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<h1 class="title toc-ignore">Gaussian derivatives applied to Smemo’s data</h1>
<h4 class="author"><em>Lei Sun</em></h4>
<h4 class="date"><em>2017-06-17</em></h4>
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<p><strong>Last updated:</strong> 2018-05-15</p>
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</details>
<hr />
<div id="introduction" class="section level2">
<h2>Introduction</h2>
<p>Re-analyze <a href="http://www.nature.com/nature/journal/v507/n7492/abs/nature13138.html">Smemo et al 2014</a>’s mouse heart RNA-seq data after discussion with Matthew.</p>
<pre class="r"><code>counts.mat = read.table("../data/smemo.txt", header = T, row.name = 1)
counts.mat = counts.mat[, -5]</code></pre>
</div>
<div id="gene-selection" class="section level2">
<h2>Gene selection</h2>
<p>Only use genes with total counts of <span class="math inline">\(4\)</span> samples <span class="math inline">\(\geq 5\)</span>.</p>
<pre class="r"><code>counts = counts.mat[rowSums(counts.mat) >= 5, ]
design = model.matrix(~c(0, 0, 1, 1))</code></pre>
<pre><code>Number of selected genes: 17191</code></pre>
</div>
<div id="summary-statistics" class="section level2">
<h2>Summary statistics</h2>
<pre class="r"><code>source("../code/count_to_summary.R")
summary <- count_to_summary(counts, design)
betahat <- summary$betahat
sebetahat <- summary$sebetahat
z <- summary$z</code></pre>
</div>
<div id="fitting-z-with-gaussian-derivatives" class="section level2">
<h2>Fitting <span class="math inline">\(z\)</span> with Gaussian derivatives</h2>
<p>With stretch GD can fit <span class="math inline">\(z\)</span> scores, but it seems there should be signals.</p>
<pre><code>GD Coefficients:</code></pre>
<pre><code>0 : 1 ; 1 : 0.011943001812549 ; 2 : 1.61071078428794 ; 3 : 0.366170906280825 ; 4 : 1.70110410088397 ; 5 : 0.676196157714041 ; 6 : 0.938754567207026 ; 7 : 0.550191966320357 ; 8 : 0.238942600377754 ; 9 : 0.161306266268357 ; 10 : 0.0430996146901972 ;</code></pre>
<p><img src="figure/smemo_2.rmd/fitting%20gaussian%20derivatives-1.png" width="672" style="display: block; margin: auto;" /></p>
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2017-12-21
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/f2fdaf0302de9e19bf098e28bd7c2c9a886611d3/docs/figure/smemo_2.rmd/fitting gaussian derivatives-1.png" target="_blank">f2fdaf0</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-06-18
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/smemo_2.rmd/fitting%20gaussian%20derivatives-2.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of fitting gaussian derivatives-2.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/LSun/truncash/blob/140be7fbea9ced9a42fd8bdd03b7254989ca4938/docs/figure/smemo_2.rmd/fitting gaussian derivatives-2.png" target="_blank">140be7f</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-12
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/0f36d998db26444c5dd01502ea1af7fbd1129b22/docs/figure/smemo_2.rmd/fitting gaussian derivatives-2.png" target="_blank">0f36d99</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-12-21
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/f2fdaf0302de9e19bf098e28bd7c2c9a886611d3/docs/figure/smemo_2.rmd/fitting gaussian derivatives-2.png" target="_blank">f2fdaf0</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-06-18
</td>
</tr>
</tbody>
</table>
</details>
</div>
<div id="discovered-by-bh-and-ash" class="section level2">
<h2>Discovered by <code>BH</code> and <code>ASH</code></h2>
<p>Feeding summary statistics to <code>BH</code> and <code>ASH</code>, both give thousands of discoveries.</p>
<pre class="r"><code>fit.BH = p.adjust((1 - pnorm(abs(z))) * 2, method = "BH")
## Number of discoveries by BH
sum(fit.BH <= 0.05)</code></pre>
<pre><code>[1] 2541</code></pre>
<pre class="r"><code>fit.ash = ashr::ash(betahat, sebetahat, method = "fdr")
## Number of discoveries by ASH
sum(get_svalue(fit.ash) <= 0.05)</code></pre>
<pre><code>[1] 6440</code></pre>
</div>
<div id="fitting-ash-first-or-gaussian-derivatives-first" class="section level2">
<h2>Fitting <code>ASH</code> first or Gaussian derivatives first</h2>
<p>Using default setting <span class="math inline">\(L = 10\)</span>, <span class="math inline">\(\lambda = 10\)</span>, <span class="math inline">\(\rho = 0.5\)</span>, compare the <code>GD-ASH</code> results by fitting <code>ASH</code> first vs fitting <code>GD</code> first. They indeed arrive at different local minima.</p>
<pre class="r"><code>fit.gdash.ASH <- gdash(betahat, sebetahat,
gd.priority = FALSE)
## Regularized log-likelihood by fitting ASH first
fit.gdash.ASH$loglik</code></pre>
<pre><code>[1] -12483.86</code></pre>
<pre class="r"><code>fit.gdash.GD <- gdash(betahat, sebetahat)
## Regularized log-likelihood by fitting GD first
fit.gdash.GD$loglik</code></pre>
<pre><code>[1] -22136.92</code></pre>
</div>
<div id="gd-ash-with-larger-penalties-on-w" class="section level2">
<h2><code>GD-ASH</code> with larger penalties on <span class="math inline">\(w\)</span></h2>
<p>Using <span class="math inline">\(\lambda = 50\)</span>, <span class="math inline">\(\rho = 0.1\)</span>, fitting <code>ASH</code> first and <code>GD</code> first give the same result, and produce 1400+ discoveries with <span class="math inline">\(q\)</span> values <span class="math inline">\(\leq 0.05\)</span>, all of which are discovered by <code>BH</code>.</p>
<pre class="r"><code>L = 10
lambda = 50
rho = 0.1
fit.gdash.ASH <- gdash(betahat, sebetahat,
gd.ord = L, w.lambda = lambda, w.rho = rho,
gd.priority = FALSE)
## Regularized log-likelihood by fitting ASH first
fit.gdash.ASH$loglik</code></pre>
<pre><code>[1] -13651.59</code></pre>
<pre class="r"><code>## Number of discoveries
sum(fit.gdash.ASH$qvalue <= 0.05)</code></pre>
<pre><code>[1] 1431</code></pre>
<pre class="r"><code>fit.gdash.GD <- gdash(betahat, sebetahat,
gd.ord = L, w.lambda = lambda, w.rho = rho,
gd.priority = TRUE)
## Regularized log-likelihood by fitting GD first
fit.gdash.GD$loglik</code></pre>
<pre><code>[1] -13651.59</code></pre>
<pre class="r"><code>## Number of discoveries
sum(fit.gdash.GD$qvalue <= 0.05)</code></pre>
<pre><code>[1] 1431</code></pre>
<pre><code>GD Coefficients:</code></pre>
<pre><code>0 : 1 ; 1 : -0.0475544308510135 ; 2 : 0.707888470469342 ; 3 : 0.149489828947119 ; 4 : -8.97499076623316e-14 ; 5 : 0.109281416075664 ; 6 : -3.00530934822662e-13 ; 7 : 0.0783545592042359 ; 8 : -2.99572304462426e-13 ; 9 : 0.0911488252640105 ; 10 : -2.99578347875936e-13 ;</code></pre>
<p><img src="figure/smemo_2.rmd/GD-ASH%20discoveries%20histogram-1.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of GD-ASH discoveries histogram-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/LSun/truncash/blob/0f36d998db26444c5dd01502ea1af7fbd1129b22/docs/figure/smemo_2.rmd/GD-ASH discoveries histogram-1.png" target="_blank">0f36d99</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-12-21
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/f2fdaf0302de9e19bf098e28bd7c2c9a886611d3/docs/figure/smemo_2.rmd/GD-ASH discoveries histogram-1.png" target="_blank">f2fdaf0</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-06-18
</td>
</tr>
</tbody>
</table>
</details>
</div>
<div id="session-information" class="section level2">
<h2>Session information</h2>
<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 10.13.4
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
other attached packages:
[1] ashr_2.2-2 Rmosek_8.0.69 PolynomF_1.0-1 CVXR_0.95
[5] REBayes_1.2 Matrix_1.2-12 SQUAREM_2017.10-1 EQL_1.0-0
[9] ttutils_1.0-1
loaded via a namespace (and not attached):
[1] gmp_0.5-13.1 Rcpp_0.12.16 compiler_3.4.3
[4] git2r_0.21.0 workflowr_1.0.1 R.methodsS3_1.7.1
[7] R.utils_2.6.0 iterators_1.0.9 tools_3.4.3
[10] digest_0.6.15 bit_1.1-12 evaluate_0.10.1
[13] lattice_0.20-35 foreach_1.4.4 parallel_3.4.3
[16] yaml_2.1.18 Rmpfr_0.6-1 ECOSolveR_0.4
[19] stringr_1.3.0 knitr_1.20 locfit_1.5-9.1
[22] rprojroot_1.3-2 bit64_0.9-7 grid_3.4.3
[25] R6_2.2.2 rmarkdown_1.9 limma_3.34.4
[28] edgeR_3.20.2 magrittr_1.5 whisker_0.3-2
[31] MASS_7.3-47 codetools_0.2-15 backports_1.1.2
[34] htmltools_0.3.6 scs_1.1-1 assertthat_0.2.0
[37] stringi_1.1.6 pscl_1.5.2 doParallel_1.0.11
[40] truncnorm_1.0-7 R.oo_1.21.0 </code></pre>
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