym>

4.3 Setting the options for the annotator

Conceptmapper includes 7 different options controlling the annotation step. These are documented in detail in the documentation of the CMoptions function. They can be listed through the listCMOptions function. The CMoptions constructor instantiates an object of class CMoptions with the different parameters that will be required for the subsequent step of annotation. We also provided getter and setter methods for each of the 7 parameters.

#Creating a CMoptions object and showing hte default parameters 
opts <- CMoptions()  
show(opts)

## CMoptions object to set ConceptMapper Options

## SearchStrategy: CONTIGUOUS_MATCH
## CaseMatch: CASE_INSENSITIVE
## Stemmer: NONE
## StopWords: NONE
## OrderIndependentLookup: ON
## FindAllMatches: YES
## SynonymType: ALL

To obtain the list of all the possible combinations:

combinations <- listCMOptions()

To create a CMoptions object having has SynonymType ‘EXACT_ONLY’, that considers only exact synonyms, rather than ‘ALL’ other types included in OBO (RELATED, NARROW, BROAD)

myopts <- CMoptions(SynonymType='EXACT_ONLY')
myopts

## CMoptions object to set ConceptMapper Options

## SearchStrategy: CONTIGUOUS_MATCH
## CaseMatch: CASE_INSENSITIVE
## Stemmer: NONE
## StopWords: NONE
## OrderIndependentLookup: ON
## FindAllMatches: YES
## SynonymType: EXACT_ONLY

To change a given parameter, for example to use a search strategy based on the Longest match of not-necessarily contiguous tokens where overlapping matches are allowed:

#Changing the SearchStrategy parameter
SearchStrategy(myopts) <- 'SKIP_ANY_MATCH_ALLOW_OVERLAP'
myopts

## CMoptions object to set ConceptMapper Options

## SearchStrategy: SKIP_ANY_MATCH_ALLOW_OVERLAP
## CaseMatch: CASE_INSENSITIVE
## Stemmer: NONE
## StopWords: NONE
## OrderIndependentLookup: ON
## FindAllMatches: YES
## SynonymType: EXACT_ONLY

4.4 Running the entity finder

The class EntityFinder defines a type system and runs the Conceptmapper pipeline. It can search for concepts of any OBO ontology in a given text. The findEntities and annotateDF methods accept text within files or data.frame, respectively, as described in Section 4.1. The function EntityFinder automatically adapts to the provided input type, creates an instance of the EntityFinder class to initialize the type system and runs Conceptmapper with the provided options and dictionary. For example, to annotate the metadata derived from ChIP-seq experiments obtained from SRA with tissue and cell type concepts belonging to the sample ontology available in Onassis and containing tissues and cell names, the following code can be used:

sra_chip_seq <- readRDS(system.file('extdata', 'vignette_data', 'GEO_human_chip.rds',  package='Onassis'))
chipseq_dict_annot <- EntityFinder(sra_chip_seq[1:50, c('experiment_accession', 'title', 'experiment_attribute', 'sample_attribute', 'description')], dictionary=sample_dict, options=myopts)

The resulting data.frame contains, for each row, a match to the provided dictionary for the document/sample indicated in the first column. The annotation is reported with the id of the concept (term_id), its canonical name (term name), its URL in the obo format, and the matching sentence of the document.

The function filterTerms can be used to remove all the occurrences of unwanted terms, for example very generic terms.

chipseq_dict_annot <- filterTerms(chipseq_dict_annot, c('cell', 'tissue'))

The function EntityFinder can also be used to identify the targeted entity of each ChIP-seq experiment, by retrieving gene names and epigenetic marks in the ChIP-seq metadata.

#Finding the TARGET entities
target_entities <- EntityFinder(input=sra_chip_seq[1:50, c('experiment_accession', 'title', 'experiment_attribute', 'sample_attribute', 'description')], options = myopts, dictionary=targets)

5.1 Semantic similarity between ontology terms

The following example shows pairwise similarities between the individual concepts of previously annotated ChIP-seq experiments metadata. The lin similarity measure is used by default, which relies on a ratio between the Information content (IC) of the terms most specific common ancestor, and the sum of their IC (based on the information content of their most informative common ancestor). In particular, the seco information content is used by default, which determines the specificity of each concept based on the number of concepts it subsumes.

#Retrieving URLS of concepts
found_terms <- as.character(unique(chipseq_dict_annot$term_url))

# Creating a dataframe with all possible couples of terms and adding a column to store the similarity
pairwise_results <- t(combn(found_terms, 2))
pairwise_results <- cbind(pairwise_results, rep(0, nrow(pairwise_results)))

# Similarity computation for each couple of terms
for(i in 1:nrow(pairwise_results)){
    pairwise_results[i, 3] <- Similarity(obo, pairwise_results[i,1], pairwise_results[i, 2])
}
colnames(pairwise_results) <- c('term1', 'term2', 'value')  

# Adding the term names from the annotation table to the comparison results 
pairwise_results <- merge(pairwise_results, chipseq_dict_annot[, c('term_url', 'term_name')], by.x='term2', by.y='term_url')
colnames(pairwise_results)[length(colnames(pairwise_results))] <- 'term2_name'
pairwise_results <- merge(pairwise_results, chipseq_dict_annot[, c('term_url', 'term_name')], by.x='term1', by.y='term_url')
colnames(pairwise_results)[length(colnames(pairwise_results))] <- 'term1_name'
pairwise_results <- unique(pairwise_results)
# Reordering the columns
pairwise_results <- pairwise_results[, c('term1', 'term1_name', 'term2', 'term2_name', "value")]

Noteworthy, the terms ‘B-cell’ and ‘lymphocyte’ are closer (similarity 0.83) than ‘B cell’ and ‘epithelial cell’ (similarity 0.26). It is also possible to compute the semantic similarity between two groups of terms. For example, to determine a value of similarity for the combination of (‘non-terminally differentiated cell’, ‘epithelial cell’) and the combination of (‘lymphocyte’ , ‘B cell’) we can use the ui measure (set as default measure in Onassis), a groupwise direct measure combining the intersection and the union of the set of ancestors of the two groups of concepts.

oboprefix <- 'http://purl.obolibrary.org/obo/'
Similarity(obo, paste0(oboprefix, c('CL_0000055', 'CL_0000066')) , paste0(oboprefix, c('CL_0000542', 'CL_0000236')))

## [1] 0.1764706

The similarity between these two groups of terms is low (in the interval [0, 1]), while the addition of the term ‘lymphocyte of B lineage’ to the first group the group similarity increases.

Similarity(obo, paste0(oboprefix, c('CL_0000055', 'CL_0000236' ,'CL_0000236')), paste0(oboprefix, c('CL_0000542', 'CL_0000066')))

## [1] 0.6470588

5.2 Semantic similarity between annotated samples

Similarity also supports the computation of the similarity between annotated samples. Since each sample is typically associated tu multiple terms, Similarity runs in the groupwise mode when applied to samples. To this end, samples identifiers and a data frame with previously annotated concepts returned by EntityFinder are required.

# Extracting all the couples of samples 
annotated_samples <- as.character(as.vector(unique(chipseq_dict_annot$sample_id)))

samples_couples <- t(combn(annotated_samples, 2))

# Computing the samples semantic similarity 
similarity_results <- apply(samples_couples, 1, function(couple_of_samples){
    Similarity(obo, couple_of_samples[1], couple_of_samples[2], chipseq_dict_annot)
})


#Creating a matrix to store the results of the similarity between samples
similarity_matrix <- matrix(0, nrow=length(annotated_samples), ncol=length(annotated_samples))
rownames(similarity_matrix) <- colnames(similarity_matrix) <- annotated_samples

# Filling the matrix with similarity values 
similarity_matrix[lower.tri(similarity_matrix, diag=FALSE)] <- similarity_results
similarity_matrix <- t(similarity_matrix)
similarity_matrix[lower.tri(similarity_matrix, diag=FALSE)] <- similarity_results 
# Setting the diagonal to 1
diag(similarity_matrix) <- 1

# Pasting the annotations to the sample identifiers
samples_legend <- aggregate(term_name ~ sample_id, chipseq_dict_annot, function(aggregation) paste(unique(aggregation), collapse=',' ))
rownames(similarity_matrix) <- paste0(rownames(similarity_matrix), ' (', samples_legend[match(rownames(similarity_matrix), samples_legend$sample_id), c('term_name')], ')')

# Showing a heatmap of the similarity between samples
heatmap.2(similarity_matrix, density.info = "none", trace="none", main='Samples\n semantic\n similarity', margins=c(12,50), cexRow = 2, cexCol = 2, keysize = 0.5)

6.1 Metadata annotation

In this section we illustrate the use of the Onassis class to annotate the metadata of ChIP-seq samples having as target H3K27ac. The dataset used for the following examples was obtained by annotating the all the ChIP-seq samples from SRA with target entities (as described in Section 4.2) and selecting the sample identifiers having H3K27ac as target. To load it from the vignette data:

h3k27ac_chip <- readRDS(system.file('extdata', 'vignette_data', 'h3k27ac_metadata.rds',  package='Onassis'))

The method annotate takes as input a data frame of metadata to annotate, the type of dictionary and the path of an ontology file and returns an instance of class Onassis. The input data frame should have unique identifiers in the first column (sample identifiers or generic document identifiers) and for each row one or more columns containing the metadata related to the identifier. Importantly, to subsequently compute the semantic similarities, the dictionary given to the method needs to be an ‘OBO’ ontology. To annotate tissue and cell types we used the previously loaded dictionary available in OnassisJavaLibs containing a sample of the Cell Line ontology CL merged with UBERON terms to identify also tissues.

cell_annotations <- annotate(h3k27ac_chip, 'OBO', obo, FindAllMatches='YES' )

To slot entities of an Onassis object reports for each sample the unique list of concepts found in the corresponding metadata. Specifically, term ids, term urls and term names are reported, and multiple entries per sample are comma separated. We usually refer to these unique lists as semantic sets.

To retrieve the semantic sets in an object of class Onassis we provided the accessor method entities

cell_entities <- entities(cell_annotations) 

The filterconcepts method can be used to filter out unwanted annotations, for example terms that we consider redundant or too generic. The method modifies the entities slot of the Onassis object and returns a new Onassis object with filtered semantic sets.

filtered_cells <- filterconcepts(cell_annotations, c('cell', 'tissue'))

6.2 Semantic similarity of semantic sets

The method sim populates the similarity slot within an Onassis object. Specifically, it generates a matrix containing semantic similarities between the semantic sets for each pair of samples annotated in the entities slot.

filtered_cells <- sim(filtered_cells)

The matrix of similarities can be accessed using the method simil(filtered_cells).

Semantic sets with semantic similarities above a given threshold can be combined using the method collapse. This method, based on hierarchical clustering, unifies the similar semantic sets by concatenating their unique concepts. Term names and term urls in the entities slot will be updated accordingly. For each concept, the number of samples associated is also reported in bracket squares, while the total number of samples associated to a given semantic set is indicated in parentheses. After the collapse, the similarity matrix in the similarity slot is consequently updated with the similarities of the new semantic sets.

collapsed_cells <- Onassis::collapse(filtered_cells, 0.9)

In the following heatmap the similarity values of collapsed cell/tissue semantic sets is reported.

heatmap.2(simil(collapsed_cells), density.info = "none", trace="none", margins=c(36, 36), cexRow = 1.5, cexCol = 1.5, keysize=0.5)

6.3 Integrating the annotations from different ontologies

In typical integrative analyses scenarios, users could be interested in annotating concepts from different domains of interest. In this case, one possibility could be building a tailored application ontology including the concepts from different ontologies and their relationships. However this is complicated, since it requires to match and integrate the relationships from one ontology to the other. Rather, Onassis allows integrating two ontologies by repeating the annotation process with another ontology, while keeping separate the semantic sets from the two ontologies. In the following example ChIP-seq samples will be annotated with information about disease conditions. For this particular semantic type, Onassis provides also a boolean variable disease that can be set to TRUE to recognize samples metadata explicitly annotated as Healthy conditions, to be differentiated from metadata where disease terms are simply lacking.

obo2 <- system.file('extdata', 'sample.do.obo', package='OnassisJavaLibs')
disease_annotations <- annotate(h3k27ac_chip, 'OBO',obo2, disease=TRUE )

The method mergeonassis can be used to combine two Onassis objects in which the same set of samples was annotated with two different ontologies. This is useful to perform a nested analysis driven by the annotation provided by the two ontologies. The first object associates the samples metadata to semantic sets from a primary domain of interest. For each semantic set, the associated samples will be further separated based on the semantic sets belonging to a secondary domain. For example, users could be interested in comparing different diseases (secondary domain) within each cell type (primary domain), for a set of cell type.

cell_disease_onassis <- mergeonassis(collapsed_cells, disease_annotations)

The following table shows merged entities:

6.4 Semantically-driven analysis of omics data

The method compare exploits the Onassis object to analyze the actual omics data. To this end, a score matrix containing measurements for any arbitrary genomic unit (rows) within each sample (columns) is necessary. For example, genomics units can be genes, for expression analyses, or genomic regions (such as promoters) for enrichment analyses (such as ChIP-seq experiments). We suggest to take advantage of data repositories where omics data were reanalyzed with standardazied analysis pipelines. This would minimize confunding issues related to the differences due to alternative analysis and normalization procedures. For example, CistromeDB provides ChIP-seq data from GEO re-analyzed with a standardized pipeline (Mei et al. 2017). To illustrate the compare method, we obtained from Cistrome the genomic positions of H3K27ac peaks for the previously annotated ChIP-seq samples. Cistrome samples can be retrieved using GSMs (GEO) sample identifiers, which were matched with those reported in the SRA ChIP-seq metadata table. We precomputed a score matrix having as rows human promoter regions in chromosome 20, and as columns the sample identifiers. Each entry of the matrix contains the peak score value reported by Cistrome if there was a peak for a given promoter region in a given sample, or 0 if there was no peak overlapping that promoter region. Promoters for the human genome were obtained using the Bioconductor annotation package TxDb.Hsapiens.UCSC.hg19.knownGene considering 2000 bases upstream and 2000 bases downstream transcription start sites of genes. The score table can be retrieved from the vignette_data:

score_matrix <- readRDS(system.file('extdata', 'vignette_data', 'score_matrix.rds', package='Onassis'))

The method compare can be used with any test function to compare scores across different semantic sets. When by = ‘col’ samples will be compared, meaning that the distribution of all the scores of the samples associated to a given semantic state will be compared with those of any other semantic state. This process will be then repeated for any pair of semantic states. Hence, test statistic and p-values are reported. In this example, these measure global differences in the distribution of H3K27ac at promoters among variuos cell types. The method returns a matrix whose each elements includes test statistic and p-value.

cell_comparisons_by_col <- compare(collapsed_cells, score_matrix=as.matrix(score_matrix), by='col', fun_name='wilcox.test')

matrix_of_p_values <- matrix(NA, nrow=nrow(cell_comparisons_by_col), ncol=ncol(cell_comparisons_by_col))
for(i in 1:nrow(cell_comparisons_by_col)){
    for(j in 1:nrow(cell_comparisons_by_col)){
     result_list <- cell_comparisons_by_col[i,j][[1]]
     matrix_of_p_values[i, j] <- result_list[2]
    }
}
colnames(matrix_of_p_values) <- rownames(matrix_of_p_values) <- colnames(cell_comparisons_by_col)

In the following heatmap -log10 p-values of the test are shown:

heatmap.2(-log10(matrix_of_p_values), density.info = "none", trace="none", main='Changes in\n H3K27ac signal \nin promoter regions', margins=c(36,36), cexRow = 1.5, cexCol = 1.5, keysize=1)

By setting by=‘row’, we can use compare to test for differences for each genomic unit in the different tissue/cell type semantic sets. In this example, for each promoter, the distribution of the scores within samples associated to a given semantic state, will be compared with those of any other semantic state. This process will be then repeated for any pair of semantic states. This allows measuring differences in the distribution of H3K27ac among variuos cell types within each specific promoter. Indeed, compare returns a matrix whose elements are lists with genomic regions including test statistics and p-values. After the application of the wilcoxon test we extracted for each couple of semantic sets the number of regions having a p.value <= 0.1.

cell_comparisons <- compare(collapsed_cells, score_matrix=as.matrix(score_matrix), by='row', fun_name='wilcox.test', fun_args=list(exact=FALSE))

# Extraction of p-values less than 0.1
significant_features <- matrix(0, nrow=nrow(cell_comparisons), ncol=ncol(cell_comparisons))
colnames(significant_features) <- rownames(significant_features) <- rownames(cell_comparisons)
for(i in 1:nrow(cell_comparisons)){
    for(j in 1:nrow(cell_comparisons)){
     result_list <- cell_comparisons[i,j][[1]]
     significant_features[i, j] <- length(which(result_list[,2]<=0.1))
    }
}

In the following table we report, for each pair of semantic states, the number of promoter regions with different H3K27ac binding patterns

If annotations from two ontologies are provided, for example cell types and diseases, compare returns a nested analysis: the method iterates for each cell type, and performs all pair-wise comparisons (of the scores) between the diseases associated to a given cell type. Therefore, a named list with the semantic sets of the first level ontology (cell type) is returned. Each entry of the list contains a matrix with the results of the test for each pair of second level semantic sets (diseases). For example, to use a wilcoxon test to compare H3K27ac between different diseases within each tissue/cell type, promoter by promoter, the following code can be used:

disease_comparisons <- compare(cell_disease_onassis, score_matrix=as.matrix(score_matrix), by='row', fun_name='wilcox.test', fun_args=list(exact=FALSE))

To visualize the diseases associated with the tissue semantic set “breast [8], mammary gland epithelial cell [2], gland [1] (11)” the following code can be used:

rownames(disease_comparisons$`breast [8], mammary gland epithelial cell [2], gland [1] (11)`)

## [1] "cancer"  "Healthy"

To access to the test results for the the comparison of “Healthy”" with “breast cancer, cancer”

selprom <- (disease_comparisons$`breast [8], mammary gland epithelial cell [2], gland [1] (11)`[2,1][[1]])
selprom <- selprom[is.finite(selprom[,2]),]
head(selprom)

##                       statistic    p.value
## chr20:236377-240376          12 0.08011831
## chr20:304215-308214          12 0.08011831
## chr20:325370-329369           5 0.42188125
## chr20:359308-363307           7 0.80258735
## chr20:359941-363940           7 0.80258735
## chr20:2841102-2845101        12 0.08011831

To determine the number of promoter regions having p.value <= 0.1 within each comparison

disease_matrix <- disease_comparisons[[1]]

# Extracting significant p-values
significant_features <- matrix(0, nrow=nrow(disease_matrix), ncol=ncol(disease_matrix))
colnames(significant_features) <- rownames(significant_features) <- rownames(disease_matrix)
for(i in 1:nrow(disease_matrix)){
    for(j in 1:nrow(disease_matrix)){
     result_list <- disease_matrix[i,j][[1]]
     significant_features[i, j] <- length(which(result_list[,2]<=0.1))
    }
}

Noteworthy, 5 of the 19 promoters that were differential for H3K27ac in breast cancer, refer to genes found to be important in that disease (according to GeneCards). In particular, these include CDC25B, which was recently identifed as therapeutic target for triple-negative breast cancer (Liu et al. 2018).

Alternatively, when not available within R libraries, personalized test functions can be applied. The code below for example implements a function named signal to noise statistic that could be applied as an alternative to the wilcoxon test.

personal_t <- function(x, y){
        if(is.matrix(x))
            x <- apply(x, 1, mean)
        if(is.matrix(y))
            y <- apply(y, 1, mean)
        signal_to_noise_statistic <- abs(mean(x) - mean(y)) / (sd(x) + sd(y))
        return(list(statistic=signal_to_noise_statistic, p.value=NA))
}

disease_comparisons <- compare(cell_disease_onassis, score_matrix=as.matrix(score_matrix), by='col', fun_name='personal_t')

Further details and examples about compare are available in the help page of the method.