Last updated: 2018-06-18

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Expand here to see past versions:
    File Version Author Date Message
    Rmd 6314ce0 Gao Wang 2018-06-16 Relabel ‘test’ to ‘strong’ in data and code
    html 6eee6a9 Peter Carbonetto 2018-06-06 Updated the webpages for a bunch of R Markdown files after minor revisions.
    Rmd 3dc0ba5 Peter Carbonetto 2018-06-06 wflow_publish(c(“ExpressionAnalysis.Rmd”, “fastqtl2mash.Rmd”,
    html 64a343f Peter Carbonetto 2018-06-06 Build site.
    Rmd 1534f7b Peter Carbonetto 2018-06-06 wflow_publish(“SharingHist.Rmd”)
    html 5aaf7c2 Peter Carbonetto 2018-06-06 Rebuilt page for revised SharingHist analysis.
    Rmd 1fcccc4 Peter Carbonetto 2018-06-06 wflow_publish(“SharingHist.Rmd”)
    html e37a93d Peter Carbonetto 2018-06-06 I have a first complete revision of the SharingHist analysis without
    Rmd dd35bf1 Peter Carbonetto 2018-06-06 wflow_publish(“SharingHist.Rmd”)
    Rmd 35ca901 Peter Carbonetto 2018-06-06 Revised data/results loading steps in HeterogeneityTables.Rmd.
    Rmd 0fa57df Peter Carbonetto 2018-06-06 wflow_publish(“Tspecific.Rmd”)

Here we develop another summary of sharing of eQTLs across tissues by showing the estimated distribution of sharing; specifically, the distribution of the number of tissues shared by sign and by magnitude. This complements this summary and this one.

Compare the plots below to the plots in Figure 5 of the paper.

Set up environment

First, we load some functions defined for the mash analyses.

source("../code/normfuncs.R")

This is the threshold used to determine whether a gene has an eQTL in a given tissue.

thresh <- 0.05

Load data and mash results

Load some GTEx summary statistics, as well as some of the results generated from the mash analysis of the GTEx data.

out     <- readRDS("../data/MatrixEQTLSumStats.Portable.Z.rds")
maxbeta <- out$strong.b
maxz    <- out$strong.z
out <- readRDS(paste("../output/MatrixEQTLSumStats.Portable.Z.coved.K3.P3",
                     "lite.single.expanded.V1.posterior.rds",sep = "."))
lfsr           <- out$lfsr
pm.mash        <- out$posterior.means
standard.error <- maxbeta/maxz
pm.mash.beta   <- pm.mash * standard.error

Histograms of sharing by magnitude

Sharing by magnitude means that two eQTLs have similar effect size (within a factor of 2).

The histograms below summarize sharing by magnitude across all tissues (left), tissues other than brain (middle), and brain tissues only (right).

sigmat <- (lfsr <= thresh)
nsig   <- rowSums(sigmat)
par(mar = c(4,4,2,1))
par(oma = c(8,4,0,0) + 0.1)
par(mfrow = c(1,3))
hist((het.func(het.norm(effectsize=pm.mash.beta[nsig>0,]),threshold=0.5)),
     main="",xlab="",breaks=0.5:44.5,col="grey",freq=FALSE,ylim=c(0,0.9),
     xaxt="n")
axis(1,at = seq(1, 44, by=1),labels = c(1:44))
mtext("All Tissues")

sigmat <- (lfsr[,-c(7:16)] <= thresh)
nsig   <- rowSums(sigmat)
hist((het.func(het.norm(effectsize=pm.mash.beta[nsig>0,-c(7:16)]),
     threshold=0.5)),main="",xlab="",breaks=0.5:34.5,col="grey",
     freq=FALSE,ylim=c(0,0.9),xaxt="n")
axis(1,at = seq(1, 34, by=1),labels = c(1:34))
mtext("Non-Brain Tissues")

sigmat     <- (lfsr[,c(7:16)]<=thresh)
nsig       <-  rowSums(sigmat)
brain.norm <- het.norm(effectsize=pm.mash.beta[nsig>0,c(7:16)])
hist(het.func(brain.norm,threshold=0.5),main="",xlab="",breaks=0.5:10.5,
     col="grey",freq=FALSE,xaxt="n",ylim=c(0,0.9))
axis(1, at=seq(1, 10, by=1), labels=c(1:10))
mtext("Brain Tissues")

Expand here to see past versions of hindex-plot-magnitude-1.png:
Version Author Date
e37a93d Peter Carbonetto 2018-06-06

Observe that the distribution of the number of tissues in which an eQTL is shared by magnitude has a mode at 1. This is a subset of eQTLs that have much stronger effect in one tissue than in any other (“tissue-specific”).

Histogram of sharing by magnitude

Sharing by sign means that the eQTLs have the same sign of effect.

The histograms below summarize sharing by sign across all tissues (left), tissues other than brain (middle), and brain tissues only (right).

sign.func <- function (normeffectsize)
  apply(normeffectsize,1,function(x)(sum(x>0)))
sigmat <- (lfsr<=thresh)
nsig   <- rowSums(sigmat)
par(mar = c(4,4.5,2,1))
par(oma = c(8,4,0,0) + 0.1)
par(mfrow = c(1,3))
hist(sign.func(het.norm(effectsize=pm.mash.beta[nsig>0,])),main="",xlab="",
     breaks=0.5:44.5,col="grey",freq=FALSE,xaxt="n",ylim=c(0,0.9))
axis(1, at=seq(1, 44, by=1), labels=c(1:44))
mtext("All Tissues")

sigmat <- (lfsr[,-c(7:16)] <= thresh)
nsig   <- rowSums(sigmat)
hist(sign.func(het.norm(effectsize = pm.mash.beta[nsig>0,-c(7:16)])),
     main="",xlab="",breaks=0.5:34.5,col="grey",freq=FALSE,ylim=c(0,0.9),
     xaxt="n")
axis(1, at=seq(1, 34, by=1), labels=c(1:34))
mtext("Non-Brain Tissues")

sigmat     <- (lfsr[,c(7:16)]<=thresh)
nsig       <-  rowSums(sigmat)
brain.norm <- het.norm(effectsize=pm.mash.beta[nsig>0,c(7:16)])
hist(sign.func(brain.norm),main="",xlab="",breaks=0.5:10.5,col="grey",
     freq=FALSE,xaxt="n",ylim=c(0,0.9))
axis(1, at=seq(1, 10, by=1), labels=c(1:10))
mtext("Brain Tissues")

Expand here to see past versions of hindex-plot-sign-1.png:
Version Author Date
e37a93d Peter Carbonetto 2018-06-06

Similar to other summaries of the mash analysis, we see that eQTLs exhibit a high level of sharing across tissues.

Session information

sessionInfo()
# R version 3.4.3 (2017-11-30)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS High Sierra 10.13.5
# 
# 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     
# 
# loaded via a namespace (and not attached):
#  [1] workflowr_1.0.1.9000 Rcpp_0.12.17         digest_0.6.15       
#  [4] rprojroot_1.3-2      R.methodsS3_1.7.1    backports_1.1.2     
#  [7] git2r_0.21.0         magrittr_1.5         evaluate_0.10.1     
# [10] stringi_1.1.7        whisker_0.3-2        R.oo_1.21.0         
# [13] R.utils_2.6.0        rmarkdown_1.9        tools_3.4.3         
# [16] stringr_1.3.0        yaml_2.1.18          compiler_3.4.3      
# [19] htmltools_0.3.6      knitr_1.20

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