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<h1 class="title toc-ignore">Primary correlation patterns identified by mash in GTEx data</h1>
<h4 class="author"><em>Sarah Urbut</em></h4>
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<p><strong>Last updated:</strong> 2018-05-18</p>
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<p></details></p>
<hr />
<p>“Uk3” is the covariance matrix corresponding to the output of the ExtremeDeconvolution algorithm that was initialized with the rank3 SVD approximation of <span class="math inline">\(X^TX\)</span>. It is the pattern of sharing identified from the dominant covariance matrix (the one with the largest mixture weight).</p>
<p>Here we plot the correlation matrix and the first 3 eigenvectors of “Uk3”. This provides a visualization of the primary patterns of genetic sharing identified by our method, MASH. This code should closely reproduce Figure 3 of the paper.</p>
<div id="set-up-environment" class="section level2">
<h2>Set up environment</h2>
<p>First, we load a couple plotting packages used in the code chunks below.</p>
<pre class="r"><code>library(lattice)
library(colorRamps)</code></pre>
</div>
<div id="load-data-and-mash-results" class="section level2">
<h2>Load data and MASH results</h2>
<p>We load some GTEx summary statistics, as well as some of the results generated from the MASH analysis of the GTEx data.</p>
<pre class="r"><code>covmat <- readRDS(paste("../output/MatrixEQTLSumStats.Portable.Z.coved.K3.P3",
"lite.single.expanded.rds",sep = "."))
pis <- readRDS(paste("../output/MatrixEQTLSumStats.Portable.Z.coved.K3.P3",
"lite.single.expanded.V1.pihat.rds",sep = "."))$pihat
z.stat <- readRDS("../data/MatrixEQTLSumStats.Portable.Z.rds")$test.z
pi.mat <- matrix(pis[-length(pis)],ncol = 54,nrow = 22,byrow = TRUE)
names <- colnames(z.stat)
colnames(pi.mat) <-
c("ID","X'X","SVD","F1","F2","F3","F4","F5","SFA_Rank5",names,"ALL")</code></pre>
<p>Compute the correlations from the <span class="math inline">\(k=3\)</span> covariance matrix.</p>
<pre class="r"><code>k <- 3
x <- cov2cor(covmat[[k]])
x[x < 0] <- 0</code></pre>
<p>Next, we load the tissue indices and tissue names:</p>
<pre class="r"><code>colnames(x) <- names
rownames(x) <- names
h <- read.table("../output/uk3rowindices.txt")[,1]</code></pre>
<p>For the plots of the eigenvectors, we load the colours that are conventionally used to represent the tissues in plots.</p>
<pre class="r"><code>missing.tissues <- c(7,8,19,20,24,25,31,34,37)
color.gtex <- read.table("../data/GTExColors.txt",sep = "\t",
comment.char = '')[-missing.tissues,]</code></pre>
</div>
<div id="summarize-relative-importance-of-the-covariance-matrices" class="section level2">
<h2>Summarize relative importance of the covariance matrices</h2>
<p>The posterior mixture weights give the relative importance of the covariance matrices for capturing patterns in the data.</p>
<pre class="r"><code>barplot(colSums(pi.mat),las = 2,cex.names = 0.5)</code></pre>
<p><img src="figure/Fig.Uk3.Rmd/plot-mixture-weights-1.png" width="768" style="display: block; margin: auto;" /></p>
<p>Here we see that the SVD component has the largest weight.</p>
</div>
<div id="generate-heatmap-of-uk3-covariance-matrix" class="section level2">
<h2>Generate heatmap of Uk3 covariance matrix</h2>
<p>Now we produce the heatmap showing the full covariance matrix.</p>
<pre class="r"><code>smat <- (x[(h),(h)])
smat[lower.tri(smat)] <- NA
clrs <- colorRampPalette(rev(c("#D73027","#FC8D59","#FEE090","#FFFFBF",
"#E0F3F8","#91BFDB","#4575B4")))(64)
lat <- x[rev(h),rev(h)]
lat[lower.tri(lat)] <- NA
n <- nrow(lat)
print(levelplot(lat[n:1,],col.regions = clrs,xlab = "",ylab = "",
colorkey = TRUE,at = seq(0,1,length.out = 64),
scales = list(cex = 0.6,x = list(rot = 45))))</code></pre>
<p><img src="figure/Fig.Uk3.Rmd/heatmap-uk3-1.png" width="960" style="display: block; margin: auto;" /></p>
</div>
<div id="plot-eigenvectors-capturing-predominant-patterns" class="section level2">
<h2>Plot eigenvectors capturing predominant patterns</h2>
<p>The eigenvectors capture the predominant patterns in the Uk3 covariance matrix.</p>
<pre class="r"><code>k <- 3
vold <- svd(covmat[[k]])$v
u <- svd(covmat[[k]])$u
d <- svd(covmat[[k]])$d
v <- vold[h,] # Shuffle so correct order
names <- names[h]
color.gtex <- color.gtex[h,]
for (j in 1:3)
barplot(v[,j]/v[,j][which.max(abs(v[,j]))],names = "",cex.names = 0.5,
las = 2,main = paste0("EigenVector",j,"Uk",k),
col = as.character(color.gtex[,2]))</code></pre>
<p><img src="figure/Fig.Uk3.Rmd/plot-eigenvectors-1.png" width="576" style="display: block; margin: auto;" /><img src="figure/Fig.Uk3.Rmd/plot-eigenvectors-2.png" width="576" style="display: block; margin: auto;" /><img src="figure/Fig.Uk3.Rmd/plot-eigenvectors-3.png" width="576" style="display: block; margin: auto;" /></p>
<p>The first eigenvector reflects broad sharing among tissues, with all effects in the same direction; the second eigenvector captures differences between brain (and, to a less extent, testis and pituitary) vs other tissues; the third eigenvector primarily captures effects that are stronger in whole blood than elsewhere.</p>
</div>
<div id="session-information" class="section level2">
<h2>Session information</h2>
<pre class="r"><code>sessionInfo()
R version 3.4.3 (2017-11-30)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.4
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] colorRamps_2.3 lattice_0.20-35
loaded via a namespace (and not attached):
[1] workflowr_1.0.1.9000 Rcpp_0.12.16 digest_0.6.15
[4] rprojroot_1.3-2 R.methodsS3_1.7.1 grid_3.4.3
[7] backports_1.1.2 git2r_0.21.0 magrittr_1.5
[10] evaluate_0.10.1 stringi_1.1.7 whisker_0.3-2
[13] R.oo_1.21.0 R.utils_2.6.0 rmarkdown_1.9
[16] tools_3.4.3 stringr_1.3.0 yaml_2.1.18
[19] compiler_3.4.3 htmltools_0.3.6 knitr_1.20 </code></pre>
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