# 1 Introduction

Projects in biomedicine are generating information about multiple types of omics data. Most of these datasets are publicly available through on-line data backs like GEO (Gene Expression Omnibus), TCGA (The Cancer Genome Atlas) or EGA (European Genome-phenome Archive) among others. Standard association analyses between a given phenotype and a single omic dataset (aka. SNPs, gene expression, methylations,…) are insufficient to address most of the scientific questions that rely on knowing the mechanisms involved in complex diseases. Methods to properly integrate multi-data sets have to be used to analyze such amount of information.

One of the computational challenges when dealing with multi-omic data is to define an easy way to compact multiple pieces of information. This methodology must allow retrieving data for common-samples, subsetting individuals having a specific characteristic or selecting features from a given genomic region or a selected gene. MultiDataSet is conceived as a container and manager of multiple omic datasets while allowing performing common object operations such as accession to elements or subsetting among others. The vignette of MultiDataSet describes how to manipulate a MultiDataSet object as well as how to perform other basic operations.

In this document, we learn how to create a MultiDataSet object to be used in an integrative analysis implemented in omicade4. This Bioconductor package implements multiple coinertia analysis (mcia), a method that generalizes principal component analysis (PCA) in the case of having more than two tables. This package deals with multi-omic data by using lists. However, it requires analyzing complete cases (i.e. having common samples across datasets). Here, we illustrate how to encapsulate three different omic datasets (two microarray and one methylation experiments), how to get an object having complete cases and how to perform integration analysis. The same procedure is described in the case of using iClusterPlus, a method to perform cluster analysis having multiple datasets.

# 2 Objective

The objective of this document is to illustrate how to use MultiDataSet to store multiple omic datasets. We also illustrate how to use an object of class MultiDataSet in third party integration packages/pipelines. The document includes two different examples. One illustrates how to analyze a MultiDataSet object using omicade4, an R package designed to perform mcia analysis. The second example illustrates how to use iClusterPlus to perform clustering analysis on multiple datasets.

# 3 Implementation

This section includes three subsections. In the first subsection, Loading Data, three dummy datasets are loaded. These datasets correspond to two microarray experiments, which are encapsulated as an ExpressionSet and one methylation experiment stored as a GenomicRatioSet. The second, Packaging Data, illustrates how MultiDataSet is used to package multiple pieces of information. Notice that our package allows the possibility of having datasets of the same type. The third section, Integrative Analysis, shows how to perform the integration analysis of the three datasets by using omicade4 and iClusterPlus.

Two libraries are required to manage the three dummy datasets: MultiDataSet, Biobase and minfi. These libraries contain the required classes of objects we are dealing with: MultiDataSet, ExpressionSet, and GenomicRatioSet:

library(MultiDataSet)
library(Biobase)
library(minfi)

Three dummy datasets have been generated for creating this document. They can be downloaded from the Supplementary Material of the manuscript. The gene expression file (expression.RData) has two ExpressionSets corresponding to gene expression measured at two different time points. The methylation file (methylation.RData) contains a GenomicRatioSet, which is having information about beta values of 450K CpGs. The three datasets belong to the same experiment.

load("expression.RData")
ls()
##  [1] "brge_gexp"   "brge_gexp2"  "brge_methy"  "brge_methy2" "gSet1"
##  [6] "gSet2"       "mSet"        "multi"       "multi2"      "range"
## [11] "range2"      "samples"

The result of the command ls from the previous chunk tells us that objects containing the information are called gSet1, gSet2, and mSet. The first two are the ExpressionSets while the last one corresponds to the GenomicRatioSet. The following table shows the number of samples of each set and the number of common samples between each pair of sets:

gSet1 gSet2 mSet
gSet1 50 16 13
gSet2 - 27 10
mSet - - 20

The table should be read as:

• gSet1 has 50 samples, gSet2 has 27 samples and mSet has 20 samples
• gSet1 and gSet2 have 16 samples in common
• gSet1 and mSet have 13 samples in common
• gSet2 and mSet have 10 samples in common

The following three commands show the number of samples that each pair of objects has in common. They were used to create the previous table.

## gSet1 intersection gSet2
length(intersect(sampleNames(gSet1), sampleNames(gSet2)))
## [1] 16
## gSet1 intersection mSet
length(intersect(sampleNames(gSet1), sampleNames(mSet)))
## [1] 13
## gSet2 intersection mSet
length(intersect(sampleNames(gSet2), sampleNames(mSet)))
## [1] 10

The number of common samples along the three datasets is 6:

## gSet1 intersection gSet2 intersection mSet
length(intersect(intersect(
sampleNames(gSet1), sampleNames(gSet2)), sampleNames(mSet)))
## [1] 6

## 3.2 Packaging Data

With the three sets into the current R session, we can proceed to package them in a MultiDataSet object. There are four required steps:

1. Create an empty MultiDataSet object
2. Add the content of the first ExpressionSet
3. Add the content of the second ExpressionSet
4. Add the content of the MethylationSet

An empty MultiDataSet is created by using the function createMultiDataSet. This empty object is called md:

md <- createMultiDataSet()
md
## Object of class 'MultiDataSet'
##  . assayData: 0 elements
##  . featureData:
##  . rowRanges:
##  . phenoData:

The generic function show of MultiDataSet objects informs that md contains zero elements (see assayData section). After that, the three sets can be added.

MultiDataSet has specific functions to add each type of dataset. The function add_genexp allows adding objects of class ExpressionSet. The following code adds gSet1 to the empty MultiDataSet creating md.e.

md.e <- add_genexp(md, gSet1)
md.e
## Object of class 'MultiDataSet'
##  . assayData: 1 elements
##     . expression: 300 features, 50 samples
##  . featureData:
##     . expression: 300 rows, 11 cols (transcript_cluster_id, ..., gene_assignment)
##  . rowRanges:
##     . expression: YES
##  . phenoData:
##     . expression: 50 samples, 3 cols (age, ..., sex)

Now, md.e only contains a set of type expression. This set is tagged as expression and contains 300 features for 50 samples. Next step is to add gSet2 to the MultiDataSet.

md.e <- add_genexp(md.e, gSet2)
## Error in add_eset(object, gexpSet, dataset.type = "expression", GRanges = range, : There is already an object in this slot. Set overwrite = TRUE to overwrite the previous set.

The function add_genexp raised an error. The error indicates that a set using the slot "expression" already exists.

MultiDataSet objects can only contain a single set with the same name. By default, add_genexp uses "expression" as the name of the new expression dataset. This name was used when adding the object gSet1, and therefore, it cannot be used again when adding gSet2. To solve this, add_genexp includes the argument dataset.name to specify the name of each dataset (ExpressionSet).

md <- add_genexp(md, gSet1, dataset.name = "gSet1")
md <- add_genexp(md, gSet2, dataset.name = "gSet2")
md
## Object of class 'MultiDataSet'
##  . assayData: 2 elements
##     . expression+gSet1: 300 features, 50 samples
##     . expression+gSet2: 300 features, 27 samples
##  . featureData:
##     . expression+gSet1: 300 rows, 11 cols (transcript_cluster_id, ..., gene_assignment)
##     . expression+gSet2: 300 rows, 11 cols (transcript_cluster_id, ..., gene_assignment)
##  . rowRanges:
##     . expression+gSet1: YES
##     . expression+gSet2: YES
##  . phenoData:
##     . expression+gSet1: 50 samples, 3 cols (age, ..., sex)
##     . expression+gSet2: 27 samples, 3 cols (age, ..., sex)

The previous three lines of code depict how to add gSet1 and gSet2 to the empty MultiDataSet object called md. We observe that the resulting MultiDataSet object is containing two expression data. The show method also informs about the number of features and samples of each dataset. The names of each dataset added into the MultiDataSet object follows the following structure: the type of dataset, the character + and the name of the dataset.

Finally, the methylation data is added using the method add_methy:

md <- add_methy(md, mSet)
md
## Object of class 'MultiDataSet'
##  . assayData: 3 elements
##     . expression+gSet1: 300 features, 50 samples
##     . expression+gSet2: 300 features, 27 samples
##     . methylation: 300 features, 20 samples
##  . featureData:
##     . expression+gSet1: 300 rows, 11 cols (transcript_cluster_id, ..., gene_assignment)
##     . expression+gSet2: 300 rows, 11 cols (transcript_cluster_id, ..., gene_assignment)
##     . methylation: 300 rows, 19 cols (seqnames, ..., Regulatory_Feature_Group)
##  . rowRanges:
##     . expression+gSet1: YES
##     . expression+gSet2: YES
##     . methylation: YES
##  . phenoData:
##     . expression+gSet1: 50 samples, 3 cols (age, ..., sex)
##     . expression+gSet2: 27 samples, 3 cols (age, ..., sex)
##     . methylation: 20 samples, 10 cols (age, ..., Neu)

The final MultiDataSet object md encapsulates three datasets. This can be checked with the general functions length and names:

length(md)
## [1] 3
names(md)
## [1] "expression+gSet1" "expression+gSet2" "methylation"

## 3.3 Integrative Analysis

Once the MultiDataSet object has been created, we can use it in other packages that have been designed to perform integration analyses. The vast majority of existing R/Bioconductor packages that have been developed for this purpose assumes that the different tables contain the same individuals (i.e. complete cases). This is the case of omicade4 method. Here, we illustrate how to easily obtain complete cases having a MultiDataSet object as input.

### 3.3.1 Interacting with omicade4

omicade4 provides functions for multiple co-inertia analysis as well as for data visualization that will help the interpretation when integrating several omic datasets.

omicade4 can be loaded by executing:

library(omicade4)

The function mcia was designed to perform multiple co-inertia analysis. It requires a list having the three omic datasets as each component. Herein, we start by illustrating how to perform this analysis in the case of using original ExpressionSet and MethylatioSet objects. That is, in the case of not using a MultiDataSet. By doing that we will illustrate how having a proper way of encapsulating multi-omic data may help downstream analyses.

The function assayDataElement can be used to retrieve the matrix having gene expression or methylation levels from an ExpressionSet or MethylationSet, respectively. Therefore, the required list to be passed through mcia function can be obtained by executing:

dat <- list(
assayDataElement(gSet1, "exprs"),
assayDataElement(gSet2, "exprs"),
assay(mSet, "Beta")
)

Then, this list is used to perform multiple coinertia analysis

fit <- mcia(dat)
## Error in mcia(dat): Nonequal number of individual across data.frames

However, an error message is obtained. The error is caused because the matrices have a different number of samples (columns). That is, there are samples not present in all datasets. This could be overcome by writing some code to get tables having the same samples in each matrix. This can be easily addressed by using a MultiDataSet object as input because the function commonSamples performs the selection of complete cases.

The following code creates a new MultiDataSet with common samples

md.r <- commonSamples(md)

We can verify that the three datasets are having the same samples by executing:

lapply(as.list(md.r), dim)
## $expression+gSet1 ## [1] 300 6 ## ##$expression+gSet2
## [1] 300   6
##
## $methylation ## [1] 300 6 The object md.r can be passed through mcia as a list to perform multiple co-inertia analysis. fit <- mcia(as.list(md.r)) fit contains the output of mcia function. For more information about mcia and the content of fit type ?omicade4::mcia in the R session. To make this process easier to the user, MultiDataSet includes a wrapper to apply mcia to a MultiDataSet object: fit <- w_mcia(md) fit ##$call
##
## $mcoa ## Multiple Co-inertia Analysis ## list of class mcoa ## ##$pseudoeig: 6 pseudo eigen values
## 1.03 0.6364 0.4806 0.4134 0.403 ...
##
## $call: mcoa2(X = ktcoa, scannf = FALSE, nf = cia.nf) ## ##$nf: 2 axis saved
##
##    data.frame nrow ncol content
## 1  $SynVar 6 2 synthetic scores ## 2$axis      900  2    co-inertia axis
## 3  $Tli 18 2 co-inertia coordinates ## 4$Tl1       18   2    co-inertia normed scores
## 5  $Tax 12 2 inertia axes onto co-inertia axis ## 6$Tco       900  2    columns onto synthetic scores
## 7  $TL 18 2 factors for Tli Tl1 ## 8$TC        900  2    factors for Tco
## 9  $T4 12 2 factors for Tax ## 10$lambda    3    2    eigen values (separate analysis)
## 11 $cov2 3 2 pseudo eigen values (synthetic analysis) ## other elements: Tlw Tcw blo Tc1 RV ## ##$coa
## $coa$expression+gSet1
## Duality diagramm
## class: nsc dudi
## $call: FUN(df = X[[i]], scannf = FALSE, nf = ..2) ## ##$nf: 2 axis-components saved
## $rank: 5 ## eigen values: 0.001339 0.0008261 0.0006457 0.0004673 0.0003958 ## vector length mode content ## 1$cw    6      numeric column weights
## 2 $lw 300 numeric row weights ## 3$eig   5      numeric eigen values
##
##   data.frame nrow ncol content
## 1 $tab 300 6 modified array ## 2$li        300  2    row coordinates
## 3 $l1 300 2 row normed scores ## 4$co        6    2    column coordinates
## 5 $c1 6 2 column normed scores ## other elements: N ## ##$coa$expression+gSet2 ## Duality diagramm ## class: nsc dudi ##$call: FUN(df = X[[i]], scannf = FALSE, nf = ..2)
##
## $nf: 2 axis-components saved ##$rank: 5
## eigen values: 0.001051 0.0007264 0.0006114 0.0005047 0.0004428
##   vector length mode    content
## 1 $cw 6 numeric column weights ## 2$lw    300    numeric row weights
## 3 $eig 5 numeric eigen values ## ## data.frame nrow ncol content ## 1$tab       300  6    modified array
## 2 $li 300 2 row coordinates ## 3$l1        300  2    row normed scores
## 4 $co 6 2 column coordinates ## 5$c1        6    2    column normed scores
## other elements: N
##
## $coa$methylation
## Duality diagramm
## class: nsc dudi
## $call: FUN(df = X[[i]], scannf = FALSE, nf = ..2) ## ##$nf: 2 axis-components saved
## $rank: 5 ## eigen values: 0.002201 0.00128 0.0009001 0.0006561 0.0006023 ## vector length mode content ## 1$cw    6      numeric column weights
## 2 $lw 300 numeric row weights ## 3$eig   5      numeric eigen values
##
##   data.frame nrow ncol content
## 1 $tab 300 6 modified array ## 2$li        300  2    row coordinates
## 3 $l1 300 2 row normed scores ## 4$co        6    2    column coordinates
## 5 \$c1        6    2    column normed scores
## other elements: N
##
##
## attr(,"class")
## [1] "mcia"

### 3.3.2 Interacting with iClusterPlus

iClusterPlus was developed for integrative clustering analysis of multi-type genomic data. Hence, MultiDataSet is the perfect candidate to be established as the default type of input type.

To start the analysis iClusterPlus needs to be loaded:

library(iClusterPlus)

The typical call to iClusterPlus, using our three datasets, should be:

fit <- iClusterPlus(
dt1 = assayDataElement(gSet1, "exprs"),
dt2 = assayDataElement(gSet2, "exprs"),
dt3 = assay(mSet, "Beta"),
type = c("gaussian", "gaussian", "gaussian"),
lambda = c(0.04,0.61,0.90),
K = 3,
maxiter = 10
)

We refer the reader to the help of iClusterPlus and to the manual entitled “iClusterPlus: integrative clustering of multiple genomic data sets” for more information about the arguments lambda, K and maxiter. This document will only shortly cover dt* and type arguments.

In this case, the package can deal with tables having a different number of samples. To make the call to iClusterPlus function easier for the user, MultiDataSet includes a wrapper to apply iClusterPlus to a MultiDataSet object. This method automatically creates the argument type required by iClusterPlus. This argument is created by taking into account the type of datasets included in MultiDataSet object. In particular:

• The type assigned to ExpressionSet is gaussian
• The type assigned to MethylationSet is gaussian
• The type assigned to SnpSet is multinomial

The other arguments accepted by iClusterPlus can be given to the function through the wrapper:

fit <- w_iclusterplus(
md,
lambda = c(0.04,0.61,0.90),
K = 3,
maxiter = 10
)

The obtained result is homologous to the previous version of iClusterPlus call. Both of them can be plotted as suggested in iClusterPlus’s vignette.

library(lattice) # Required for iClusterPlus's plotHeatmap
library(gplots) # Required to generate the colour-schemes

col.scheme <- alist()
col.scheme[[1]] <- bluered(256) # colours for gSet1
col.scheme[[2]] <- bluered(256) # colours for gSet2
col.scheme[[3]] <- greenred(256) # colours for mSet

plotHeatmap(fit=fit,datasets=lapply(as.list(commonSamples(md)), t),
type=c("gaussian","gaussian","gaussian"), col.scheme = col.scheme,
row.order=c(TRUE,TRUE,TRUE),sparse=c(TRUE,FALSE,TRUE),cap=c(FALSE,FALSE,FALSE)
)

In this case, the first two rectangles correspond to the two ExpressionSets while the last rectangle to the GenomicRatioSet.

# 4 Summary and Conclusion

This document aimed to illustrate how MultiDataSet can be used jointly with third party R/Bioconductor packages implementing methods for data analysis and integration. The first part of the document describes how to create MultiDataSet objects and how the functions add_genexp and add_methy are used to add gene expression and methylation data. The second part deals with the use of MultiDataSet objects and the use of mcia function of omicade4 and iClusterPlus.

The current version of MultiDataSet supports two downstream analyses: iCluster (by Shen 2009) implemented in iClusterPlus R package and multiple co-inertia analysis (by Bady 2004) implemented in omicade4. The appendix of the document includes the code we wrote for developing the wrappers for mcia and iClusterPlus (also included in MultiDataSet R package). As can be seen, the code takes profit of MultiDataSet features and it is very easy to understand. We are working on developing more wrappers for integrative and data analysis that will be incorporated in future versions of MultiDataSet.

# 5 Appendix: Wrappers

## 5.1 Wrapper for omicade4

The following is the definition of the wrapper include in MultiDataSet for omicade4’s function mcia. It follows the steps explained in the main document.

setMethod(
f = "w_mcia",
signature = "MultiDataSet",
definition = function(object, ...) {
# Obtain the common samples between datasets
object <- commonSamples(object)

# Call mcia with the generated arguments and the user's arguments
}
)

## 5.2 Wrapper for iClusterPlus

The following is the code written to create the wrapper for iClusterPlus, that allows using a MultiDataSet object as input. The method has three parts:

1. It used the function commonSamples to reduce the amount of samples included in each dataset to the common samples along the datasets. This is a way to speed-up iClusterPlus. The argument commonSamples, by default set to TRUE, allows changing this feature.
2. It creates the argument type requested by iClusterPlus by using the name of each dataset. Here we consider that gene expression as gaussian, methylation as gaussian and snps as multinomial.
3. Apply iCluserPlus by accepting other argument saved into ...
setMethod(
f = "w_iclusterplus",
signature = "MultiDataSet",
definition = function(object, commonSamples=TRUE, ...) {
if(length(object) > 4) {
stop("'iClusterPlus' only allows four datasets.")
}

# Obtain the common samples between datasets
if(commonSamples) {
object <- commonSamples(object)
}

# Put the names iClusterPlus requires on the datasets
datasets <- lapply(as.list(object), t)
names(datasets) <- paste("dt", 1:length(datasets), sep="")

# Generate the "type" argument for iClusterPlus
datasets[["type"]] <- sapply(names(object), function(nm) {
ifelse(startsWith(nm, "expression"), "gaussian",
ifelse(startsWith(nm, "methylation"), "gaussian", "multinomial"))
})
names(datasets[["type"]]) <- paste("dt", 1:(length(datasets) -1), sep="")

# Call iClusterPlus with the generated arguments and the user's arguments
do.call("iClusterPlus", c(datasets, list(...)))
}
)