Exploration of multi-source BRCA data using r.jive

Loading the data

First, if you have not done so already, install and load the package via CRAN:

install.packages("r.jive")
library(r.jive)

The package requires two dependencies: SpatioTemporal for inputing missing values, and gplots for some plotting functions.

To load the BRCA data, enter
data(BRCA_data)
These data consist of a single list object Data that contains the data. The list has one entry for each of three different molecular sources:

• Data[[1]] (Data$Expression): gene expression matrix for 654 genes (rows) and 348 samples (columns)
• Data[[2]] (Data$Methylation): DNA methylation matrix for 574 cg sites (rows) and 348 samples (columns)
• Data[[3]] (Data$miRNA): miRNA expression matrix for 423 cg sites (rows) and 348 samples (columns).

The 348 columns are shared by the data sources (here, they correspond to tumor samples), and must be in the same order. This is the general data format recognived by jive.

These data were originally obtained from the data freeze for TCGA’s flagship BRCA publication (Cancer Genome Atlas Network (2012)). The data were filtered and processed as described in E. F. Lock and Dunson (2013). E. F. Lock and Dunson (2013) describe an analysis of these data to identify jointly present sample clusters, and these clusters are loaded here as the vector clusts. Here we will only use the cluster labels to visualize and interpret results.

JIVE estimation

The default function to estimate the JIVE decomposition is jive. This function involves several options, including the capability to input given ranks for joint and individual structure or to use a method to estimate these ranks. For more information on available options, enter ?jive.

Two algorithms to select the ranks are included as options. One is a permutation-based approach described in E. Lock et al. (2013), the other is a BIC-motivated approach. We find that the accuracy of permutation estimated ranks are generally better, but BIC is less computationally intensive. By default the ranks are selected via permutation, with row-orthogonality enforced between the joint and invidual estimates and also between each individual estimate. Previously orthogonality was only enforced between joint and individual estimates, but we find that also enforcing the individual estimates to be orthogonal to each other improves convergence and robustness of the results to rank mispecification.

We estimate the decomposition on the BRCA data with these and other defaults. (This can take some time to complete, about 15 min, to compute the same estimates more quickly with given ranks see below.)

Results = jive(Data)

88 iterations
2 22 14 20

88 iterations
2 32 22 24

87 iterations
2 32 22 23

87 iterations
2 32 22 23

The output shown are the ranks used for each call to the base JIVE algorithm (here, 4 calls) and the number of iterations until convergence for each call. The method ends when the ranks are the same for two consecutive calls. For this example, the chosen ranks are

• rank 2 joint structure
• rank 32 structure individual to gene expression
• rank 22 structure individual to methylation, and
• rank 23 structure individual to miRNA.

The results are given as an object of the S3 class JIVE, with values including

• Results$data: A list of the three data matrices used for JIVE estimation. These are centered and scaled versions of the original data matrices (by default, each data matrix is scaled by its total variation).
• Results$joint: A list of three data matrices giving estimated joint structure for each source.
• Results$indiv: A list of three data matrices giving estimated individual structure for each source.

Each list is labeled with the names given in the original input data (e.g., Results$data$Expression gives the scaled expression data). These are also used as labels for figures that depict the JIVE results.

To simply estimate the JIVE decomposition with the ranks determined above, enter
Results = jive(Data,method="given",rankJ=2,rankA=c(32,22,23))
these results are identical to those obtained after running the method with rank selection.

Visualization and interpretation

The r.jive package provides three functions that generate figures with very different views of the JIVE results, and we briefly illustrate each function here. All three take an object of class JIVE as input, with additional optional parameters.

The most simple function is showVarExplained, which displays a barchart of the amount of variation explained by joint and individual estimates in each data source. Here we save the resulting figure for the BRCA data as a .png file, shown below.

png("VarExplained.png",height=300,width=450)  
showVarExplained(Results)  
dev.off()

The variation explained by joint structure is similar as that for individual structure for gene expression and methylation data, despite the much higher rank of individual structure (e.g., rank 32 individual vs. rank 2 joint for expression). The overall decomposition is remarkably similar between the expression and methylation data. The estimated joint structure explains slightly less variability in the miRNA data, which has more individual structure.

We can display the actual JIVE estimates, in the form of low-rank matrix approximations, as heatmaps using the showHeatmaps function. By default, this will create heatmaps of the full JIVE decomposition (Data=Joint+Individual+Residual) and order the rows and columns of all matrices by complete linkage clustering of the joint structure. For larger datasets, performing the clustering and rendering the images can take some time; for these data the process takes less than a minute. You may need to fiddle with the image dimensions a bit for the results to look nice (if the dimensions are too small, the text may be cut-off).

png("HeatmapsBRCA.png",height=465,width=705)
showHeatmaps(Results)
dev.off() 

The columns (samples) are vertically aligned for all heatmaps, with red correspoding to higher values and blue lower values. The estimated joint structure shows clear joint patterns that can also be seen in three of the original data heatmaps. However, note that the joint structure appears less prominently in the miRNA data heatmap, as the joint structure explains less of the miRNA variability.

In addition, the showHeatmaps function includes options to specify how to order rows and columns, and which matrices to display; for details enter ?showHeatmaps. For example, we can order by the individual methylation structure (data source 2) and show only this heatmap.

png("HeatmapIndivMeth.png",height=400,width=400)
showHeatmaps(Results,order_by=2,show_all=FALSE)
dev.off() 

The dominating factor here appears to be a mean effect, distinguishing those samples with relatively high methylation genome-wide from those with relatively low methylation.

To further examine the biological relevance of the estimated joint structure, we consider the “point cloud” view provided by the showPCA function. This shows the patterns in the column space that maximize variability of joint or individual structure, analogous to principal components. Any number of components from the joint or different individual structure estimates can be shown in multi-panel scatterplots. First, we view the two components of joint structure (note: because the joint structure is rank 2, it has only 2 principal components). We color these components by the clusters defined in the clusts variable.

Colors = rep('black',348)
Colors[clusts==2] = 'green'
Colors[clusts==3] = 'purple'
png("JointPCA.png",height=400,width=400)
showPCA(Results,n_joint=2,Colors=Colors)
dev.off()

We see that the estimated joint corresponds well to the three previously identified clusters. Specifically, one pattern distinguishes Basal-like tumor samples (cluster 1) from other samples; among the remaining samples a subgroup of Luminal A tumors with a low fraction of genomic alteration and improved clinical prognosis (cluster 2) is distinguished.

For a broader view, we show the first component of joint structure with the first component of each of the three individual structures.

png("MorePCA.png",height=600,width=600)
showPCA(Results,n_joint=1,n_indiv=c(1,1,1),Colors=Colors)
dev.off()

A clustering effect is not apparant in the individual components shown, besides a very slight distinction between clusters 2 and 3 in the expression individual component. This suggests that the coordinated expression, methylation, and miRNA activity in BRCA tumors is primarily driven by the cluster effects mentioned above, whereas the activity specific to each data source is driven by other biological components.