Tissue effective sample sizes

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$strong.z
maxbeta <- out$strong.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$strong.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

Compute effective sample sizes

Compute the effective sample sizes,

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

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

Next, order the tissues by the actual sample size.

samplesize          <- apply(size,2,unique)
sampleorder         <- order(samplesize,decreasing = TRUE)
median.nj.effective <- apply(njeffective,2,median)
median.nj.increase  <- apply(increase,2,median)

Plot effective sample sizes

Plot, for each tissue, the effective sample size, and the increase in the ESS over the actual sample sample size.

par(mfrow=c(1,2))
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)

We see that the ESS values are smallest for tissue that show more “tissue-specific” behaviour (e.g. testis, whole blood), and are largest for coronary artery, reflecting its stronger correlation with other tissues.

Plot effective sample sizes and actual sample sizes

Here we plot the actual sample size and median effective sample size of each tissue, in which the tissues are ordered by their original sample size.

par(mfrow = c(1,2))
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 = TRUE,
        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 = TRUE,
        names = "",xlim = c(0,2000))
title("Effective Sample Size",cex.main = 0.8)

Observe that the effective sample sizes are consistently higher than actual sample sizes, primarily due to sharing of information among 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