GTEx V6

Last updated: 2019-01-01

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```
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File	Version	Author	Date	Message
Rmd	26398fd	zouyuxin	2019-01-01	wflow_publish(“analysis/GTExV6.Rmd”)

library(flashr)
library(mixsqp)
library(mashr)

Loading required package: ashr

library(mclust)

Package 'mclust' version 5.4.1
Type 'citation("mclust")' for citing this R package in publications.


Attaching package: 'mclust'

The following object is masked from 'package:ashr':

    dens

library(knitr)
library(kableExtra)
library(ggplot2)

gtex <- readRDS(gzcon(url("https://github.com/stephenslab/gtexresults/blob/master/data/MatrixEQTLSumStats.Portable.Z.rds?raw=TRUE")))

strong.z = gtex$strong.z
data.strong = mash_set_data(strong.z)
data.random = mash_set_data(gtex$random.b, gtex$random.s)

Data Driven Covariances

Flash:

my_init_fn <- function(Y, K = 1) {
  ret = flashr:::udv_si(Y, K)
  pos_sum = sum(ret$v[ret$v > 0])
  neg_sum = -sum(ret$v[ret$v < 0])
  if (neg_sum > pos_sum) {
    return(list(u = -ret$u, d = ret$d, v = -ret$v))
  } else
    return(ret)
}

flash_pipeline = function(data, ...) {
  ## current state-of-the art
  ## suggested by Jason Willwerscheid
  ## cf: discussion section of
  ## https://willwerscheid.github.io/MASHvFLASH/MASHvFLASHnn2.html
  ebnm_fn = "ebnm_ash"
  ebnm_param = list(l = list(mixcompdist = "normal",
                             optmethod = "mixSQP"),
                    f = list(mixcompdist = "+uniform",
                             optmethod = "mixSQP"))
  ##
  fl_g <- flashr:::flash_greedy_workhorse(data,
                                          var_type = "constant",
                                          ebnm_fn = ebnm_fn,
                                          ebnm_param = ebnm_param,
                                          init_fn = "my_init_fn",
                                          stopping_rule = "factors",
                                          tol = 1e-3,
                                          verbose_output = "odF")
  fl_b <- flashr:::flash_backfit_workhorse(data,
                                           f_init = fl_g,
                                           var_type = "constant",
                                           ebnm_fn = ebnm_fn,
                                           ebnm_param = ebnm_param,
                                           stopping_rule = "factors",
                                           tol = 1e-3,
                                           verbose_output = "odF")
  return(fl_b)
}


cov_flash = function(data, subset = NULL, non_canonical = FALSE, save_model = NULL) {
  if(is.null(subset)) subset = 1:mashr:::n_effects(data)
  b.center = apply(data$Bhat, 2, function(x) x - mean(x))
  ## Only keep factors with at least two values greater than 1 / sqrt(n)
  find_nonunique_effects <- function(fl) {
    thresh <- 1/sqrt(ncol(fl$fitted_values))
    vals_above_avg <- colSums(fl$ldf$f > thresh)
    nonuniq_effects <- which(vals_above_avg > 1)
    return(fl$ldf$f[, nonuniq_effects, drop = FALSE])
  }
  fmodel = flash_pipeline(b.center)
  if (non_canonical)
    flash_f = find_nonunique_effects(fmodel)
  else 
    flash_f = fmodel$ldf$f
  ## row.names(flash_f) = colnames(b)
  if (!is.null(save_model)) saveRDS(list(model=fmodel, factors=flash_f), save_model)
  if(ncol(flash_f) == 0){
    U.flash = list("tFLASH" = t(fmodel$fitted_values) %*% fmodel$fitted_values / nrow(fmodel$fitted_values))
  } else{
    U.flash = c(cov_from_factors(t(as.matrix(flash_f)), "FLASH"),
  list("tFLASH" = t(fmodel$fitted_values) %*% fmodel$fitted_values / nrow(fmodel$fitted_values)))
  }
  
  return(U.flash)
}

U.f = cov_flash(data.strong, non_canonical = TRUE, save_model = '../output/GTExV6/flash_model.rds')
saveRDS(U.f, 'output/GTExV6/flash_cov.rds')

missing.tissues <- c(7, 8, 19, 20, 24, 25, 31, 34, 37)
gtex.colors <- read.table("https://github.com/stephenslab/gtexresults/blob/master/data/GTExColors.txt?raw=TRUE", sep = '\t', comment.char = '')[-missing.tissues, 2]
gtex.colors <- as.character(gtex.colors)

fl_model = readRDS('output/GTExV6/flash_model.rds')$model
factors = readRDS('output/GTExV6/flash_model.rds')$factors
par(mfrow = c(2, 3))
for(k in 1:16){
  barplot(factors[,k], col=gtex.colors, names.arg = FALSE, axes = FALSE, main=paste0("Factor ", k))
}

fll_model = flash_pipeline(fl_model$ldf$l)
saveRDS(fll_model, 'output/GTExV6/flash_loading_model.rds')

U.pca = cov_pca(data.strong, 5)

U.ed = cov_ed(data.strong, c(U.f, U.pca))

U.ed = readRDS('output/GTExV6/Ued.rds')

U.c = cov_canonical(data.random)

data.strong = mash_set_data(Bhat = gtex$strong.b, Shat = gtex$strong.s)

m.ignore = mash(data.random, c(U.c, U.ed), outputlevel = 1)
m.ignore$result = mash_compute_posterior_matrices(m.ignore, data.strong)

V.simple = estimate_null_correlation_simple(data.random)

data.random.V.simple = mash_update_data(data.random, V = V.simple)
m.simple = mash(data.random.V.simple, c(U.c, U.ed), outputlevel = 1)
data.strong.V.simple = mash_update_data(data.strong, V = V.simple)
m.simple$result = mash_compute_posterior_matrices(m.simple, data.strong.V.simple)

set.seed(1)
random.subset = sample(1:nrow(gtex$random.b),5000)
data.random.s = mash_set_data(gtex$random.b[random.subset,], gtex$random.s[random.subset,])
current = estimate_null_correlation(data.random.s, c(U.c, U.ed), max_iter = 6)
V.current = current$V
data.random.V.current = mash_update_data(data.random, V = V.current)
m.current = mash(data.random.V.current, c(U.c, U.ed), outputlevel = 1)
data.strong = mash_update_data(data.strong, V = V.current)
m.current$result = mash_compute_posterior_matrices(m.current, data.strong)

V = get(load('~/Documents/GitHub/GTEx/data/genewide_ash_out_tissue_mat_halfuniform_non_mode.rda'))
# select tissue
tissue_labels <- read.table(file = "~/Documents/GitHub/GTEx/data/samples_id.txt")[,3]
U <- unique(tissue_labels)
tissues = c(1:6, 9:18, 21:23,26:30,32:33,35:36,38:53)
V = V[tissues,tissues,]

V.strong = V
for(i in 1:nrow(gtex$strong.b)){
  V.strong[,,i] = as.matrix(Matrix::nearPD(V[,,i], conv.tol=1.e-05, corr = TRUE, maxit = 200, doSym = TRUE)$mat)
}
saveRDS(V.strong, 'output/GTExV6/V_strong_genewide.rds')

# select genes
gene_names <- as.character(read.table(file = "~/Documents/GitHub/GTEx/data/gene_names_GTEX_V6.txt")[,1])
gene_names_1 <- as.character(sapply(gene_names, function(x) return(strsplit(x, "[.]")[[1]][1])))

data.random.names = rownames(data.random$Bhat)
data.random.names.1 = as.character(sapply(data.random.names, function(x) return(strsplit(x, "[.]")[[1]][1])))

V.random = array(NA, dim = c(44,44,nrow(gtex$random.b)))
for(i in 1:nrow(gtex$random.b)){
  numg <- grep(data.random.names.1[i], gene_names_1)
  V.random[,,i] = as.matrix(Matrix::nearPD(V[,,numg], conv.tol=1.e-05, corr = TRUE, doSym = TRUE)$mat)
}
saveRDS(V.random, 'output/GTExV6/V_random_genewide.rds')

data.random.V3 = mash_update_data(data.random, V = V.random)
m.V3 = mash(data.random.V3, c(U.c, U.ed), outputlevel = 1, algorithm.version = 'R')
data.strong.V3 = mash_update_data(data.strong, V = V.strong)
m.V3$result = mash_compute_posterior_matrices(m.V3, data.strong.V3, algorithm.version = 'R')

# read model
m_ignore = readRDS('output/GTExV6/m_ignore_post.rds')
m_ignore_EZ = readRDS('output/GTExV6/m_ignore_EZ_post.rds')
m_simple = readRDS('output/GTExV6/m_simple_post.rds')
m_simple_EZ = readRDS('output/GTExV6/m_simple_EZ_post.rds')
m_current = readRDS('output/GTExV6/m_current_post.rds')
m_current_EZ = readRDS('output/GTExV6/m_current_EZ_post.rds')
m_V3 = readRDS('output/GTExV6/m_V3_genewide_post.rds')
m_V3_EZ = readRDS('output/GTExV6/m_V3_genewide_EZ_post.rds')

par(mfrow = c(1,2))
# pdf('../output/GTExV6/Figures/SimpleV.pdf')
corrplot::corrplot(V.simple, method='color', type='upper', tl.col="black", tl.srt=45, tl.cex = 0.7, diag = FALSE, col=colorRampPalette(c("blue", "white", "red"))(200), cl.lim = c(-1,1), title = 'Simple', mar=c(0,0,5,0))

Warning in corrplot::corrplot(V.simple, method = "color", type = "upper", :
Not been able to calculate text margin, please try again with a clean new
empty window using {plot.new(); dev.off()} or reduce tl.cex

# dev.off()

V.current = readRDS('output/GTExV6/currentV_EZ.rds')
V.current = V.current$V
# pdf('../output/GTExV6/Figures/CurrentEZV.pdf')
corrplot::corrplot(V.current, method='color', type='upper', tl.col="black", tl.srt=45, tl.cex = 0.7, diag = FALSE, col=colorRampPalette(c("blue", "white", "red"))(200), cl.lim = c(-1,1), title = 'Current EZ', mar=c(0,0,5,0))

Warning in corrplot::corrplot(V.current, method = "color", type =
"upper", : Not been able to calculate text margin, please try again with a
clean new empty window using {plot.new(); dev.off()} or reduce tl.cex

# dev.off()

logliks = c(get_loglik(m_ignore), get_loglik(m_simple), get_loglik(m_current), get_loglik(m_V3))
logliks_EZ = c(get_loglik(m_ignore_EZ), get_loglik(m_simple_EZ), get_loglik(m_current_EZ), get_loglik(m_V3_EZ))
tmp = cbind(logliks, logliks_EZ)
row.names(tmp) = c('Ignore', 'Simple', 'Current', 'V3')
colnames(tmp) = c('EE', 'EZ')
tmp %>% kable() %>% kable_styling()

	EE	EZ
Ignore	929188.2	935288.4
Simple	933359.2	936783.2
Current	937323.7	939685.2
V3	860927.1	897029.6

barplot(get_estimated_pi(m_ignore), las=2, cex.names = 0.7, main = 'Ignore EE')

barplot(get_estimated_pi(m_simple), las=2, cex.names = 0.7, main = 'Simple EE')

barplot(get_estimated_pi(m_current), las=2, cex.names = 0.7, main = 'Current EE')

barplot(get_estimated_pi(m_V3), las=2, cex.names = 0.7, main = 'V3 EE')

barplot(get_estimated_pi(m_ignore_EZ), las=2, cex.names = 0.7, main = 'Ignore EZ')

barplot(get_estimated_pi(m_simple_EZ), las=2, cex.names = 0.7, main = 'Simple EZ')

barplot(get_estimated_pi(m_current_EZ), las=2, cex.names = 0.7, main = 'Current EZ')

barplot(get_estimated_pi(m_V3_EZ), las=2, cex.names = 0.7, main = 'V3 EZ')

Number of significant:

numsig_EE = c(length(get_significant_results(m_ignore)), 
              length(get_significant_results(m_simple)), 
              length(get_significant_results(m_current)), 
              length(get_significant_results(m_V3)))
numsig_EZ = c(length(get_significant_results(m_ignore_EZ)), 
              length(get_significant_results(m_simple_EZ)), 
              length(get_significant_results(m_current_EZ)), 
              length(get_significant_results(m_V3_EZ)))
tmp = cbind(numsig_EE, numsig_EZ)
row.names(tmp) = c('Ignore', 'Simple', 'Current', 'V3')
colnames(tmp) = c('EE', 'EZ')
tmp %>% kable() %>% kable_styling()

	EE	EZ
Ignore	14017	14221
Simple	13037	13485
Current	12803	13006
V3	16054	16069

The V3 model has more significant findings, which includes all significant findings in the other three models.

length(intersect(get_significant_results(m_V3_EZ), get_significant_results(m_current_EZ)))

[1] 13006

length(intersect(get_significant_results(m_V3_EZ), get_significant_results(m_simple_EZ)))

[1] 13485

length(intersect(get_significant_results(m_V3_EZ), get_significant_results(m_ignore_EZ)))

[1] 14221

The gene significant in simple EZ, not in current EZ:

par(mfrow=c(2,2))
stronggene = data.frame(gtex$strong.b[5034,])
colnames(stronggene) = 'EffectSize'
stronggene$Group = row.names(stronggene)
stronggene$se = gtex$strong.s[5034,]
ggplot(stronggene, aes(y = EffectSize, x = Group)) + 
  geom_point(show.legend = FALSE, color=gtex.colors) + coord_flip() + ggtitle('ENSG00000135315') + ylim(c(-0.7,1)) + geom_errorbar(aes(ymin=EffectSize-1.96*se, ymax=EffectSize+1.96*se), width=0.4, show.legend = FALSE, color=gtex.colors) + 
  theme_bw(base_size=12) + theme(axis.text.y = element_text(colour = gtex.colors, size = 6))

stronggeneSimple = data.frame(m_simple_EZ$result$PosteriorMean[5034,])
colnames(stronggeneSimple) = 'EffectSize'
stronggeneSimple$Group = row.names(stronggeneSimple)
stronggeneSimple$se = m_simple_EZ$result$PosteriorSD[5034,]
ggplot(stronggeneSimple, aes(y = EffectSize, x = Group)) + 
  geom_point(show.legend = FALSE, color=gtex.colors) + coord_flip() + ggtitle('ENSG00000135315 Simple') + ylim(c(-0.7,1)) + 
  geom_errorbar(aes(ymin=EffectSize-1.96*se, ymax=EffectSize+1.96*se), width=0.4, show.legend = FALSE, color=gtex.colors) + 
  theme_bw(base_size=12) + theme(axis.text.y = element_text(colour = gtex.colors, size = 6))

stronggeneCurrent = data.frame(m_current_EZ$result$PosteriorMean[5034,])
colnames(stronggeneCurrent) = 'EffectSize'
stronggeneCurrent$Group = row.names(stronggeneCurrent)
stronggeneCurrent$se = m_current_EZ$result$PosteriorSD[5034,]
ggplot(stronggeneCurrent, aes(y = EffectSize, x = Group)) + 
  geom_point(show.legend = FALSE, color=gtex.colors) + ylim(c(-0.7,1)) + coord_flip() + ggtitle('ENSG00000135315 Current') + 
  geom_errorbar(aes(ymin=EffectSize-1.96*se, ymax=EffectSize+1.96*se), width=0.4, show.legend = FALSE, color=gtex.colors) + 
  theme_bw(base_size=12) + theme(axis.text.y = element_text(colour = gtex.colors, size = 6))

stronggeneV3 = data.frame(m_V3_EZ$result$PosteriorMean[5034,])
colnames(stronggeneV3) = 'EffectSize'
stronggeneV3$Group = row.names(stronggeneV3)
stronggeneV3$se = m_V3_EZ$result$PosteriorSD[5034,]
ggplot(stronggeneV3, aes(y = EffectSize, x = Group)) + 
  geom_point(show.legend = FALSE, color=gtex.colors) + ylim(c(-0.7,1)) + coord_flip() + ggtitle('ENSG00000135315 V3') + 
  geom_errorbar(aes(ymin=EffectSize-1.96*se, ymax=EffectSize+1.96*se), width=0.4, show.legend = FALSE, color=gtex.colors) + 
  theme_bw(base_size=12) + theme(axis.text.y = element_text(colour = gtex.colors, size = 6))

The gene MCPH1:

par(mfrow=c(1,3))
stronggene = data.frame(gtex$strong.b[13837,])
colnames(stronggene) = 'EffectSize'
stronggene$Group = row.names(stronggene)
stronggene$se = gtex$strong.s[13837,]
ggplot(stronggene, aes(y = EffectSize, x = Group)) + 
  geom_point(show.legend = FALSE, color=gtex.colors) + coord_flip() + ggtitle('ENSG00000249898') + ylim(c(-1.3,1.1)) + geom_errorbar(aes(ymin=EffectSize-1.96*se, ymax=EffectSize+1.96*se), width=0.4, show.legend = FALSE, color=gtex.colors) + 
  theme_bw(base_size=12) + theme(axis.text.y = element_text(colour = gtex.colors, size = 6))

stronggeneCurrent = data.frame(m_current_EZ$result$PosteriorMean[13837,])
colnames(stronggeneCurrent) = 'EffectSize'
stronggeneCurrent$Group = row.names(stronggeneCurrent)
stronggeneCurrent$se = m_current_EZ$result$PosteriorSD[13837,]
ggplot(stronggeneCurrent, aes(y = EffectSize, x = Group)) + 
  geom_point(show.legend = FALSE, color=gtex.colors) + coord_flip() + ggtitle('ENSG00000249898 Current') + ylim(c(-1.3,1.1)) + 
  geom_errorbar(aes(ymin=EffectSize-1.96*se, ymax=EffectSize+1.96*se), width=0.4, show.legend = FALSE, color=gtex.colors) + 
  theme_bw(base_size=12) + theme(axis.text.y = element_text(colour = gtex.colors, size = 6))

stronggeneV3 = data.frame(m_V3_EZ$result$PosteriorMean[13837,])
colnames(stronggeneV3) = 'EffectSize'
stronggeneV3$Group = row.names(stronggeneV3)
stronggeneV3$se = m_V3_EZ$result$PosteriorSD[13837,]
ggplot(stronggeneV3, aes(y = EffectSize, x = Group)) + 
  geom_point(show.legend = FALSE, color=gtex.colors) + ylim(c(-1.3,1.1)) + coord_flip() + ggtitle('ENSG00000249898 V3') + 
  geom_errorbar(aes(ymin=EffectSize-1.96*se, ymax=EffectSize+1.96*se), width=0.4, show.legend = FALSE, color=gtex.colors) + 
  theme_bw(base_size=12) + theme(axis.text.y = element_text(colour = gtex.colors, size = 6))

The gene significant in V3 EZ, not in current EZ:

ind = setdiff(get_significant_results(m_V3_EZ), get_significant_results(m_current_EZ))[1]
par(mfrow=c(1,3))

stronggene = data.frame(gtex$strong.b[ind,])
colnames(stronggene) = 'EffectSize'
stronggene$Group = row.names(stronggene)
stronggene$se = gtex$strong.s[ind,]
ggplot(stronggene, aes(y = EffectSize, x = Group)) + 
  geom_point(show.legend = FALSE, color=gtex.colors) + coord_flip() + ggtitle('ENSG00000126243') + ylim(c(-1.3,1.1)) + geom_errorbar(aes(ymin=EffectSize-1.96*se, ymax=EffectSize+1.96*se), width=0.4, show.legend = FALSE, color=gtex.colors) + 
  theme_bw(base_size=12) + theme(axis.text.y = element_text(colour = gtex.colors, size = 6))

stronggeneCurrent = data.frame(m_current_EZ$result$PosteriorMean[ind,])
colnames(stronggeneCurrent) = 'EffectSize'
stronggeneCurrent$Group = row.names(stronggeneCurrent)
stronggeneCurrent$se = m_current_EZ$result$PosteriorSD[ind,]
ggplot(stronggeneCurrent, aes(y = EffectSize, x = Group)) + 
  geom_point(show.legend = FALSE, color=gtex.colors) + coord_flip() + ggtitle('ENSG00000126243 Current') + ylim(c(-1.3,1.1)) + 
  geom_errorbar(aes(ymin=EffectSize-1.96*se, ymax=EffectSize+1.96*se), width=0.4, show.legend = FALSE, color=gtex.colors) + 
  theme_bw(base_size=12) + theme(axis.text.y = element_text(colour = gtex.colors, size = 6))

stronggeneV3 = data.frame(m_V3_EZ$result$PosteriorMean[ind,])
colnames(stronggeneV3) = 'EffectSize'
stronggeneV3$Group = row.names(stronggeneV3)
stronggeneV3$se = m_V3_EZ$result$PosteriorSD[ind,]
ggplot(stronggeneV3, aes(y = EffectSize, x = Group)) + 
  geom_point(show.legend = FALSE, color=gtex.colors) + ylim(c(-1.3,1.1)) + coord_flip() + ggtitle('ENSG00000126243 V3') + 
  geom_errorbar(aes(ymin=EffectSize-1.96*se, ymax=EffectSize+1.96*se), width=0.4, show.legend = FALSE, color=gtex.colors) + 
  theme_bw(base_size=12) + theme(axis.text.y = element_text(colour = gtex.colors, size = 6))

The pairwise sharing by magnitude

par(mfrow = c(1,2))
x           <- get_pairwise_sharing(m_ignore_EZ)
colnames(x) <- colnames(get_lfsr(m_ignore_EZ))
rownames(x) <- colnames(x)
clrs=colorRampPalette(rev(c('darkred', 'red','orange','yellow','cadetblue1', 'cyan', 'dodgerblue4', 'blue','darkorchid1','lightgreen','green', 'forestgreen','darkolivegreen')))(200)

corrplot::corrplot(x, method='color', type='upper', tl.col="black", tl.srt=45, tl.cex = 0.7, diag = FALSE, col=clrs, cl.lim = c(0,1), title = 'Ignore EZ', mar=c(0,0,5,0))

Warning in corrplot::corrplot(x, method = "color", type = "upper", tl.col =
"black", : Not been able to calculate text margin, please try again with a
clean new empty window using {plot.new(); dev.off()} or reduce tl.cex

x           <- get_pairwise_sharing(m_simple_EZ)
colnames(x) <- colnames(get_lfsr(m_simple_EZ))
rownames(x) <- colnames(x)

corrplot::corrplot(x, method='color', type='upper', tl.col="black", tl.srt=45, tl.cex = 0.7, diag = FALSE, col=clrs, cl.lim = c(0,1), title = 'Simple EZ', mar=c(0,0,5,0))

Warning in corrplot::corrplot(x, method = "color", type = "upper", tl.col =
"black", : Not been able to calculate text margin, please try again with a
clean new empty window using {plot.new(); dev.off()} or reduce tl.cex

par(mfrow=c(1,2))
x           <- get_pairwise_sharing(m_current_EZ)
colnames(x) <- colnames(get_lfsr(m_current_EZ))
rownames(x) <- colnames(x)
corrplot::corrplot(x, method='color', type='upper', tl.col="black", tl.srt=45, tl.cex = 0.7, diag = FALSE, col=clrs, cl.lim = c(0,1), title = 'Current EZ', mar=c(0,0,5,0))

Warning in corrplot::corrplot(x, method = "color", type = "upper", tl.col =
"black", : Not been able to calculate text margin, please try again with a
clean new empty window using {plot.new(); dev.off()} or reduce tl.cex

x           <- get_pairwise_sharing(m_V3_EZ)
colnames(x) <- colnames(get_lfsr(m_V3_EZ))
rownames(x) <- colnames(x)
corrplot::corrplot(x, method='color', type='upper', tl.col="black", tl.srt=45, tl.cex = 0.7, diag = FALSE, col=clrs, cl.lim = c(0,1), title = 'V3 EZ', mar=c(0,0,5,0))

Warning in corrplot::corrplot(x, method = "color", type = "upper", tl.col =
"black", : Not been able to calculate text margin, please try again with a
clean new empty window using {plot.new(); dev.off()} or reduce tl.cex

Session information

sessionInfo()

R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.14.2

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/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     

other attached packages:
[1] ggplot2_3.1.0     kableExtra_0.9.0  knitr_1.20        mclust_5.4.1     
[5] mashr_0.2.19.0555 ashr_2.2-26       mixsqp_0.1-93     flashr_0.6-3     

loaded via a namespace (and not attached):
 [1] softImpute_1.4    tidyselect_0.2.5  corrplot_0.84    
 [4] purrr_0.2.5       reshape2_1.4.3    lattice_0.20-35  
 [7] colorspace_1.3-2  viridisLite_0.3.0 htmltools_0.3.6  
[10] yaml_2.2.0        rlang_0.3.0.1     R.oo_1.22.0      
[13] pillar_1.3.1      withr_2.1.2       glue_1.3.0       
[16] R.utils_2.7.0     bindrcpp_0.2.2    foreach_1.4.4    
[19] plyr_1.8.4        bindr_0.1.1       stringr_1.3.1    
[22] munsell_0.5.0     gtable_0.2.0      workflowr_1.1.1  
[25] rvest_0.3.2       R.methodsS3_1.7.1 mvtnorm_1.0-8    
[28] codetools_0.2-15  evaluate_0.12     labeling_0.3     
[31] pscl_1.5.2        doParallel_1.0.14 parallel_3.5.1   
[34] highr_0.7         Rcpp_1.0.0        readr_1.1.1      
[37] scales_1.0.0      backports_1.1.2   rmeta_3.0        
[40] truncnorm_1.0-8   abind_1.4-5       hms_0.4.2        
[43] digest_0.6.18     stringi_1.2.4     dplyr_0.7.6      
[46] grid_3.5.1        rprojroot_1.3-2   tools_3.5.1      
[49] magrittr_1.5      lazyeval_0.2.1    tibble_1.4.2     
[52] crayon_1.3.4      whisker_0.3-2     pkgconfig_2.0.2  
[55] MASS_7.3-50       Matrix_1.2-14     xml2_1.2.0       
[58] SQUAREM_2017.10-1 httr_1.3.1        rstudioapi_0.8   
[61] assertthat_0.2.0  rmarkdown_1.10    iterators_1.0.10 
[64] R6_2.3.0          git2r_0.23.0      compiler_3.5.1

This reproducible R Markdown analysis was created with workflowr 1.1.1

GTEx V6

Yuxin Zou

2018-12-20

Data Driven Covariances

Session information