Last updated: 2018-06-06

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Different levels of effect sharing among tissues means that effect estimates in some tissues gain more precision than others from the joint analysis. Here we quantify an “effective sample size” (ESS) per tissue and compare against the sample sizes in the data.

Load data and mash results

Load some of the results generated from the mas analysis of the GTEx data, as well as summary statistics (e.g., sample sizes, standard errors) calculated from the raw GTEx data.

missing.tissues <- c(7,8,19,20,24,25,31,34,37)
out     <- readRDS("../data/MatrixEQTLSumStats.Portable.Z.rds")
maxz    <- out$test.z
maxbeta <- out$test.b
qtl.names <- sapply(1:length(rownames(maxz)),
  function(x) unlist(strsplit(rownames(maxz)[x],"[_]"))[[1]])
standard.error.from.z <- as.matrix(maxbeta/maxz)
dat <- read.csv("../data/ExprSampleSize.csv.gz",header = TRUE)
rownames(dat) <- dat[,1]
expr.data <- dat[,-1]
expr.sort <- expr.data[rownames(expr.data)%in%qtl.names,]
a         <- match(qtl.names,rownames(expr.sort))
expr.sort <- expr.sort[a,]
exp.sort  <- expr.sort[,-missing.tissues]
colnames(exp.sort) <- colnames(maxz)
standard.error           <- out$test.s
colnames(standard.error) <- colnames(maxz)
tissue.names             <- colnames(maxz)

To draw the the bar charts, we use the colours that are used by convention used to represent the GTEx tissues in plots.

gtex.colors <- read.table('../data/GTExColors.txt',sep = '\t',
                          comment.char = '')[-missing.tissues,2]

Load the marginal posterior variances.

out <- readRDS(paste("../output/MatrixEQTLSumStats.Portable.Z.coved.K3.P3",
                     "lite.single.expanded.V1.posterior.rds",sep = "."))
marginal.var <- out$marginal.var

Now let’s plot effective sample size. Recall,

\[n_{jeff}=\frac{s_{j}^2}{\tilde{s_{j}^2}}\]

Let’s plot again with order by original sample size:

original.var <- as.matrix(standard.error.from.z)^2
size         <- as.matrix(exp.sort)
post.var     <- as.matrix(marginal.var) * standard.error.from.z^2
njeffective  <- size * original.var/post.var
increase     <- njeffective/size
par(mfrow=c(1,2))
samplesize=apply(size,2,unique)
sampleorder=order(samplesize,decreasing = T)
median.nj.effective=apply(njeffective,2,median)
median.nj.increase=apply(increase,2,median)
par(mar=c(5.1,8,4.1,0.1))
barplot(median.nj.effective[sampleorder],cex.names=0.4,las=2,
  col=as.character(gtex.colors[sampleorder]),horiz = TRUE)
title("Median(Nj_effective)",cex.main = 0.8)
par(mar=c(5.1,2,4.1,6))
barplot(median.nj.increase[sampleorder],cex.names=0.4,las=2,
  col=as.character(gtex.colors[sampleorder]),horiz = T,names="",xlim=c(16,0))
title("Median(Nj_effective/Nj_original)",cex.main=0.8)

par(mfrow=c(1,2))
samplesize=apply(size,2,function(x){unique(x)})
sampleorder=order(samplesize,decreasing = T)
median.nj.effective=apply(njeffective,2,median)
median.nj.increase=apply(increase,2,median)
par(mar=c(5.1,8,1.1,0.1))
barplot(samplesize[sampleorder],cex.names=0.4,las=2,
        col=as.character(gtex.colors[sampleorder]),horiz = T,xlim=c(0,2000))
title("Sample Size",cex.main=0.8)
par(mar=c(5.1,2,1.1,6))
barplot(median.nj.effective[sampleorder],cex.names=0.4,las=2,
        col=as.character(gtex.colors[sampleorder]),horiz = T,names="",
        xlim=c(0,2000))
title("Effective Sample Size",cex.main=0.8)

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

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