1.1 Background:

OMICsPCA is a statistical framework designed to integrate and analyse multiple types of heterogeneous assays, factors, data types or modalities (e.g. ChIP-seq, RNA-seq) from different samples or sources ( e.g. multiple cell lines, time points etc.). Biological processes in eukaryotes are complicated molecular interactions, spanned over multiple layers of regulation. In order to understand the collective effects of the interactions of biological processes, they should be studied parallelly. High throughput sequencing has enabled genome-wide assays across several disease conditions, cell types, time points etc. at a much faster rate. On the other hand, replicated experiments on diverse samples (e.g. various cell lines) help us to understand the origin of variation (e.g. the genes, TSSs, exons etc) observed between the samples. Therefore, integrative multi-omics studies on heterogeneous samples are gaining their importance every day. As a consequence, a huge number of datasets are being produced and stored in public databases, allowing researchers to perform integrative analysis of multiple data modalities.

Unfortunately, most of such studies are limited to very few samples(e.g. cell lines) or data modalities (e.g. various ChIP-seq assays) due to the huge cost, ethical issues, and scarcity of samples associated with the entire experimental process. And, most of the data integration methods rely on the condition of homogeneity of samples, i.e. the samples corresponding to each modality should be the same. As a result, integrative analysis on publicly available data sets is very much rare and extremely restricted to very few numbers of samples or modalities (or both).  

1.2 Illustration of the problem with example

Let’s illustrate the problem with an example. Suppose our objective is to decipher the collective effect of CpG methylation and H3k4me3 histone modification on the gene expression, followed by clustering of the similar genes on the basis of the consolidated effect of these 2 data modalities. Consider we have the following datasets:  

1. CpG methylation on 5 Cell lines A, B, C, D, and E  

2. H3k4me3 histone modification on 10 Cell lines A,D,E,I,K,Q,P,Z,W and G.

Here, we can not calculate the collective effect directly, since the cell lines and the number of cell lines are different in the two experiments.  

1.3 Previous approaches/frameworks towards multi-omics data integration

Several data integration frameworks have been designed over the past few years to overcome such difficulty. For example, Huang (1) proposed a regression-based joint modeling approach to integrate SNPs, DNA methylation, and gene expression; He et al. (2)developed a pattern matching method to integrated eQTL and GWAS data; Xiong et al. (3) developed a statistical framework to associate SNP and gene expression information etc. All such applications are designed to perform in a supervised manner, i.e. the integrated data modalities must be associated with labelled classes (e.g. disease and control class; pathway 1 and pathway 2 etc.). Such constraints impose a limitation on the algorithms to be used in varieties of applications (e.g., can’t be used in clustering). In contrast, Ha, et al. (4) developed an unsupervised Gaussian process model for qualitative (logical combination of binary values, e.g. 0/1 or TRUE/FALSE) integration of a large number of epigenetic factors and applied it to describe cell lineage-specific gene regulatory programs. Although this overcomes the limitation of class association to some extent, this process is only sufficient for the applications where qualitative integration is sufficient.

As mentioned earlier, there is another important application of data integration, which is associated with the disentanglement of the source of variation observed between the samples or the individuals. A common strategy used in such studies is to perform a large number of association tests between the features and the data modalities (5, 6). Alternatively, kernel or graph-based methods are also considered as methods of integration and the integrated data is then used to build common similarity networks between samples (7, 8). Although effective in accomplishing specific tasks, such approaches lack proper interpretability (9) and do not suffice to explain many other relevant queries applicable to integrated omics data. Such queries include identification of variably controlled genes, genes sharing similar epigenomic state across various samples and many more.  

1.4 OMICsPCA

OMICsPCA is a multipurpose tool designed to overcome the difficulties associated with both the applications of data integration. It is designed to identify the source of variation among the samples/variables (the columns of a table, e.g. cell lines, patients etc.) or individuals (the rows of a table, e.g. genes, exons etc.) associated with each data modality (i.e. the tables, e.g. CpG_methylation, ChIP-seq on a protein etc.). It guides the user through various analyses to decide on similar samples/variables (e.g.Cell lines). This is followed by selecting the data modalities (e.g. the assays) that can be included or excluded leading to data integration. The selected data modalities can be further integrated and analysed and the data points or individuals (e.g. genes, TSSs, exons) may be clustered on the basis of the integrated data coming from single or multiple modalities.

In short, OMICsPCA can be used in clustering genes, TSSs, exons on the basis of multiple types of heterogeneous experimental or theoretical data or vice-versa. Such kind of multivariate analyses is useful in identification of similar cell lines or assays prior to the integration process. In this vignette, we show an example of the entire analysis process done on human transcription start sites.  

3.1 Preparation of data

OMICsPCA has an inbuilt function prepare_dataset() that aggregates the samples (e.g. cell lines) of each data modality (e.g. a histone modification ChIP-seq assay) corresponding to each feature of the genome (notably gene, TSS, exon etc.) and returns a dataframe.

The rows of this dataframe object contain the features (e.g. genes) and each column contains the values corresponding to a sample (e.g. Cell line).

The arguments taken by this function is described below:

1. factdir: full path of the directory containing files corresponding to various cell lines in .bed format. This directory should contain only the files of the same assay (modality) (e.g. H3k9ac) from different samples (e.g. cell lines).

2. annofile: full path of the file containing the annotation file (e.g exons, TSSs, genes etc) in .bed format.

3. annolist: name of full set or subset of the entries in the annotation file. The .bed files should have at least 4 columns. The first column is the chromosome name, the second and third is the start and end position of the feature (e.g. a gene or a ChIP-seq peak etc). The fourth column contains the value of the described feature (e.g. expression of a gene, the ChIP-seq intensity of a peak or name of a gene etc.).

The .bed files should have at least 4 columns. The first column is the chromosome name, the second and third is the start and end of the feature (e.g. a gene or a ChIP-seq peak etc) accordingly and the fourth column contains the value (e.g. expression of a gene, ChIP-seq intensity of a peak or name of a gene etc.).

Some examples of the input file formats are given below:  

Here we show the use of prpareDataset() by integrating demo peaks (.bed format) from 2 files into a data frame named. The example data sets are packaged inside the OMICsPCAdata package  

anno <- system.file("extdata/annotation2/TSS_groups.bed",
                    package = "OMICsPCAdata")

list <- system.file("extdata/annotation2/TSS_list",
                    package = "OMICsPCAdata")

fact <- system.file("extdata/factors2/demofactor",
                    package = "OMICsPCAdata")


list.files(path = fact)
# [1] "Cell1.bed" "Cell2.bed"

prepare_dataset() will combine these 2 bed files into a dataframe. The rows of the dataframe will correspond to the entries in file entered through the variable named list and the columns will correspond to the 2 files shown above.  

all_cells <- prepare_dataset(factdir = fact,
annofile = anno, annolist = list)
# [1] "Running intersect... This may take some time"
# [1] "Merging cell lines... This may take some time"
# [1] "Total time taken is: 0.87473464012146"
# [1] "time taken to run intersect() is: 0.8532555103302"
# [1] "time taken to run merge_cells() is: 0.0214791297912598"

head(all_cells[c(1,14,15,16,20),])
# # A tibble: 5 x 2
#   Cell1.bed Cell2.bed
#       <dbl>     <dbl>
# 1      0         0   
# 2      3.67      0   
# 3      0         1.86
# 4      0         0   
# 5      4.29      0

For a different assay type repeat the process:  

factor_x  <- prepare_dataset(factdir = fact,
                            annofile = anno, annolist = list)

# where `fact` is the directory of the samples corresponding to factor_x

For example,

fact <- system.file("path to cpg")
cpg <- prepare_dataset(factdir = fact, annofile=anno, annolist = list)

3.2 Reading data

OMICsPCA is designed to read various assays done on various cell lines into an MultiAssayExperiment class object and then run various analyses on this object.  

library(MultiAssayExperiment)

datalist <- data(package = "OMICsPCAdata")
datanames <- datalist$results[,3]
data(list = datanames)

assaylist <- list("demofactor"  = all_cells)

demoMultiAssay <- MultiAssayExperiment(experiments = assaylist)
# ExperimentList contains data.frame or DataFrame,
#   potential for errors with mixed data types
# ExperimentList contains data.frame or DataFrame,
#   potential for errors with mixed data types

For ease of analysis, we compiled some preloaded data into an MultiAssayExperiment object named multi_assay.

3.3 Subsetting into groups

Once the dataframes corresponding to the assays/modalities is prepared and stored in the “MultiAssayExperiment” object“, the user may want to divide the entire annotation set into smaller groups. Here we show an example to divide 28770 GENCODE TSS groups into 4 expression groups. The grouping criteria are based on the on/off status (determined from CAGE experiments) of the TSSs in 31 cell lines.

OMICsPCA has a function create_group() to do this task. This function takes the following 4 arguments:

1. group_names : a vector containing the user-defined names of the groups to be created

2. factor : name of the data frame on which groups will be created

3. comparison : a vector of comparison symbols such as >, <, ==, >=, <=, %in% etc

4. condition : a vector of conditions corresponding to comparison. condition should be a vector or range of digits (e.g. c(1,3,7,9). or 1:5) if %in% is chosen as comparison and a single digit for other cases.

5. name : name of the MultiAssayExperiment object containing the assay data

6. grouping_factor : name of the assay/modality on which grouping will be done  

groupinfo <- create_group(name = multi_assay, group_names = c("WE" ,
"RE" ,"NE" ,"IntE"),
grouping_factor = "CAGE",
comparison = c(">=" ,"%in%" ,"==" ,"%in%"),
condition = c("25" ,"1:5" ,"0" ,"6:24"))

In the above example the dataframe CAGE is divided into 4 smaller data frames e.g; WE, RE, NE and IntE. “WE” contains TSSs expressed in >= 25 cell lines, “RE” represents TSSs expressed in 1 to 5 cell lines and so on.

The CAGE data frame looks like this:  

The groupinfo object is accessd by subsequent functions. So this object has to be present in the global environment to run other functions. If the user do not wish to divide the datasets into groups or if the user has predefined groups, then this information may be read directly from a file or object having this information. We compiled a predefined group format in a dataframe groupinfo_ext and compiled it in OMICsPCAdata.  

3.4 Exploratory data analysis (EDA) on created groups

Once the group information is read, we can study the the distribution of various Assays/factors(e.g. H2az, H3k9ac etc) on the annotations (e.g. TSSs, genes) of various groups (In the above example, the groups are created on the basis of on-off state of TSSs in 31 cell lines). OMICsPCA has several functions for EDA.  

descriptor(name = multi_assay,
factors = c(
"H2az",
"H3k4me1","H3k9ac"),
groups = c("WE","RE"),
choice = 1,
title = "Distribution of percentage of cell types overlapping
with various factors",
groupinfo = groupinfo)

descriptor(name = multi_assay,
factors = c("H2az",
"H3k4me1","H3k9ac"),
groups = c("WE","RE"),
choice = 2,
choice2group = "WE",
title = "Distribution of percentage of cell types overlapping with
a factor in various combinations of epigenetic marks in the
selected group",
groupinfo = groupinfo)

groups <- c("WE")
chart_correlation(name = multi_assay, Assay = "H2az",
groups = "WE", choice = "scatter", groupinfo = groupinfo)

chart_correlation(name = multi_assay,
Assay = "H2az",
groups = "WE", choice = "table",
groupinfo = groupinfo)
#           Gm12878     Hepg2      Hsmm      K562   Osteobl
# Gm12878 1.0000000 0.4631833 0.5542564 0.5637424 0.5693692
# Hepg2   0.4631833 1.0000000 0.4421005 0.4324214 0.4609538
# Hsmm    0.5542564 0.4421005 1.0000000 0.5003985 0.6742468
# K562    0.5637424 0.4324214 0.5003985 1.0000000 0.5058489
# Osteobl 0.5693692 0.4609538 0.6742468 0.5058489 1.0000000

chart_correlation(name = multi_assay, Assay = "H2az",
groups = "WE", choice = "hist", bins = 10,
groupinfo = groupinfo)

chart_correlation(name = multi_assay, Assay = "H2az",
groups = "WE", choice = "all",
groupinfo = groupinfo)

3.5 Integration of Multiple Cell lines

If an assay (e.g. ChIP-seq for the histone modification of type H3k9ac) is done on multiple cells/conditions/treatment/time, it might be, sometimes, necessary to integrate or combine them, in order to understand the source of variation or to calculate a common metric to be served as the representative of all variables etc. Such a combination may be done by several techniques like Principal Component Analysis (PCA) or Factor Analysis (FA). OMICsPCA has a function integrate_variables() to integrate data from multiple cells or conditions using PCA.

integrate_variables() takes 3 mandatory inputs:

1. Assays: name of the assays read in the MultiAssayExperiment object

2. name: name of the MultiAssayExperiment object containing the assays to be integrated.

3. groups: a full set or subset of groups present in groupinfo object. The group names should be provided as a vector string. e.g. c(“WE” ,“RE”)

integrate_variables() runs PCA on the assays/data modalities supplied through the Assays argument.This function is a wrapper around the function PCA() from package FactoMineR and thus can take additional arguments specific to the function PCA()

In this example, we supply two more additional arguments scale.unit = FALSE and graph = FALSE

This function returns a list containing the PCA results.  

PCAlist <- integrate_variables(Assays = c("H2az","H3k4me1",
"H3k9ac"), name = multi_assay,
groups = c("WE","RE", "NE", "IntE"), groupinfo = groupinfo,
scale.unit = FALSE, graph = FALSE)

3.6 Analysis of integrated data

The analyse_vaiables() function is designed for a quick analysis and visualization of the data integrated by integrate_variables() function. It takes 3 compulsory arguments 1) name, 2) Assay and 3) choice. The type of analysis should be selected through the choice argument. This function acts as a wrapper around a collection of functions of package “factoextra” and “corrplot” and thus can take additional arguments specific and non-conflicting to such functions. Types of analysis and their corresponding input in choice are listed below:  

Note: PC argument is mandatory for choice 4 and 5. (PC = principal component)

Note: User may use the functions listed below directly to supply more graphical parameters (e.g. ncp in choice 1, i.e. in fviz_eig, to restrict the display of the number of dimensions or use select.var in choice 2 to select columns/variables/cell lines satisfying some condition.). use ? followed by the function name listed in the above table to explore more options available for each choice of “analyse_variables()”.  

Here are some examples of different choices:  

analyse_variables(name = PCAlist, Assay = "H2az", choice = 1,
title = "variance barplot", addlabels = TRUE)

#       eigenvalue variance.percent cumulative.variance.percent
# Dim.1  35.779393        83.305644                    83.30564
# Dim.2   2.639572         6.145752                    89.45140
# Dim.3   1.787209         4.161183                    93.61258
# Dim.4   1.541631         3.589401                    97.20198
# Dim.5   1.201736         2.798019                   100.00000

analyse_variables(name = PCAlist, Assay = "H3k4me1",choice = 2,
title = "Loadings of cell lines on PC1 and PC2", xlab = "PCs")

#              Dim.1       Dim.2       Dim.3      Dim.4      Dim.5
# Gm12878  1.6122501  0.07547622  0.36835090  2.4284811 51.4717421
# H1hesc   1.5266506  0.02547903  0.53455825  1.4913785  2.6823855
# Hmec    16.1611363  0.30279710 33.70752633  3.2831916  1.6894946
# Hsmm     3.6874185  2.15453027  0.07828379 11.7724181  2.1749222
# Hsmmt    3.4691140  2.28192948  0.18369298 16.9958418  3.6659963
# Huvec   10.4436967  1.41658682 16.19028015 50.5689254 12.8392675
# K562    17.2569846 78.93580791  1.00403525  0.6481982  0.2682735
# Nha     13.8628626  2.33736031  2.44025845  0.5796352  0.5178672
# Nhek    11.5221725  3.09780299 26.27831808  2.4563523  0.6874715
# Nhlf     3.5818397  1.45169741  0.35898153  5.3904567  0.7152927
# Osteobl 16.3047489  7.85274807 18.54098951  2.3396086 21.6769279
# Nt2d1    0.5711254  0.06778439  0.31472477  2.0455125  1.6103591
#                Dim.6        Dim.7       Dim.8       Dim.9       Dim.10
# Gm12878 40.315062978  0.106080569  2.80435698  0.60963169 2.014637e-01
# H1hesc   0.828927010 23.530092377 27.87809070 23.00036062 3.597760e+00
# Hmec     0.483017979  5.251661572 31.11659053  7.94529318 4.828593e-02
# Hsmm     8.809164528  4.696128343  0.63685688  0.00421789 1.969276e+00
# Hsmmt   15.751292720 11.527108397  1.81117415  0.63102455 2.294400e+01
# Huvec    5.489527201  1.419317375  0.02773966  1.51420176 4.444542e-02
# K562     0.008995178  1.549245247  0.03621791  0.18588650 1.631878e-04
# Nha      1.463454402 31.030361269  0.02063827 44.27677390 2.799019e+00
# Nhek     1.943600174 17.543335233 29.75569789  6.61326787 7.677415e-02
# Nhlf     1.776931840  0.004438558  0.06598961  0.17687757 6.421933e+01
# Osteobl 22.348353163  0.948431674  0.02381584  9.53974191 2.355337e-01
# Nt2d1    0.781672826  2.393799388  5.82283157  5.50272257 3.863944e+00
#               Dim.11       Dim.12
# Gm12878  0.005936925 1.166628e-03
# H1hesc  14.559723336 3.445938e-01
# Hmec     0.001014659 9.990303e-03
# Hsmm     0.089383167 6.392740e+01
# Hsmmt    0.002172222 2.073665e+01
# Huvec    0.044402812 1.609120e-03
# K562     0.103230182 2.962405e-03
# Nha      0.670878054 8.912644e-04
# Nhek     0.005607470 1.959976e-02
# Nhlf     7.761651267 1.449651e+01
# Osteobl  0.175006347 1.409443e-02
# Nt2d1   76.580993559 4.445297e-01

analyse_variables(name = PCAlist, Assay = "H2az",
choice = 3,title = "Correlation matrix", xlab = "PCs")

#             Dim.1       Dim.2       Dim.3       Dim.4         Dim.5
# Gm12878 0.9257715  0.09106662  0.01566028 -0.35624071 -0.0866104415
# Hepg2   0.7485728  0.08655067  0.64588121  0.09860930  0.0725360565
# Hsmm    0.9401016 -0.18374599 -0.08173410 -0.01104782  0.2750341646
# K562    0.8968137  0.39775752 -0.11549647  0.15548198 -0.0001868809
# Osteobl 0.9418103 -0.25031371 -0.02302760  0.12489507 -0.1849523974

analyse_variables(name = PCAlist, Assay = "H2az",
choice = 4,PC = 1,
title = "Squarred loadings of Cell lines on PC1")
#             Dim.1       Dim.2        Dim.3        Dim.4        Dim.5
# Gm12878 0.8570528 0.008293130 0.0002452444 0.1269074424 7.501369e-03
# Hepg2   0.5603612 0.007491018 0.4171625418 0.0097237942 5.261479e-03
# Hsmm    0.8837911 0.033762589 0.0066804629 0.0001220544 7.564379e-02
# K562    0.8042748 0.158211041 0.0133394357 0.0241746449 3.492447e-08
# Osteobl 0.8870066 0.062656956 0.0005302702 0.0155987778 3.420739e-02

analyse_variables(name = PCAlist, Assay = "H2az",
choice = 5,PC=1,
title = "Contribution of Cell lines on PC1")

#             Dim.1     Dim.2      Dim.3       Dim.4        Dim.5
# Gm12878 20.686358  2.713278  0.1185040 71.09121587 5.390644e+00
# Hepg2    5.964017  1.080715 88.8860882  2.40192278 1.667257e+00
# Hsmm    23.693083 12.268941  3.5853877  0.07594124 6.037665e+01
# K562    21.294342 56.780069  7.0705762 14.85498595 2.753045e-05
# Osteobl 28.362200 27.156997  0.3394438 11.57593416 3.256542e+01

analyse_variables(name = PCAlist,
Assay = c("H3k9ac","H2az",
"H3k4me1"), choice = 6)
# Using PC as id variables

3.7 Analysis of individuals/annotations from integrated data

We can take the projection of each TSS on the principal components and plot them on the space of PCs.  

analyse_individuals(name = PCAlist,
Assay = "H3k9ac", groupinfo = groupinfo,
choice = 1, PC = c(1,2))

# selecting top 40 TSS groups according to their contribution on
# PC 1 and PC 2 using the argument "select.ind"

selected <- analyse_individuals(name = PCAlist,
Assay = "H3k4me1",
choice = 1, PC = c(1,2),
select.ind = list(contrib = 100),
groupinfo = groupinfo)

# plot selected individuals
plot(selected)

# extracted information of the selected individuals
head(selected$data)
# # A tibble: 6 x 7
#   name                  x     y coord  cos2 contrib Col. 
#   <fct>             <dbl> <dbl> <dbl> <dbl>   <dbl> <fct>
# 1 ENST00000419582.1  21.4  2.99  469. 0.835  0.0127 NE   
# 2 ENST00000432651.1  21.4  2.99  469. 0.835  0.0127 NE   
# 3 ENST00000435132.1  21.4  2.99  469. 0.835  0.0127 RE   
# 4 ENST00000434095.1  21.4  2.99  469. 0.835  0.0127 IntE 
# 5 ENST00000423100.1  20.8  2.87  443. 0.844  0.0120 RE   
# 6 ENST00000524946.2  20.8  2.87  443. 0.844  0.0120 IntE

# The TSSs used in this example (each row) are obtained by combining
# many neighboring TSSs together. The combinations should be uncombined
# to find the corresponding annotations.

names  <- gsub(";",",",paste(as.character(selected$data$name),
                             collapse = ","))

names <- as.vector(strsplit(names, ",", fixed = TRUE)[[1]])

## The top 100 combined TSS_groups actually come from 115 TSSs

length(names)
# [1] 115

# retrieve details of top 100 individuals
# transcript details contains the GENCODE v 17
# annotation of TSSs.

details <- transcript_details[
transcript_details$transcript_id %in% names,,drop = FALSE]

head(details)
# # A tibble: 6 x 8
#   gene_id transcript_id gene_type gene_status gene_name transcript_type
#   <fct>   <fct>         <fct>     <fct>       <fct>     <fct>          
# 1 ENSG00… ENST00000494… protein_… KNOWN       ZBTB17    processed_tran…
# 2 ENSG00… ENST00000480… protein_… KNOWN       EPHA2     processed_tran…
# 3 ENSG00… ENST00000270… protein_… KNOWN       SH3BGRL3  protein_coding 
# 4 ENSG00… ENST00000472… protein_… KNOWN       ZC3H12A   retained_intron
# 5 ENSG00… ENST00000483… protein_… KNOWN       FHL3      processed_tran…
# 6 ENSG00… ENST00000339… protein_… NOVEL       TCTEX1D4  protein_coding 
# # … with 2 more variables: transcript_status <fct>, transcript_name <fct>

## checking the gene type

table(details$gene_type)
# 
# 3prime_overlapping_ncrna                antisense                IG_C_gene 
#                        0                        7                        0 
#          IG_C_pseudogene                IG_D_gene                IG_J_gene 
#                        0                        0                        0 
#          IG_J_pseudogene                IG_V_gene          IG_V_pseudogene 
#                        0                        0                        0 
#                  lincRNA                    miRNA                 misc_RNA 
#                        4                        2                        0 
#                  Mt_rRNA                  Mt_tRNA   polymorphic_pseudogene 
#                        0                        0                        0 
#     processed_transcript           protein_coding               pseudogene 
#                        4                       97                        1 
#                     rRNA           sense_intronic        sense_overlapping 
#                        0                        0                        0 
#                   snoRNA                    snRNA                TR_C_gene 
#                        0                        0                        0 
#                TR_D_gene                TR_J_gene          TR_J_pseudogene 
#                        0                        0                        0 
#                TR_V_gene          TR_V_pseudogene 
#                        0                        0

# find GO annotation 

library(clusterProfiler)
library(org.Hs.eg.db)

gene <- details$gene_name

gene.df <- bitr(gene, fromType = "SYMBOL",
                toType = c("ENSEMBL", "ENTREZID"),
                OrgDb = org.Hs.eg.db)

ggo <- groupGO(gene     = unique(gene.df$ENTREZID),
               OrgDb    = org.Hs.eg.db,
               ont      = "MF",
               level    = 5,
               readable = TRUE)

# If we want to see the top results, we need to reorder
#the list. So, the following line is strictly optional.

#ggo@result <- ggo@result[order(-ggo@result$Count),]
#head(ggo@result)


# The barplot may not fit to the Rstudio window, therefore
# we may plot it in a different window

#grDevices::windows()
#barplot(ggo, drop=TRUE, showCategory=20)

analyse_individuals(name = PCAlist, Assay = "H3k9ac",
choice = 2, PC = c(1,2,3),
col = c("RED", "BLACK"), groupinfo = groupinfo)

3.8 Density analysis

The scatter plot of data points (here, rows/TSSs/individuals) may be highly disorganized. In such a situation, we may take the help of density functions to understand the overall structure of the dataset.  

Once the cell lines of an assay are integrated into PCs, we may check the density distribution of scores on various principal components. OMICsPCA has a function plot_desnity() to calculate and plot the density distribution of PC scores. This function uses ggplot(), geom_density() and other additional functions from package ggplot2. Additional arguments of geom_density (e.g. adjust) may be also supplied through this function. The returned value is a “gg,ggplot” object.

Such kind of analysis may help us to choose factors (e.g. H2az, H3k4me1) that can discriminate between various groups (e.g. our expression groups “WE”, “RE”, “NE” and “IntE”).

NOTE : the groups argument should not contain a value that is not used in integrate_variables.  

#head(groupinfo)
densityplot <- plot_density(name = PCAlist,
Assay = "H2az", groupinfo = groupinfo,
PC = 1, groups = c("WE","RE","IntE"),
adjust = 1)

library(ggplot2)
library(graphics)

densityplot <- densityplot+xlim(as.numeric(c("-8", "23")))
densityplot

densityplot <- plot_density(name = PCAlist, Assay = "H3k4me1",
PC = 1, groups = c("WE" ,"RE"), adjust = 2,
groupinfo = groupinfo)

densityplot <- densityplot+xlim(as.numeric(c("-8", "15")))

print(densityplot)
# Warning: Removed 163 rows containing non-finite values (stat_density).

plot_density_3D(name = PCAlist, Assay = "H2az",
group = "WE", PC1 = 1,PC2 = 2, grid_size = 100,
groupinfo = groupinfo,
static = FALSE)

plot_density_3D(name = PCAlist, Assay = "H2az", group = "WE",
groupinfo = groupinfo,
PC1 = 1,PC2 = 2, grid_size = 100, static = TRUE, theta = -50,
phi = 40, box = TRUE, shade = 0.1, ticktype = "detailed", d = 10)
# Warning in persp.default(x = bivn.kde, col = col1, xlab = labx, ylab =
# laby, : "grid_size" is not a graphical parameter

3.9 Integration of multiple assays/ modalities

Once the discriminatory Assays between the groups are identified by previous analyses, we may integrate all such assays together.  

Assays = c("H2az", "H3k9ac")

In this process it is possible to observe that some variables (Cell lines) are not similar to others and thus can be excluded :  

exclude <- list(0,c(1,9))

The length of the list “exclude” should be equal to the Number of assays (i.e. length of “Assays”“). If no columns are selected for exclusion, a”0" should be placed in the “exclude” list. In the above example, we are excluding none of the columns from “H2az” and column 1 and 9 from “H3k9ac”

The integration of multiple assays is handled by integrate_pca function in OMICsPCA. It works in 2 modes:

1. runs PCA on selected groups

2. runs PCA on all individuals (e.g. annotations: gene, TSS etc.)

The type of merging the assays should be entered by the argument mergetype

integrate_pca() returns a list of 2 elements containing 1) the start and end column of each Assay in the integrated Assay

2. and the integrated PCA results  

int_PCA <- integrate_pca(Assays = c("H2az",
"H3k9ac"),
groupinfo = groupinfo,
name = multi_assay, mergetype = 2,
exclude = exclude, graph = FALSE)

if mergetype is set to 1, then integrate_pca asks for the name of groups to be integrated.  

Enter a vector of strings containing group names:

Here is an example of the allowed input  

Enter a vector of strings containing group names: c("WE","RE")

Let’s split the output into different variables

start_end = int_PCA$start_end

name = int_PCA$int_PCA

  ## Analysis of integrated data

All the analyses on variables and individuals of integrated Assays are designed to be done by the functions analyse_integrated_variables() and analyse_integrated_individuals(). These functions work similarly as analyse_variables() and analyse_individuals() described in section 3.6 and 3.7. The only difference between the analyses in section 3.6 and 3.7 is that in those sections multiple cell lines from a single type of assay were integrated. Whereas, the analyses described in this section will be on multiple assays or modalities.  

analyse_integrated_variables(start_end = start_end, name = name,
choice = 1, title = "variance barplot", Assay = 1, addlabels = TRUE)

#        eigenvalue variance.percent cumulative.variance.percent
# Dim.1  11.2785626       70.4910162                    70.49102
# Dim.2   0.8238060        5.1487873                    75.63980
# Dim.3   0.6662760        4.1642251                    79.80403
# Dim.4   0.4757188        2.9732428                    82.77727
# Dim.5   0.4634762        2.8967263                    85.67400
# Dim.6   0.3769878        2.3561736                    88.03017
# Dim.7   0.2944345        1.8402155                    89.87039
# Dim.8   0.2854485        1.7840531                    91.65444
# Dim.9   0.2348603        1.4678766                    93.12232
# Dim.10  0.2063641        1.2897757                    94.41209
# Dim.11  0.2040527        1.2753297                    95.68742
# Dim.12  0.1681539        1.0509619                    96.73838
# Dim.13  0.1558582        0.9741139                    97.71250
# Dim.14  0.1534076        0.9587973                    98.67129
# Dim.15  0.1106141        0.6913379                    99.36263
# Dim.16  0.1019787        0.6373671                   100.00000

analyse_integrated_variables(start_end = start_end, Assay = 1,
name = name, choice = 2 ,
title = "Loadings of cell lines on PC1 and PC2",
var_type = "contrib")

#            Dim.1      Dim.2     Dim.3       Dim.4      Dim.5      Dim.6
# Gm12878 7.019011  1.2022488  4.363976 0.291303442  1.9215282  4.6885934
# Hepg2   4.393136 11.1677691 39.321690 0.000174136  1.5736144 23.4659659
# Hsmm    7.301528  0.1798474  2.212726 0.368788009  6.7670216  2.1489352
# K562    6.377948  2.1539977  5.903030 0.341823532  0.4280165  8.4930567
# Osteobl 6.939920  0.6948640  4.231786 0.553465147 11.1108419  0.2422759
#              Dim.7        Dim.8     Dim.9       Dim.10   Dim.11
# Gm12878  3.7985466  0.063925338 0.1367839 3.538108e-03 8.438047
# Hepg2    7.1821780  8.436740487 1.7452647 6.803952e-04 2.551384
# Hsmm     1.7167732  6.699253439 8.4147624 2.608879e+00 1.240043
# K562    38.2841992  0.001052331 7.6878611 1.426352e+01 2.104304
# Osteobl  0.5608388 10.062792723 8.5792964 7.950644e+00 1.982927
#               Dim.12      Dim.13      Dim.14       Dim.15      Dim.16
# Gm12878 53.461394565 14.24693821 0.002776747 2.371410e-01  0.12424788
# Hepg2    0.001205519  0.11738886 0.005801164 2.622110e-03  0.03438516
# Hsmm     0.573802616  0.89098246 3.173102481 3.667644e+01 19.02711452
# K562    13.829331294  0.03768112 0.073091240 2.339767e-06  0.02108900
# Osteobl  4.834482288  7.16367507 1.044890125 1.989426e+01 14.15303909

analyse_integrated_variables(start_end = start_end, Assay = 1,
name = name, choice = 3,
title = "Correlation of Cell lines with PCs of integrated Assays",
is.cor = TRUE)

#             Dim.1       Dim.2     Dim.3         Dim.4       Dim.5
# Gm12878 0.8897436 -0.09951983 0.1705172  0.0372261383 -0.09437068
# Hepg2   0.7039052 -0.30331625 0.5118506 -0.0009101637  0.08540099
# Hsmm    0.9074731 -0.03849147 0.1214202  0.0418854875 -0.17709753
# K562    0.8481397 -0.13320947 0.1983191  0.0403251654 -0.04453936
# Osteobl 0.8847165 -0.07565931 0.1679148  0.0513121624 -0.22692754
#               Dim.6       Dim.7        Dim.8       Dim.9       Dim.10
# Gm12878 -0.13294895 -0.10575552 -0.013508290  0.01792347  0.002702108
# Hepg2    0.29742869  0.14541942  0.155185529 -0.06402291  0.001184944
# Hsmm    -0.09000679  0.07109692 -0.138285638  0.14058070 -0.073374309
# K562    -0.17893514 -0.33574080 -0.001733166 -0.13437161  0.171565664
# Osteobl -0.03022169  0.04063622 -0.169481827  0.14194843 -0.128090890
#              Dim.11       Dim.12       Dim.13       Dim.14        Dim.15
# Gm12878 -0.13121763 -0.299828990 -0.149013504  0.002063914  1.619603e-02
# Hepg2    0.07215379  0.001423772 -0.013526278  0.002983190  1.703063e-03
# Hsmm     0.05030250  0.031062381  0.037264855 -0.069769474 -2.014182e-01
# K562     0.06552779  0.152494462  0.007663493  0.010589027 -5.087348e-05
# Osteobl -0.06360988  0.090163024  0.105665399  0.040036741  1.483437e-01
#               Dim.16
# Gm12878  0.011256395
# Hepg2   -0.005921617
# Hsmm    -0.139296847
# K562    -0.004637489
# Osteobl  0.120137799

analyse_integrated_variables(start_end = start_end, Assay = 1,
name = name, choice = 4, PC = 1,
title = "Squarred loadings of Cell lines on PC1 of integrated Assays")
#             Dim.1       Dim.2      Dim.3        Dim.4       Dim.5
# Gm12878 0.7916436 0.009904198 0.02907612 1.385785e-03 0.008905826
# Hepg2   0.4954826 0.092000749 0.26199099 8.283980e-07 0.007293328
# Hsmm    0.8235074 0.001481594 0.01474286 1.754394e-03 0.031363535
# K562    0.7193409 0.017744762 0.03933047 1.626119e-03 0.001983755
# Osteobl 0.7827232 0.005724331 0.02819537 2.632938e-03 0.051496109
#                Dim.6       Dim.7        Dim.8        Dim.9       Dim.10
# Gm12878 0.0176754239 0.011184231 1.824739e-04 0.0003212509 7.301386e-06
# Hepg2   0.0884638233 0.021146808 2.408255e-02 0.0040989330 1.404092e-06
# Hsmm    0.0081012231 0.005054772 1.912292e-02 0.0197629320 5.383789e-03
# K562    0.0320177857 0.112721882 3.003863e-06 0.0180557298 2.943478e-02
# Osteobl 0.0009133506 0.001651303 2.872409e-02 0.0201493570 1.640728e-02
#              Dim.11       Dim.12       Dim.13       Dim.14       Dim.15
# Gm12878 0.017218066 8.989742e-02 2.220502e-02 4.259741e-06 2.623114e-04
# Hepg2   0.005206169 2.027127e-06 1.829602e-04 8.899424e-06 2.900422e-06
# Hsmm    0.002530342 9.648715e-04 1.388669e-03 4.867780e-03 4.056930e-02
# K562    0.004293891 2.325456e-02 5.872913e-05 1.121275e-04 2.588111e-09
# Osteobl 0.004046217 8.129371e-03 1.116518e-02 1.602941e-03 2.200585e-02
#               Dim.16
# Gm12878 1.267064e-04
# Hepg2   3.506555e-05
# Hsmm    1.940361e-02
# K562    2.150630e-05
# Osteobl 1.443309e-02

analyse_integrated_variables(start_end = start_end, Assay = 1,
name = name, choice = 5, PC=1,
title = "Contribution of Cell lines on PC1 of integrated Assays")

#            Dim.1      Dim.2     Dim.3       Dim.4      Dim.5      Dim.6
# Gm12878 7.019011  1.2022488  4.363976 0.291303442  1.9215282  4.6885934
# Hepg2   4.393136 11.1677691 39.321690 0.000174136  1.5736144 23.4659659
# Hsmm    7.301528  0.1798474  2.212726 0.368788009  6.7670216  2.1489352
# K562    6.377948  2.1539977  5.903030 0.341823532  0.4280165  8.4930567
# Osteobl 6.939920  0.6948640  4.231786 0.553465147 11.1108419  0.2422759
#              Dim.7        Dim.8     Dim.9       Dim.10   Dim.11
# Gm12878  3.7985466  0.063925338 0.1367839 3.538108e-03 8.438047
# Hepg2    7.1821780  8.436740487 1.7452647 6.803952e-04 2.551384
# Hsmm     1.7167732  6.699253439 8.4147624 2.608879e+00 1.240043
# K562    38.2841992  0.001052331 7.6878611 1.426352e+01 2.104304
# Osteobl  0.5608388 10.062792723 8.5792964 7.950644e+00 1.982927
#               Dim.12      Dim.13      Dim.14       Dim.15      Dim.16
# Gm12878 53.461394565 14.24693821 0.002776747 2.371410e-01  0.12424788
# Hepg2    0.001205519  0.11738886 0.005801164 2.622110e-03  0.03438516
# Hsmm     0.573802616  0.89098246 3.173102481 3.667644e+01 19.02711452
# K562    13.829331294  0.03768112 0.073091240 2.339767e-06  0.02108900
# Osteobl  4.834482288  7.16367507 1.044890125 1.989426e+01 14.15303909

analyse_integrated_individuals(
name = name, choice = 1, PC = c(1,2),
groupinfo = groupinfo)

analyse_integrated_individuals(
name = name,
choice = 2, PC = c(1,2,3),
col = c("RED", "BLACK","GREEN"),
groupinfo = groupinfo)

densityplot <- plot_integrated_density(name = name, PC = 1,
groups = c("WE","RE","IntE","NE"), groupinfo = groupinfo)

# additional graphical functions (e.g. xlim, ylim, theme) may be
#added with densityplot (see section VIII. Density analysis)

densityplot

plot_integrated_density_3D(name = name, PC1 = 1, PC2 = 2,
group = c("RE","RE"), gridsize = 100, static = TRUE,
groupinfo = groupinfo)

plot_integrated_density_3D(name = name, PC1 = 1, PC2 = 2,
group = c("WE","RE"), gridsize = 100, static = FALSE,
groupinfo = groupinfo)

3.10 Cluster Analysis

The principal components obtained by combining multiple assays represent the overall epigenetic state of each annotation (here TSSs). Our next objective is to find out groups of similar TSSs in terms of the combined epigenetic state. We will use a suitable clustering technique(s) to accomplish this job.

There are various clustering techniques available, each is designed to perform specific tasks. Most of the partition based clustering algorithms need the number of clusters as an input. From our density analysis, we observed two dense regions in the data space of PC1 and PC2. This suggests that the number of clusters should be set at 2. However, there are sophisticated indices designed to validate the number of clusters.

OMICsPCA has a function “cluster_parameters()” to perform this job. It runs two algorithms “clvalid” and “NbClust” in the background, which in turn use different sets of validation techniques to decide the number of clusters.

“cluster_parameters()” extracts data from the PCA the object object supplied through name argument via the “extract()” function. Both the algorithms used in “cluster_parameters()” function takes huge memory and CPU for a higher number of samples. Therefore, it is recommended to use a subset of original data while running this function. A subset of rows can be selected randomly through the rand argument of “extract()”. The user may also choose whether to use integrated assays or nonintegrated assays through the logical argument integrated of the function “extract()”.  

# extracting data from integrated PCA
data <- extract(name = name, PC = c(1:4),
groups = c("WE","RE"), integrated = TRUE, rand = 600,
groupinfo = groupinfo)

#or

# extracting PCA data from an individual assay
# if integrated = TRUE, an assay name should be entered by 
# Assay == "assayname"

data <- extract(name = PCAlist, PC = c(1:4),
groups = c("WE","RE"), integrated = FALSE, rand = 600,
Assay = "H2az", groupinfo = groupinfo)

“cluster_parameters()” uses the output of “extract()” and runs one of the algorithms between “clvalid” or “NbClust” to determine the number of clusters.

The parameters of “clvalid” and “NbClust” are passed through the clusteringMethods, validationMethods and distance argument of “cluster_parameters()” function. The argument pairs are different in “NbClust” and “clvalid” and thus should be chosen carefully.  

#### Using "clValid" ####

clusterstats <- cluster_parameters(name = data,
optimal = FALSE, n = 2:6, comparisonAlgorithm = "clValid",
distance = "euclidean", clusteringMethods = c("kmeans","pam"),
validationMethods = c("internal","stability"))
# 
# Clustering Methods:
#  kmeans pam 
# 
# Cluster sizes:
#  2 3 4 5 6 
# 
# Validation Measures:
#                             2        3        4        5        6
#                                                                  
# kmeans APN             0.1121   0.1608   0.2101   0.2728   0.3303
#        AD              5.9022   5.2298   4.9408   4.8903   4.6331
#        ADM             1.3394   1.8684   2.2105   2.4605   2.5719
#        FOM             2.8844   2.8158   2.8028   2.7762   2.5840
#        Connectivity   40.4504  76.4349  90.8996  96.0845 120.0901
#        Dunn            0.0566   0.0265   0.0357   0.0518   0.0363
#        Silhouette      0.5560   0.4403   0.4370   0.4357   0.4343
# pam    APN             0.1096   0.1832   0.2589   0.3506   0.2821
#        AD              5.8387   5.0701   4.7638   4.6746   4.1197
#        ADM             1.3971   1.6660   2.1372   2.6045   1.8475
#        FOM             2.6997   2.6405   2.5994   2.5288   2.4882
#        Connectivity   47.8571  74.2782 112.2889 149.2131 135.6901
#        Dunn            0.0324   0.0283   0.0101   0.0154   0.0123
#        Silhouette      0.5589   0.4355   0.4025   0.3332   0.4340
# 
# Optimal Scores:
# 
#              Score   Method Clusters
# APN           0.1096 pam    2       
# AD            4.1197 pam    6       
# ADM           1.3394 kmeans 2       
# FOM           2.4882 pam    6       
# Connectivity 40.4504 kmeans 2       
# Dunn          0.0566 kmeans 2       
# Silhouette    0.5589 pam    2

#### plot indexes vs cluster numbers returned by clValid
#plot(clusterstats)


#### using "NbClust"

data <- extract(name = name, PC = c(1:4),
groups = c("WE","RE"),integrated = TRUE, rand = 400,
groupinfo = groupinfo)

clusterstats <- cluster_parameters(name = data, n = 2:6,
comparisonAlgorithm = "NbClust", distance = "euclidean",
clusteringMethods = "kmeans",
validationMethods = "all")

# *** : The Hubert index is a graphical method of determining the number of clusters.
#                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
#                 significant increase of the value of the measure i.e the significant peak in Hubert
#                 index second differences plot. 
# 

# *** : The D index is a graphical method of determining the number of clusters. 
#                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
#                 second differences plot) that corresponds to a significant increase of the value of
#                 the measure. 
#  
# ******************************************************************* 
# * Among all indices:                                                
# * 11 proposed 2 as the best number of clusters 
# * 3 proposed 3 as the best number of clusters 
# * 8 proposed 4 as the best number of clusters 
# * 1 proposed 5 as the best number of clusters 
# * 1 proposed 6 as the best number of clusters 
# 
#                    ***** Conclusion *****                            
#  
# * According to the majority rule, the best number of clusters is  2 
#  
#  
# *******************************************************************

library(factoextra)
# Welcome! Related Books: `Practical Guide To Cluster Analysis in R` at https://goo.gl/13EFCZ

fviz_nbclust(clusterstats, method = c("silhouette",
"wss", "gap_stat"))
# Among all indices: 
# ===================
# * 2 proposed  0 as the best number of clusters
# * 11 proposed  2 as the best number of clusters
# * 3 proposed  3 as the best number of clusters
# * 8 proposed  4 as the best number of clusters
# * 1 proposed  5 as the best number of clusters
# * 1 proposed  6 as the best number of clusters
# 
# Conclusion
# =========================
# * According to the majority rule, the best number of clusters is  2 .

Now, depending on the output of “cluster_parameters()”, we may choose the appropriate clustering algorithm and number of clusters.

OMICsPCA has a function “cluster()” that is designed for the clustering task. “cluster()” has many clustering options which should be chosen through choice argument. The class of the returned value by “cluster()” depends on the type of clustering method chosen. So, extraction and visualization of data from cluster objects are different for different choices.  

data <- extract(name = name, PC = c(1:4),
groups = c("WE","RE"), integrated = TRUE, rand = 1000,
groupinfo = groupinfo)

library(factoextra)

### kmeans clustering

clusters <- cluster(name = data, n = 2, choice = "kmeans",
title = "kmeans on 2 clusters")

# visualization of clusters

print(clusters$plot)

clustered_data <- cbind(data,clusters$cluster$cluster)
plot3d(data[,1:3], col = clusters$cluster$cluster)

### density-based clustering

clusters <- cluster(name = data, choice = "density",
eps = 2, MinPts = 100, graph = TRUE,
title = "eps = 1 and MinPts = 1.5")

# visualization of clusters
print(clusters$plot)

clustered_data <- as.data.frame(cbind(data,clusters$cluster$cluster))

#removing unclustered points
clustered_data <- clustered_data[clustered_data$V5 != 0, ]

library(rgl)
#plotting clusters on first 3 PCs
plot3d(clustered_data[,1:3], col = clustered_data$V5)

#### Using silhouette index
# calculating the distance matrix
library(cluster)
dist <- daisy(data)

sil = silhouette(clusters$cluster$cluster,dist)

# RStudio sometimes does not display silhouette plots
#correctly. So sometimes, it is required to plot in separate
#window.

#grDevices::windows()
#plot(sil)

# Identification of misclassified data points
# silhouette width of misclassified points are negative
misclassified <- which(sil[,3] < 0)

head(sil[misclassified,])
#      cluster neighbor   sil_width
# [1,]       0        2 -0.02700430
# [2,]       0        1 -0.01348814
# [3,]       0        1 -0.02585614
# [4,]       0        2 -0.05228407
# [5,]       0        2 -0.12282850
# [6,]       2        0 -0.06407522

data[misclassified[3:7],]
#                                        Dim.1    Dim.2     Dim.3      Dim.4
# ENST00000552049.1;ENST00000546756.1 1.720252 0.313471 0.9095707 -1.3984965
# ENST00000219240.4                   5.843969 3.244593 0.7721712  0.9258375
# ENST00000295500.4                   5.130447 1.081242 3.0519371 -2.8619556
# ENST00000456580.2                   5.149236 3.350805 0.6372836  0.6221167
# ENST00000273860.4;ENST00000514576.1 2.527538 1.024538 0.2592180  0.3716006

bp <- cluster_boxplot(name = multi_assay,
Assay = "H2az", clusterobject = clustered_data,
clustercolumn = 5)


bp <- bp+xlab("Cell lines") + ylab(
"value")+ggtitle(
"Distribution of H2az_cell_wise in various clusters")+theme(
plot.title=element_text(hjust=0.5),
legend.position = "top")+guides(
fill=guide_legend("Cell lines"))

bp