Last updated: 2018-06-06

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Expand here to see past versions:
    File Version Author Date Message
    Rmd dae0caf Peter Carbonetto 2018-06-06 Renamed Tspecific analysis.
    html d2a04cf Peter Carbonetto 2018-06-06 I’ve completed a rewrite of the “tissue effective sample sizes”
    Rmd 680e18c Peter Carbonetto 2018-06-06 wflow_publish(“SampleSize.Rmd”)
    html 6d8379d Peter Carbonetto 2018-06-06 Re-built revised SampleSize page.
    Rmd 32c92c7 Peter Carbonetto 2018-06-06 wflow_publish(“SampleSize.Rmd”)
    Rmd 4eb658f Peter Carbonetto 2018-06-06 Code in SampleSize.Rmd now runs successfully; need to polish it up.
    html afc401f Peter Carbonetto 2017-09-20 Moved doc to docs.
    Rmd e1e48df Peter Carbonetto 2017-09-20 Reorganized many of the files.

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 actual sample sizes.

Compare the last plot, at the bottom of this page, against Supplementary Figure 1 in the manuscript.

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] <- dat[,-1]
expr.sort <-[rownames(,]
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

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.

  col=as.character(gtex.colors[sampleorder]),horiz = TRUE)
title("Median(Nj_effective)",cex.main = 0.8)
  col=as.character(gtex.colors[sampleorder]),horiz = T,names="",xlim=c(16,0))

Expand here to see past versions of plot1-1.png:
Version Author Date
d2a04cf Peter Carbonetto 2018-06-06
6d8379d Peter Carbonetto 2018-06-06

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))
        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)

Expand here to see past versions of plot2-1.png:
Version Author Date
d2a04cf Peter Carbonetto 2018-06-06
6d8379d Peter Carbonetto 2018-06-06

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

Session information

# 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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