Exploratory Analysis

Sample Groups

Traits in the table of phenotypic information were automatically selected based on criteria for defining sample groups. The table below summarizes these traits.

Trait Number of groups
Sample_Group 2
Treatment 2
CellType 2
Predicted Gender 2

Region Annotations

In addition to CpG sites, there are 4 sets of genomic regions to be covered in the analysis. The table below gives a summary of these annotations.

Annotation Description Regions in the Dataset
tiling

Genome tiling regions of length 5000

133950
genes

Ensembl genes, version Ensembl Genes 75

30784
promoters

Promoter regions of Ensembl genes, version Ensembl Genes 75

30969
cpgislands

CpG island track of the UCSC Genome browser

26610

Region length distributions

The plots below show region size distributions for the region types above.

Region type

Figure 1

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Distribution of region lengths

Number of sites per region

The plots below show the distributions of the number of sites per region type.

Region type

Figure 2

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Distribution of the number of sites per region

Region site distributions

The plots below show distributions of sites across the different region types.

Region type

Figure 3

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Distribution of sites across regions. relative coordinates of 0 and 1 corresponds to the start and end coordinates of that region respectively. Coordinates smaller than 0 and greater than 1 denote flanking regions normalized by region length.

Low-dimensional Representation

Dimension reduction is used to visually inspect the dataset for a strong signal in the methylation values that is related to samples' clinical or batch processing annotation. RnBeads implements two methods for dimension reduction - principal component analysis (PCA) and multidimensional scaling (MDS).

One or more of the methylation matrices was augmented before applying the dimension reduction techniques because it contains missing values. The column Missing lists the number of dimensions ignored due to missing values. In the case of MDS, dimensions are ignored only if they contain missing values for all samples. In contrast, sites or regions with missing values in any sample are ignored prior to PCA.

Sites/regions Technique Dimensions Missing Selected
sites MDS 471549 0 471549
sites PCA 471549 15 471534
tiling MDS 133950 0 133950
tiling PCA 133950 0 133950
genes MDS 30784 0 30784
genes PCA 30784 0 30784
promoters MDS 30969 0 30969
promoters PCA 30969 0 30969
cpgislands MDS 26610 0 26610
cpgislands PCA 26610 0 26610

Multidimensional Scaling

The scatter plot below visualizes the samples transformed into a two-dimensional space using MDS.

Location type
Distance
Sample representation
Sample color

Figure 4

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Scatter plot showing samples after performing Kruskal's non-metric mutidimensional scaling.

Principal Component Analysis

Similarly, the figure below shows the values of selected principal components in a scatter plot.

Location type
Principal components
Sample representation
Sample color

Figure 5

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Scatter plot showing the samples' coordinates on principal components.

The figure below shows the cumulative distribution functions of variance explained by the principal components.

Location type

Figure 6

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Cumulative distribution function of percentange of variance explained.

The table below gives for each location type a number of principal components that explain at least 95 percent of the total variance. The full tables of variances explained by all components are available in comma-separated values files accompanying this report.

Location Type Number of Components Full Table File
sites 9 csv
tiling 9 csv
genes 8 csv
promoters 8 csv
cpgislands 8 csv

Batch Effects

In this section, different properties of the dataset are tested for significant associations. The properties can include sample coordinates in the principal component space, phenotype traits and intensities of control probes. The tests used to calculate a p-value given two properties depend on the essence of the data:

Note that the p-values presented in this report are not corrected for multiple testing.

Associations between Principal Components and Traits

The computed sample coordinates in the principal component space were tested for association with the available traits. Below is a list of the traits and the tests performed.

Trait Test
Sample_Group Wilcoxon
Cell_Line Kruskal-Wallis
Passage_No Correlation
Treatment Wilcoxon
CellType Wilcoxon
Predicted Male Probability Correlation
Predicted Gender Wilcoxon
predicted_ages Correlation
Immune Cell Content (LUMP) Correlation

The next figure shows the computed correlations between the first 8 principal components and the sample traits.

Region type

Figure 7

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Heatmap presenting a table of correlations. Grey cells, if present, denote missing values.

The values presented in the figure above are avaialable in CSV (comma-separated value) files accompanying this report.

Location type Table file
sites csv
tiling csv
genes csv
promoters csv
cpgislands csv

The heatmap below summarizes the results of permutation tests performed for associations. Significant p-values (values less than 0.01) are displayed in pink background.

Region type

Figure 8

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Heatmap presenting a table of p-values. Significant p-values (less than 0.01) are printed in pink boxes. Non-significant values are represented by blue boxes. Bright grey cells, if present, denote missing values.

The full tables of p-values for each location type are available in CSV (comma-separated value) files below.

Location Type File Name
sites csv
tiling csv
genes csv
promoters csv
cpgislands csv

Associations between Traits

This section summarizes the associations between pairs of traits.

The figure below visualizes the tests that were performed on trait pairs based on the description provided above. In some cases, pairs of traits could not be tested for associations. These scenarios are marked by grey shapes, and the underlying reason is given in the figure legend. In addition, the calculated p-values for associations between traits are shown. Significant p-values (values less than 0.01) are displayed in pink background. The full table of p-values is available in a dedicated file that accompanies this report.

Heatmap of

Figure 9

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(1) Table of performed tests on pairs of traits. Test names (Correlation + permutation test, Fisher's exact test, Wilcoxon rank sum test and/or Kruskal-Wallis one-way analysis of variance) are color-coded according to the legend given above.
(2) Table of resulting p-values from the performed tests on pairs of traits. Significant p-values (less than 0.01) are printed in pink boxes Non-significant values are represented by blue boxes. White cells, if present, denote missing values.

In some cases, a correlation was computed between a pair of traits. As described earlier in this report, these correlation values are used as the basis for a permutation-based test. The table of computed correlations is available as a comma-separated file accompanying this report.

Quality-associated Batch Effects

This section examines the methylation values of the dataset for quality-associated batch effects.

The heatmaps below visualize the Pearson correlation coefficients between the principal components and the signal levels of selected quality control probes.

Location type
Channel
Probe group

Figure 10

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Heatmap presenting a table of correlations. Grey cells, if present, denote missing values.

In a complete analogy to the heatmaps above, the figure below visualizes the p-values calculated using permutation tests.

Location type
Channel
Probe group

Figure 11

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Heatmap presenting a table of p-values. Significant p-values (less than 0.01) are printed in pink boxes. Non-significant values are represented by blue boxes. Bright grey cells, if present, denote missing values.

All computed p-values for associations are available as comma-separated files that accompany this report. The links to the dedicated files are provided in the table below.

Location type

Control probe type \ Target - Channel Green Red
bisulfite conversion I csv csv
bisulfite conversion II csv csv
extension csv csv
hybridization csv csv
non-polymorphic csv csv
specificity I csv csv
specificity II csv csv
staining csv csv
target removal csv csv

Methylation Value Distributions

Methylation value distributions were assessed based on selected sample groups. This was done on probe and region levels. This section contains the generated density plots.

Methylation Value Densities of Sample Groups

The plots below compare the distributions of methylation values in different sample groups, as defined by the traits listed above.

Sample trait
Methylation of

Figure 12

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Beta value density estimation according to sample grouping.

Methylation Value Densities of Probe Categories

In a similar fashion, the plot below compares the distributions of beta values in different probe types.

Sample group
Probe category

Figure 13

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Methylation value density estimation according to sample grouping and probe category.

Inter-sample Variability

The variability of the methylation values is measured in two aspects: (1) intra-sample variance, that is, differences of methylation between genomic locations/regions within the same sample, and (2) inter-sample variance, i.e. variability in the methylation degree at a specific locus/region across a group of samples.

The following figure shows the relationship between average methylation and methylation variability of a probe.

Sample group
Point color based on

Figure 14

Figure 14

Scatter plot showing the correlation betweeen probe mean methylation and the variance across a group of samples. Every point corresponds to one probe.

In a complete analogy to the plots above, the figure below shows the relationship between average methylation and methylation variability of a genomic region.

Regions
Sample group
Point color based on

Figure 15

Figure 15

Scatter plot showing the correlation betweeen region mean methylation and the variance across a group of samples. Every point corresponds to one region.

The figure below shows a methylation deviation plot for all samples in the dataset, as well as other sample groups inferred from the table of phenotypic information.

Sample group
Color legend based on

Figure 16

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Deviation plot of a sample group. Probes are sorted in increasing order of their median methylation and are binned in groups of up to 118. The horizontal axis in the plot iterates over probe groups, and the vertical axis measures methylation degree. Median β values are depicted by a blue curve. Grey borders mark the 5th and 95th percentiles of β values in a probe (averaged over the group), ensuring that 90 percent of the observed values lie in the yellow area.
Relative frequencies of probe categories in every group are color-coded and plotted below the horizontal axis. Every segment in the color legend shows the distribution of probe categories that underlie the corresponding segment in the deviation plot above it.

In a similar fashion, the figure below shows deviation plots on the region level.

Regions
Sample group
Color legend based on

Figure 17

Open PDF Figure 17

Deviation plot of a sample group. Regions are sorted in increasing order of their median methylation and are binned in groups of up to 34. The horizontal axis in the plot iterates over region groups, and the vertical axis measures methylation degree. Median β values are depicted by a blue curve. Grey borders mark the 5th and 95th percentiles of β values in a region (averaged over the group), ensuring that 90 percent of the observed values lie in the yellow area.
Relative frequencies of region categories in every group are color-coded and plotted below the horizontal axis. Every segment in the color legend shows the distribution of region categories that underlie the corresponding segment in the deviation plot above it.

The variability of a sample group is the span between 5th and 95th percentile of β values , averaged over all valid locations/regions. This amounts to a number between 0 and 1 and corresponds to the relative area of deviation in the plots presented above. The table below lists the variabilities of the studied sample groups.

Loci/regions Sample Group Based on Trait Size Variability
sites all samples 12 0.0890
sites hESC Sample_Group 5 0.0665
sites hiPSC Sample_Group 7 0.0746
sites KOSR Treatment 2 0.0294
sites TeSR Treatment 2 0.0351
sites CT1 CellType 2 0.0360
sites CT2 CellType 2 0.0336
sites female Predicted Gender 6 0.0685
sites male Predicted Gender 6 0.0715
tiling all samples 12 0.0784
tiling hESC Sample_Group 5 0.0573
tiling hiPSC Sample_Group 7 0.0661
tiling KOSR Treatment 2 0.0239
tiling TeSR Treatment 2 0.0311
tiling CT1 CellType 2 0.0306
tiling CT2 CellType 2 0.0295
tiling female Predicted Gender 6 0.0625
tiling male Predicted Gender 6 0.0639
genes all samples 12 0.0610
genes hESC Sample_Group 5 0.0454
genes hiPSC Sample_Group 7 0.0510
genes KOSR Treatment 2 0.0206
genes TeSR Treatment 2 0.0248
genes CT1 CellType 2 0.0244
genes CT2 CellType 2 0.0226
genes female Predicted Gender 6 0.0461
genes male Predicted Gender 6 0.0471
promoters all samples 12 0.0693
promoters hESC Sample_Group 5 0.0523
promoters hiPSC Sample_Group 7 0.0578
promoters KOSR Treatment 2 0.0231
promoters TeSR Treatment 2 0.0281
promoters CT1 CellType 2 0.0281
promoters CT2 CellType 2 0.0255
promoters female Predicted Gender 6 0.0519
promoters male Predicted Gender 6 0.0533
cpgislands all samples 12 0.0781
cpgislands hESC Sample_Group 5 0.0581
cpgislands hiPSC Sample_Group 7 0.0652
cpgislands KOSR Treatment 2 0.0290
cpgislands TeSR Treatment 2 0.0317
cpgislands CT1 CellType 2 0.0307
cpgislands CT2 CellType 2 0.0285
cpgislands female Predicted Gender 6 0.0568
cpgislands male Predicted Gender 6 0.0589

Clustering

The figure below shows clustering of samples using several algorithms and distance metrics.

Site/region level
Dissimilarity metric
Agglomeration strategy (linkage)
Sample color based on

Figure 18

Figure 18

Hierarchical clustering of samples based on all methylation values. The heatmap displays methylation percentiles per sample. The legend for sample coloring can be found in the figure below.

Site/region level
Dissimilarity metric
Agglomeration strategy (linkage)
Sample color based on
Site/region color based on
Visualize

Figure 19

Figure 19

Hierarchical clustering of samples based on all methylation values. The heatmap displays only selected sites/regions with the highest variance across all samples. The legend for locus and sample coloring can be found in the figure below.

Site/region level
Sample color based on
Site/region color based on

Figure 20

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Probe and sample colors used in the heatmaps in the previous figures.

Identified Clusters

Using the average silhouette value as a measure of cluster assignment [1], it is possible to infer the number of clusters produced by each of the studied methods. The figure below shows the corresponding mean silhouette value for every observed separation into clusters.

Site/region level
Dissimilarity metric

Figure 21

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Line plot visualizing mean silhouette values of the clustering algorithm outcomes for each applicable value of K (number of clusters).

The table below summarizes the number of clusters identified by the algorithms.

Site/region level

Metric Algorithm Clusters
correlation-based hierarchical (average linkage) 7
correlation-based hierarchical (complete linkage) 7
correlation-based hierarchical (median linkage) 7
Manhattan distance hierarchical (average linkage) 7
Manhattan distance hierarchical (complete linkage) 6
Manhattan distance hierarchical (median linkage) 8
Euclidean distance hierarchical (average linkage) 7
Euclidean distance hierarchical (complete linkage) 7
Euclidean distance hierarchical (median linkage) 7

Clusters and Traits

The figure below shows associations between clusterings and the examined traits. Associations are quantified using the adjusted Rand index [2]. Rand indices near 1 indicate high agreement while values close to -1 indicate seperation. The full table of all computed indices is stored in the following comma separated files:

Site/region level
Dissimilarity metric

Figure 22

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Heatmap visualizing Rand indices computed between sample traits (rows) and clustering algorithm outcomes (columns).

Regional Methylation Profiles

Methylation profiles were computed for the specified region types. Composite plots are shown

Region type
Sample trait

Figure 23

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Regional methylation profiles (composite plots) according to sample groups. For each region in the corresponding region type, relative coordinates of 0 and 1 corresponds to the start and end coordinates of that region respectively. Coordinates smaller than 0 and greater than 1 denote flanking regions normalized by region length. Scatterplot smoothers for each sample and sample group were fit. Horizontal lines indicate region boundaries. For smoothing, generalized additive models with cubic spine smoothing were used. Deviation bands indicate 95% confidence intervals

References

  1. Rousseeuw, P. J. (1987) Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20, 53-65
  2. Hubert, L. and Arabie, P. (1985) Comparing partitions. Journal of Classification, 2(1), 193-218