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<h1 class="title toc-ignore">Table 2</h1>
<h4 class="author"><em>Yuxin Zou</em></h4>
<h4 class="date"><em>2018-2-1</em></h4>
</div>
<!-- Update knitr chunk options -->
<!-- Insert the date the file was last updated -->
<p><strong>Last updated:</strong> 2018-03-06</p>
<!-- Insert the code version (Git commit SHA1) if Git repository exists and R
package git2r is installed -->
<p><strong>Code version:</strong> 866f1eb</p>
<pre class="r"><code>library(gdata); library(mashr);library(flashr)</code></pre>
<pre><code>gdata: read.xls support for 'XLS' (Excel 97-2004) files ENABLED.</code></pre>
<pre><code></code></pre>
<pre><code>gdata: read.xls support for 'XLSX' (Excel 2007+) files ENABLED.</code></pre>
<pre><code>
Attaching package: 'gdata'</code></pre>
<pre><code>The following object is masked from 'package:stats':
nobs</code></pre>
<pre><code>The following object is masked from 'package:utils':
object.size</code></pre>
<pre><code>The following object is masked from 'package:base':
startsWith</code></pre>
<pre><code>Loading required package: ashr</code></pre>
<pre class="r"><code>library(mclust); library(plyr); library(corrplot)</code></pre>
<pre><code>Package 'mclust' version 5.4
Type 'citation("mclust")' for citing this R package in publications.</code></pre>
<pre><code>
Attaching package: 'mclust'</code></pre>
<pre><code>The following object is masked from 'package:ashr':
dens</code></pre>
<pre><code>corrplot 0.84 loaded</code></pre>
<pre class="r"><code>library(ggplot2); library(ggpubr)</code></pre>
<pre><code>Loading required package: magrittr</code></pre>
<div id="read-table-2" class="section level1">
<h1>Read Table 2</h1>
<pre class="r"><code>SupplTable2 = read.xls('../data/Suppl.Table.2.xlsx')
saveRDS(SupplTable2, '../data/SupplTable2.rds')</code></pre>
<p>There are missing value in the data. I guess this is caused by the 0 count, since the effect is <span class="math inline">\(\log_{2} (X_{1}/X_{2})\)</span>. We set these NAs to 0 with huge variance.</p>
<pre class="r"><code>Genename = as.character(SupplTable2$Gene.ID)
colname = colnames(SupplTable2)[seq(3,89,by=3)]
Tissue = gsub( "_.*$", "", colname)
p.value = SupplTable2[,seq(3,89,by=3)]
logFC = SupplTable2[,seq(4,89,by=3)]
missing = is.na(as.matrix(logFC))
p.value[is.na(as.matrix(p.value))] = 1
logFC[is.na(as.matrix(logFC))] = 0
row.names(p.value) = Genename
row.names(logFC) = Genename
colnames(p.value) = Tissue
colnames(logFC) = Tissue
saveRDS(list(logFC = as.matrix(logFC), pval = as.matrix(p.value), category = SupplTable2$category, region = SupplTable2$region, missing = missing), '../data/SupplTable2_0.rds')</code></pre>
<p>Since the sample size is large, we assume the p value is from normal distribution.</p>
<pre class="r"><code>mash.data = mash_set_data(Bhat = data$logFC, pval = data$pval)
# set large variance to missing data
mash.data$Shat[is.na(mash.data$Shat)] = 1000
mash.data$Shat[is.infinite(mash.data$Shat)] = 1000
# find strong genes
m.1by1 = mash_1by1(mash.data, alpha=0)
strong = get_significant_results(m.1by1, 0.01)
# estimate cor V on non strong genes
Z = mash.data$Bhat/mash.data$Shat
Z.null = Z[setdiff(1:349,strong),]</code></pre>
</div>
<div id="estimate-covariance-structure-using-strong-genes" class="section level1">
<h1>Estimate covariance structure using strong genes</h1>
<pre class="r"><code>Z.strong = Z[strong,]
# center
Z.center = apply(Z.strong, 2, function(x) x - mean(x))</code></pre>
<div id="flash" class="section level2">
<h2>Flash</h2>
<p><span class="math display">\[ \tilde{Z} = LF' + E \]</span> where F is <span class="math inline">\(29 \times K\)</span>, L is <span class="math inline">\(n \times K\)</span>, E is <span class="math inline">\(n\times 29\)</span>.</p>
<pre class="r"><code>mash_data_flash = flash_set_data(as.matrix(Z.center))
fmodel = flash(mash_data_flash, greedy = TRUE, backfit = TRUE)
saveRDS(fmodel, '../output/Flash_T2_0.rds')</code></pre>
<div id="flash-result" class="section level3">
<h3>Flash result</h3>
<p>The first factor explains the main proportion of variance in effects.</p>
<pre class="r"><code>flash_get_pve(fmodel)</code></pre>
<pre><code>[1] 0.786204732 0.009596396 0.011735441 0.008650019 0.003879352</code></pre>
<p>The first factor is the overall summary of treatment effects.</p>
<pre class="r"><code>factors = flash_get_ldf(fmodel)$f
row.names(factors) = colnames(data$logFC)
layout(matrix(c(1,2,3,4,5,6), 3, 2, byrow = TRUE))
for(i in 1:5){
barplot(factors[,i], las=2, main=paste0('Factor ', i), cex.names = 0.7)
}</code></pre>
<p><img src="figure/sexbias_Table2.Rmd/unnamed-chunk-12-1.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="clustering-loadings" class="section level3">
<h3>Clustering loadings</h3>
<pre class="r"><code>loading = fmodel$EL[,1:5]
row.names(loading) = rownames(Z.strong)
colnames(loading) = paste0('F',seq(1,5))
mod = Mclust(loading)
summary(mod$BIC)
saveRDS(mod, '../output/Flash_T2_0_mclust.rds')</code></pre>
<p>Using clustering result to fit <code>mash</code>:</p>
<p><span class="math display">\[l_{i}\sim \sum_{i=1}^{m}N(\mu_{i}, \Sigma_{i})\]</span> We estimate the covariance as <span class="math inline">\(F(\Sigma_i + \mu_{i}\mu_{i}')F'\)</span>.</p>
<pre class="r"><code>U_list = alply(mod$parameters$variance$sigma,3)
mu_list = alply(mod$parameters$mean,2)
ll = list()
for (i in 1:length(U_list)){
ll[[i]] = U_list[[i]] + mu_list[[i]] %*% t(mu_list[[i]])
}
U.loading = lapply(ll, function(U){factors %*% (U %*% t(factors))})
names(U.loading) = paste0('Load', "_", (1:length(U.loading)))
# rank 1
Flash_res = flash_get_lf(fmodel)
U.Flash = c(mashr::cov_from_factors(t(as.matrix(factors)), "Flash"),
list("tFlash" = t(Flash_res) %*% Flash_res / nrow(Z.center)))</code></pre>
</div>
</div>
<div id="pca" class="section level2">
<h2>PCA</h2>
<pre class="r"><code>U.pca = cov_pca(mash_set_data(Z.center), 7)</code></pre>
</div>
<div id="canonical" class="section level2">
<h2>Canonical</h2>
<pre class="r"><code>U.c = cov_canonical(mash_set_data(Z.center))</code></pre>
</div>
<div id="extreme-deconvolution" class="section level2">
<h2>Extreme Deconvolution</h2>
<pre class="r"><code>U.dd = c(U.pca, U.loading, U.Flash, list('XX' = t(Z.center) %*% Z.center / nrow(Z.center) ))
mash.data.ed = mash.data
mash.data.ed$Bhat = mash.data$Bhat[strong,]
mash.data.ed$Shat = mash.data$Shat[strong,]
mash.data.ed$Shat_alpha = mash.data$Shat_alpha[strong,]
saveRDS(cov_ed(mash.data.ed, U.dd), '../output/Mash_EE_Cov_0_plusR1.rds')</code></pre>
</div>
</div>
<div id="mash-model" class="section level1">
<h1>mash model</h1>
<pre class="r"><code>vhat = 1
if (vhat == 1) {
V = cor(Z.null)
} else {
V = diag(ncol(Z.null))
}
mash_data = mash_set_data(Bhat = mash.data$Bhat, Shat = mash.data$Shat, V = V, alpha = 0)
saveRDS(mash(mash_data, c(U.c, U.ed)), '../output/Mash_model_0_plusR1.rds') </code></pre>
<pre><code> - Computing 959 x 1711 likelihood matrix.
- Likelihood calculations took 17.60 seconds.
- Fitting model with 1711 mixture components.
- Model fitting took 15.55 seconds.
- Computing posterior matrices.
- Computation allocated took 3.72 seconds.</code></pre>
</div>
<div id="v1-ee-result" class="section level1">
<h1>V1 EE result</h1>
<p>The log-likelihood of fit is</p>
<pre class="r"><code>get_loglik(mash.model)</code></pre>
<pre><code>[1] -80852.06</code></pre>
<p>Here is a plot of weights learned.</p>
<pre class="r"><code>options(repr.plot.width=12, repr.plot.height=4)
barplot(get_estimated_pi(mash.model), las = 2, cex.names = 0.7)</code></pre>
<p><img src="figure/sexbias_Table2.Rmd/unnamed-chunk-23-1.png" width="672" style="display: block; margin: auto;" /></p>
<p>Check <code>ED_XX</code> and <code>ED_tPCA</code>:</p>
<pre class="r"><code>layout(matrix(c(1,2,3,4), 2, 2, byrow=TRUE))
svd.out = svd(mash.model$fitted_g$Ulist[["ED_XX"]])
v = svd.out$v
colnames(v) = colnames(get_lfsr(mash.model))
rownames(v) = colnames(v)
options(repr.plot.width=10, repr.plot.height=5)
for (j in 1:4)
barplot(v[,j]/v[,j][which.max(abs(v[,j]))], cex.names = 0.7,
las = 2, main = paste0("EigenVector ", j, " for XX"))</code></pre>
<p><img src="figure/sexbias_Table2.Rmd/unnamed-chunk-24-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre class="r"><code>svd.out = svd(mash.model$fitted_g$Ulist[["ED_tPCA"]])
v = svd.out$v
colnames(v) = colnames(get_lfsr(mash.model))
rownames(v) = colnames(v)
options(repr.plot.width=10, repr.plot.height=5)
for (j in 1:4)
barplot(v[,j]/v[,j][which.max(abs(v[,j]))], cex.names = 0.7,
las = 2, main = paste0("EigenVector ", j, " for tPCA"))</code></pre>
<p><img src="figure/sexbias_Table2.Rmd/unnamed-chunk-24-2.png" width="672" style="display: block; margin: auto;" /></p>
<p>Among the 959 genes, <code>MASH</code> found 372 to be significant in at least one treatment.</p>
<p>There are 84 effects are estimated as significant, even though they are originally missing! This is caused by the borrowing information from other samples.</p>
<p>The plot below compares the data with the <code>mash</code> output. The gene ASMT has lots of missing vales in tissues. The <code>mash</code> model estimates all effects as significant.</p>
<pre class="r"><code># before
gene667 = data.frame(mash.data$Bhat[667,])
colnames(gene667) = 'EffectSize'
gene667$Group = row.names(gene667)
gene667$se = data.frame(ifelse(mash.data$Shat[667,]>100, 0, mash.data$Shat[667,]))
gene667$EffectSize[gene667$se == 0] = NA
# after
gene667.post = data.frame(mash.model$result$PosteriorMean[667,])
colnames(gene667.post) = 'EffectSize'
gene667.post$Group = row.names(gene667)
gene667.post$se = data.frame(mash.model$result$PosteriorSD[667,])
p.orig = ggplot(gene667, aes(y = EffectSize, x = Group, color=Group)) +
geom_point() +
geom_errorbar(aes(ymin=EffectSize-1.96*se, ymax=EffectSize+1.96*se), width=0.4) +
theme_bw(base_size=12) + coord_flip() + ggtitle('ASMT original' )
p.post = ggplot(gene667.post, aes(y = EffectSize, x = Group, color=Group)) +
geom_point() +
geom_errorbar(aes(ymin=EffectSize-1.96*se, ymax=EffectSize+1.96*se), width=0.4) +
theme_bw(base_size=12) + coord_flip() + ggtitle('ASMT mash') + theme(legend.position = 'bottom')
ggarrange(p.orig, p.post, ncol=2, nrow=1, common.legend = TRUE, legend="right")</code></pre>
<pre><code>Warning: Removed 24 rows containing missing values (geom_point).</code></pre>
<pre><code>Warning: Removed 24 rows containing missing values (geom_errorbar).</code></pre>
<pre><code>Warning: Removed 24 rows containing missing values (geom_point).</code></pre>
<pre><code>Warning: Removed 24 rows containing missing values (geom_errorbar).</code></pre>
<p><img src="figure/sexbias_Table2.Rmd/unnamed-chunk-26-1.png" width="672" style="display: block; margin: auto;" /></p>
<p>Proportion of significantly biased (FDR < 1%) genes in each tissue by reported XCI status.</p>
<pre class="r"><code>Escape.prop = numeric(29)
for(i in 1:29){
Escape.prop[i] = length(which(data$category[get_significant_results(mash.model,0.01, conditions = i)] == 'Escape')) / length(which(data$category == 'Escape'))
}
Variable.prop = numeric(29)
for(i in 1:29){
Variable.prop[i] = length(which(data$category[get_significant_results(mash.model,0.01, conditions = i)] == 'Variable')) / length(which(data$category == 'Variable'))
}
Inac.prop = numeric(29)
for(i in 1:29){
Inac.prop[i] = length(which(data$category[get_significant_results(mash.model,0.01, conditions = i)] == 'Inactive')) / length(which(data$category == 'Inactive'))
}
Unknown.prop = numeric(29)
for(i in 1:29){
Unknown.prop[i] = length(which(data$category[get_significant_results(mash.model,0.01, conditions = i)] == 'Unknown')) / length(which(data$category == 'Unknown'))
}
prop = c(Escape.prop, Variable.prop, Inac.prop, Unknown.prop)
group = rep(c('Escape', 'Variable', 'Inactive', 'Unknown'), each=29)
boxplot(prop*100~group, ylab='Sex-bias per tissue (% of genes)')</code></pre>
<p><img src="figure/sexbias_Table2.Rmd/unnamed-chunk-27-1.png" width="672" style="display: block; margin: auto;" /></p>
<p>Sex biased expression is enriched in escape genes.</p>
</div>
<div id="session-information" class="section level1">
<h1>Session information</h1>
<!-- Insert the session information into the document -->
<pre class="r"><code>sessionInfo()</code></pre>
<pre><code>R version 3.4.3 (2017-11-30)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.3
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
other attached packages:
[1] ggpubr_0.1.6 magrittr_1.5 ggplot2_2.2.1 corrplot_0.84 plyr_1.8.4
[6] mclust_5.4 flashr_0.5-6 mashr_0.2-6 ashr_2.2-7 gdata_2.18.0
loaded via a namespace (and not attached):
[1] Rcpp_0.12.15 bindr_0.1 compiler_3.4.3
[4] git2r_0.20.0 iterators_1.0.9 tools_3.4.3
[7] digest_0.6.13 tibble_1.3.4 evaluate_0.10.1
[10] gtable_0.2.0 lattice_0.20-35 pkgconfig_2.0.1
[13] rlang_0.1.6 Matrix_1.2-12 foreach_1.4.4
[16] yaml_2.1.17 parallel_3.4.3 mvtnorm_1.0-7
[19] ebnm_0.1-10 bindrcpp_0.2 gridExtra_2.3
[22] dplyr_0.7.4 stringr_1.3.0 knitr_1.20
[25] REBayes_1.2 gtools_3.5.0 cowplot_0.9.2
[28] rprojroot_1.2 grid_3.4.3 glue_1.2.0
[31] R6_2.2.2 rmarkdown_1.8 rmeta_2.16
[34] purrr_0.2.4 backports_1.1.2 scales_0.5.0
[37] codetools_0.2-15 htmltools_0.3.6 MASS_7.3-47
[40] assertthat_0.2.0 softImpute_1.4 colorspace_1.3-2
[43] labeling_0.3 stringi_1.1.6 Rmosek_8.0.69
[46] lazyeval_0.2.1 doParallel_1.0.11 pscl_1.5.2
[49] munsell_0.4.3 truncnorm_1.0-8 SQUAREM_2017.10-1</code></pre>
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