Overall sharing among top eQTLs

Set up environment

First, we load some functions defined for mash analyses.

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

This is the threshold used to determine which genes have at least one significant effect across tissues.

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$test.b
maxz           <- out$test.z
standard.error <- out$test.s
out  <- readRDS(paste("../output/MatrixEQTLSumStats.Portable.Z.coved.K3.P3",
                      "lite.single.expanded.V1.posterior.rds",sep = "."))
pm.mash        <- out$posterior.means
pm.mash.beta   <- pm.mash*standard.error
lfsr           <- out$lfsr
lfsr[lfsr < 0] <- 0
tissue.names   <- as.character(read.table("../data/abbreviate.names.txt")[,2])
colnames(lfsr) <- tissue.names

Load the results generated from the mash analysis of the GTEx data after removing the data from the brain tissues.

lfsr.nobrain           <- read.table("../output/nobrainlfsr.txt")[,-1]
colnames(lfsr.nobrain) <- tissue.names[-c(7:16)]
pm.mash.nobrain <-
  as.matrix(read.table("../output/nobrainposterior.means.txt")[,-1]) *
    standard.error[,-c(7:16)]

Load the results generated from the mash analysis of the GTEx data for the brain tissues only.

lfsr.brain.only           <- read.table("../output/brainonlylfsr.txt")[,-1]
colnames(lfsr.brain.only) <- tissue.names[c(7:16)]
pm.mash.brain.only <-
  as.matrix(read.table("../output/brainonlyposterior.means.txt")[,-1]) *
    standard.error[,c(7:16)]

Compute overall sharing of eQTLs by sign and magnitude

Compute the amount of sharing by sign, in all tissues, and separately in brain and non-brain tissues. Sharing by sign requires that the effect has the same sign as the strongest effect among tissues.

sigmat  <- (lfsr<=thresh)
nsig    <-  rowSums(sigmat)
signall <- mean(het.norm(pm.mash.beta[nsig>0,])>0)

sigmat          <- (lfsr[,-c(7:16)]<=thresh)
nsig            <-  rowSums(sigmat)
signall.nobrain <- mean(het.norm(pm.mash.beta[nsig,-c(7:16)])>0)

sigmat            <- (lfsr[,c(7:16)]<=thresh)
nsig              <- rowSums(sigmat)
signall.brainonly <- mean(het.norm(pm.mash.beta[nsig>0,c(7:16)])>0)

sigmat      <- (lfsr.nobrain<=thresh)
nsig        <- rowSums(sigmat)
signnobrain <- mean(het.norm(pm.mash.nobrain[nsig>0,])>0)

sigmat        <- (lfsr.brain.only<=thresh)
nsig          <- rowSums(sigmat)
signbrainonly <- mean(het.norm(pm.mash.brain.only[nsig>0,])>0)

Compute the amount of sharing by magnitude, in all tissues, and separately in brain and non-brain tissues. “Sharing by Magnitude” requires that the effect is also within a factor of 2 of the strongest effect.

sigmat <- (lfsr<=thresh)
nsig   <- rowSums(sigmat)
magall <- mean(het.norm(pm.mash.beta[nsig>0,])>0.5)

sigmat <- (lfsr[,-c(7:16)]<=thresh)
nsig   <- rowSums(sigmat)
magall.excludingbrain <- mean(het.norm(pm.mash.beta[nsig>0,-c(7:16)]) > 0.5)

sigmat <- (lfsr[,c(7:16)]<=thresh)
nsig   <- rowSums(sigmat)
magall.brainonly <- mean(het.norm(pm.mash.beta[nsig>0,c(7:16)]) > 0.5)

sigmat     <- (lfsr.nobrain<=thresh)
nsig       <- rowSums(sigmat)
magnobrain <- mean(het.norm(pm.mash.nobrain[nsig>0,]) > 0.5)

sigmat   <- (lfsr.brain.only<=thresh)
nsig     <- rowSums(sigmat)
magbrain <- mean(het.norm(pm.mash.brain.only[nsig>0,]) > 0.5)

Summarize these calculations in a single table. The numbers in parentheses are obtained by the secondary mash analyses on the brain-only and non-brain tissue subsets.

round(matrix(rbind(c(signall,signall.nobrain,signnobrain,
               signall.brainonly,signbrainonly),
             c(magall,magall.excludingbrain,magnobrain,
               magall.brainonly,magbrain)),
         nrow = 2,ncol = 5,
         dimnames = list(c("shared by sign","shared by magnitude"),
                         c("all tissues","non-brain","(non-brain)",
                           "brain","(brain)"))),
      digits = 3)
#                     all tissues non-brain (non-brain) brain (brain)
# shared by sign            0.850     0.849       0.882 0.959   0.984
# shared by magnitude       0.359     0.398       0.445 0.764   0.859

The results confirm extensive eQTL sharing among tissues, particularly among the brain tissues; sharing in sign exceeds 85% in all cases, and is as high as 98% among the brain tissues.

Sharing in magnitude is inevitably lower, because sharing in magnitude implies sharing in sign. Overall, on average 37% of tissues show an effect within a factor of 2 of the strongest effect at each top eQTL.

However, within brain tissues this number increases to 78%. That is, not only do eQTLs tend to be shared among the brain tissues, but the effect sizes tend to be quite homogeneous.

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 10.13.4
# 
# 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     
# 
# 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    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