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<h1 class="title toc-ignore">MASH Null – Real Data (GTEx random set)</h1>
<h4 class="author"><em>Yuxin Zou</em></h4>
<h4 class="date"><em>2018-08-29</em></h4>
</div>
<p><strong>Last updated:</strong> 2018-08-31</p>
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<p></details></p>
<hr />
<pre class="r"><code>library(mashr)</code></pre>
<pre><code>Loading required package: ashr</code></pre>
<pre class="r"><code>library(knitr)
library(kableExtra)</code></pre>
<p>There are two random sets in the <a href="https://github.com/stephenslab/gtexresults/blob/master/data/MatrixEQTLSumStats.Portable.Z.rds?raw=TRUE">GTEx summary data set</a>. We don’t know the null in the real data. If we have the individual level data, we can do a permutation to generate null. With the summary statistics, we select the null set using threshold on z scores.</p>
<p>Using qvalues 0.05 as the threshold, the corresponding non-significant |z| value is around 3.1. Since lfsr and lfdr are both more conservative than q values, we select the samples with <span class="math inline">\(\max_{r} |Z_{jr}| < 3.5\)</span> from each data set as the null set. We estimate data driven covariance matrices from data 1, estimate noise correlation from data 2, fit mash model on data 2 and calculate posterior on data 1.</p>
<pre class="r"><code>data = readRDS('../output/GTEx_3.5_nullData.rds')
model = readRDS('../output/GTEx_3.5_nullModel.rds')</code></pre>
<p>Sample size:</p>
<pre class="r"><code>samplesize = matrix(c(nrow(data$m.data1.null$Bhat), nrow(data$m.data2.null$Bhat)))
row.names(samplesize) = c('data 1', 'data 2')
samplesize %>% kable() %>% kable_styling()</code></pre>
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data 1
</td>
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18189
</td>
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data 2
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25718
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<pre class="r"><code>barplot(get_estimated_pi(model), las=2, cex.names = 0.7)</code></pre>
<p><img src="figure/MashLowSignalGTEx3.5.Rmd/unnamed-chunk-4-1.png" width="672" style="display: block; margin: auto;" /></p>
<p>The estimated weights <span class="math inline">\(\hat{\pi}\)</span> on null part is not large. The weight on the other covariance structures may concentrate on the small grid (small <span class="math inline">\(\omega_{l}\)</span>). So they are very close to null, but we cannot view it in the plot. I modified the <code>get_estimated_pi</code> function to have a threshold for grid. The weights on the grid less than the threshold are merged into the null part.</p>
<pre class="r"><code>get_estimated_pi = function(m, dimension = c("cov", "grid", "all"), thres = NULL){
dimension = match.arg(dimension)
if (dimension == "all") {
get_estimated_pi_no_collapse(m)
}
else {
g = get_fitted_g(m)
pihat = g$pi
pihat_names = NULL
pi_null = NULL
if (g$usepointmass) {
pihat_names = c("null", pihat_names)
pi_null = pihat[1]
pihat = pihat[-1]
}
pihat = matrix(pihat, nrow = length(g$Ulist))
if(!is.null(thres)){
pi_null = sum(pihat[, g$grid <= thres]) + pi_null
pihat = pihat[, g$grid > thres]
}
if (dimension == "cov"){
pihat = rowSums(pihat)
pihat_names = c(pihat_names, names(g$Ulist))
}
else if (dimension == "grid") {
pihat = colSums(pihat)
pihat_names = c(pihat_names, 1:length(g$grid))
}
pihat = c(pi_null, pihat)
names(pihat) = pihat_names
return(pihat)
}
}</code></pre>
<pre class="r"><code>barplot(get_estimated_pi(model, thres = 0.01), las=2, cex.names = 0.7)</code></pre>
<p><img src="figure/MashLowSignalGTEx3.5.Rmd/unnamed-chunk-6-1.png" width="672" style="display: block; margin: auto;" /></p>
<details> <summary><em>Expand here to see past versions of unnamed-chunk-6-1.png:</em></summary>
<table style="border-collapse:separate; border-spacing:5px;">
<thead>
<tr>
<th style="text-align:left;">
Version
</th>
<th style="text-align:left;">
Author
</th>
<th style="text-align:left;">
Date
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/zouyuxin/mash_application/blob/e9f5a3480a5a6f13c7a1f3c63b451c6d33b3fd4a/docs/figure/MashLowSignalGTEx3.5.Rmd/unnamed-chunk-6-1.png" target="_blank">e9f5a34</a>
</td>
<td style="text-align:left;">
zouyuxin
</td>
<td style="text-align:left;">
2018-08-30
</td>
</tr>
</tbody>
</table>
<p></details></p>
<p>The correlation for the <code>ED_tPCA</code> is</p>
<pre class="r"><code>corrplot::corrplot(cov2cor(model$fitted_g$Ulist[['ED_tPCA']]))</code></pre>
<p><img src="figure/MashLowSignalGTEx3.5.Rmd/unnamed-chunk-7-1.png" width="672" style="display: block; margin: auto;" /></p>
<details> <summary><em>Expand here to see past versions of unnamed-chunk-7-1.png:</em></summary>
<table style="border-collapse:separate; border-spacing:5px;">
<thead>
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<th style="text-align:left;">
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Author
</th>
<th style="text-align:left;">
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</th>
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</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/zouyuxin/mash_application/blob/e9f5a3480a5a6f13c7a1f3c63b451c6d33b3fd4a/docs/figure/MashLowSignalGTEx3.5.Rmd/unnamed-chunk-7-1.png" target="_blank">e9f5a34</a>
</td>
<td style="text-align:left;">
zouyuxin
</td>
<td style="text-align:left;">
2018-08-30
</td>
</tr>
</tbody>
</table>
<p></details></p>
<p>There are 483 significant samples in data 1.</p>
<div id="permute-samples-in-each-condition-to-break-the-sharing" class="section level2">
<h2>Permute samples in each condition to break the sharing</h2>
<p><code>mash</code> increases power, because it considers the sharing among conditions. We permute samples in each condition to break the sharing.</p>
<pre class="r"><code>data = readRDS('../output/GTEx_3.5_nullPermData.rds')
model = readRDS('../output/GTEx_3.5_nullPermModel.rds')</code></pre>
<p>Sample size:</p>
<pre class="r"><code>samplesize = matrix(c(nrow(data$m.data1.p.null$Bhat), nrow(data$m.data2.p.null$Bhat)))
row.names(samplesize) = c('data 1', 'data 2')
samplesize %>% kable() %>% kable_styling()</code></pre>
<table class="table" style="margin-left: auto; margin-right: auto;">
<tbody>
<tr>
<td style="text-align:left;">
data 1
</td>
<td style="text-align:right;">
18189
</td>
</tr>
<tr>
<td style="text-align:left;">
data 2
</td>
<td style="text-align:right;">
25718
</td>
</tr>
</tbody>
</table>
<pre class="r"><code>barplot(get_estimated_pi(model), las=2, cex.names = 0.7, main = 'Estiamted pi')</code></pre>
<p><img src="figure/MashLowSignalGTEx3.5.Rmd/unnamed-chunk-10-1.png" width="672" style="display: block; margin: auto;" /></p>
<details> <summary><em>Expand here to see past versions of unnamed-chunk-10-1.png:</em></summary>
<table style="border-collapse:separate; border-spacing:5px;">
<thead>
<tr>
<th style="text-align:left;">
Version
</th>
<th style="text-align:left;">
Author
</th>
<th style="text-align:left;">
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</th>
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</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/zouyuxin/mash_application/blob/e9f5a3480a5a6f13c7a1f3c63b451c6d33b3fd4a/docs/figure/MashLowSignalGTEx3.5.Rmd/unnamed-chunk-10-1.png" target="_blank">e9f5a34</a>
</td>
<td style="text-align:left;">
zouyuxin
</td>
<td style="text-align:left;">
2018-08-30
</td>
</tr>
</tbody>
</table>
<p></details></p>
<pre class="r"><code>barplot(get_estimated_pi(model, thres = 0.01), las=2, cex.names = 0.7, main='Estimated pi with threshold (0.01) in scale')</code></pre>
<p><img src="figure/MashLowSignalGTEx3.5.Rmd/unnamed-chunk-11-1.png" width="672" style="display: block; margin: auto;" /></p>
<details> <summary><em>Expand here to see past versions of unnamed-chunk-11-1.png:</em></summary>
<table style="border-collapse:separate; border-spacing:5px;">
<thead>
<tr>
<th style="text-align:left;">
Version
</th>
<th style="text-align:left;">
Author
</th>
<th style="text-align:left;">
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</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/zouyuxin/mash_application/blob/e9f5a3480a5a6f13c7a1f3c63b451c6d33b3fd4a/docs/figure/MashLowSignalGTEx3.5.Rmd/unnamed-chunk-11-1.png" target="_blank">e9f5a34</a>
</td>
<td style="text-align:left;">
zouyuxin
</td>
<td style="text-align:left;">
2018-08-30
</td>
</tr>
</tbody>
</table>
<p></details></p>
<p>There are 44 significant samples in data 1.</p>
<p>There is no overfitting issue.</p>
</div>
<div id="session-information" class="section level2">
<h2>Session information</h2>
<pre class="r"><code>sessionInfo()</code></pre>
<pre><code>R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.6
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] kableExtra_0.9.0 knitr_1.20 mashr_0.2-11 ashr_2.2-10
loaded via a namespace (and not attached):
[1] Rcpp_0.12.18 highr_0.7 pillar_1.3.0
[4] compiler_3.5.1 git2r_0.23.0 plyr_1.8.4
[7] workflowr_1.1.1 R.methodsS3_1.7.1 R.utils_2.6.0
[10] iterators_1.0.10 tools_3.5.1 corrplot_0.84
[13] digest_0.6.15 viridisLite_0.3.0 tibble_1.4.2
[16] evaluate_0.11 lattice_0.20-35 pkgconfig_2.0.2
[19] rlang_0.2.2 Matrix_1.2-14 foreach_1.4.4
[22] rstudioapi_0.7 yaml_2.2.0 parallel_3.5.1
[25] mvtnorm_1.0-8 xml2_1.2.0 httr_1.3.1
[28] stringr_1.3.1 hms_0.4.2 rprojroot_1.3-2
[31] grid_3.5.1 R6_2.2.2 rmarkdown_1.10
[34] rmeta_3.0 readr_1.1.1 magrittr_1.5
[37] whisker_0.3-2 scales_1.0.0 backports_1.1.2
[40] codetools_0.2-15 htmltools_0.3.6 MASS_7.3-50
[43] rvest_0.3.2 assertthat_0.2.0 colorspace_1.3-2
[46] stringi_1.2.4 munsell_0.5.0 doParallel_1.0.11
[49] pscl_1.5.2 truncnorm_1.0-8 SQUAREM_2017.10-1
[52] crayon_1.3.4 R.oo_1.22.0 </code></pre>
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