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<h1 class="title toc-ignore">Voom on null data - multiple examples</h1>
<h4 class="author"><em>M Stephens</em></h4>
<h4 class="date"><em>2016-10-21</em></h4>
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<p><strong>Last updated:</strong> 2018-05-12</p>
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<p><strong>Last updated:</strong> 2018-05-12</p>
<p><strong>Code version:</strong> ac438b4697e1e3025d37654d1430ba1c44be19ba</p>
<div id="introduction" class="section level1">
<h1>Introduction</h1>
<p>This document simply simulates some null data by randomly sampling two groups of 5 samples from some RNA-seq data (GTEx liver samples). We plot <span class="math inline">\(p\)</span> value histograms and see the effects of inflation: some distributions are inflated near 0 and others are inflated near 1. However, when we look at the qqplots (here of the z scores, but should be same for p values) we see something that is interesting, although obvious in hindsight: the most extreme p values (z scores) are never “too extreme” (although they are sometimes not extreme enough). The inflation comes from the “not quite so extreme” p values and z scores. This makes sense: when you have positively correlated variables, the most extreme values will tend to be less extreme than when you have independent samples, because you have “effectively” fewer independent samples.</p>
<p>It seems likely this can be exploited to help avoid false positives under positive correlation.</p>
<p>Load in the gtex liver data</p>
<pre class="r"><code>library(limma)
library(edgeR)
library(qvalue)
library(ashr)
r = read.csv("../data/Liver.csv")
r = r[,-(1:2)] # remove outliers
#extract top g genes from G by n matrix X of expression
top_genes_index=function(g,X){return(order(rowSums(X),decreasing =TRUE)[1:g])}
lcpm = function(r){R = colSums(r); t(log2(((t(r)+0.5)/(R+1))* 10^6))}
Y=lcpm(r)
subset = top_genes_index(10000,Y)
Y = Y[subset,]
r = r[subset,]</code></pre>
<p>Define voom transform (using code from Mengyin Lu)</p>
<pre class="r"><code>voom_transform = function(counts, condition, W=NULL){
dgecounts = calcNormFactors(DGEList(counts=counts,group=condition))
#dgecounts = DGEList(counts=counts,group=condition)
if (is.null(W)){
design = model.matrix(~condition)
}else{
design = model.matrix(~condition+W)
}
v = voom(dgecounts,design,plot=FALSE)
lim = lmFit(v)
betahat.voom = lim$coefficients[,2]
sebetahat.voom = lim$stdev.unscaled[,2]*lim$sigma
df.voom = length(condition)-2-!is.null(W)
return(list(v=v,lim=lim,betahat=betahat.voom, sebetahat=sebetahat.voom, df=df.voom, v=v))
}</code></pre>
<p>Make 2 groups of size n, and repeat random sampling.</p>
<pre class="r"><code>set.seed(101)
n = 5 # number in each group
p = list()
z = list()
tscore =list()
for(i in 1:10){
counts = r[,sample(1:ncol(r),2*n)]
condition = c(rep(0,n),rep(1,n))
r.voom = voom_transform(counts,condition)
r.ebayes = eBayes(r.voom$lim)
p[[i]] = r.ebayes$p.value[,2]
tscore[[i]] = r.ebayes$t[,2]
z[[i]] = sign(r.ebayes$t[,2]) * qnorm(p[[i]]/2)
hist(p[[i]],main="histogram of effect tests")
qqnorm(z[[i]])
abline(a=0,b=1,col=1)
}</code></pre>
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<a href="https://github.com/LSun/truncash/blob/0f36d998db26444c5dd01502ea1af7fbd1129b22/docs/figure/voom_null.Rmd/unnamed-chunk-3-17.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/858f0e45c2e4fd91c36b4a01ecff242b9c8a8fcc/docs/figure/voom_null.Rmd/unnamed-chunk-3-17.png" target="_blank">858f0e4</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-02-01
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/voom_null.Rmd/unnamed-chunk-3-18.png" width="672" style="display: block; margin: auto;" /></p>
<details>
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<a href="https://github.com/LSun/truncash/blob/0f36d998db26444c5dd01502ea1af7fbd1129b22/docs/figure/voom_null.Rmd/unnamed-chunk-3-18.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/858f0e45c2e4fd91c36b4a01ecff242b9c8a8fcc/docs/figure/voom_null.Rmd/unnamed-chunk-3-18.png" target="_blank">858f0e4</a>
</td>
<td style="text-align:left;">
LSun
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<td style="text-align:left;">
2017-02-01
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</tbody>
</table>
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</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/858f0e45c2e4fd91c36b4a01ecff242b9c8a8fcc/docs/figure/voom_null.Rmd/unnamed-chunk-3-19.png" target="_blank">858f0e4</a>
</td>
<td style="text-align:left;">
LSun
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<td style="text-align:left;">
2017-02-01
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</tbody>
</table>
</details>
<p><img src="figure/voom_null.Rmd/unnamed-chunk-3-20.png" width="672" style="display: block; margin: auto;" /></p>
<details>
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<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/0f36d998db26444c5dd01502ea1af7fbd1129b22/docs/figure/voom_null.Rmd/unnamed-chunk-3-20.png" target="_blank">0f36d99</a>
</td>
<td style="text-align:left;">
LSun
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<td style="text-align:left;">
2017-12-21
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</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/858f0e45c2e4fd91c36b4a01ecff242b9c8a8fcc/docs/figure/voom_null.Rmd/unnamed-chunk-3-20.png" target="_blank">858f0e4</a>
</td>
<td style="text-align:left;">
LSun
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<td style="text-align:left;">
2017-02-01
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</details>
<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 qvalue_2.10.0 edgeR_3.20.2 limma_3.34.4
loaded via a namespace (and not attached):
[1] Rcpp_0.12.16 compiler_3.4.3 pillar_1.0.1
[4] git2r_0.21.0 plyr_1.8.4 workflowr_1.0.1
[7] iterators_1.0.9 R.methodsS3_1.7.1 R.utils_2.6.0
[10] tools_3.4.3 digest_0.6.15 evaluate_0.10.1
[13] tibble_1.4.1 gtable_0.2.0 lattice_0.20-35
[16] rlang_0.1.6 foreach_1.4.4 Matrix_1.2-12
[19] parallel_3.4.3 yaml_2.1.18 stringr_1.3.0
[22] knitr_1.20 locfit_1.5-9.1 rprojroot_1.3-2
[25] grid_3.4.3 rmarkdown_1.9 ggplot2_2.2.1
[28] reshape2_1.4.3 magrittr_1.5 whisker_0.3-2
[31] MASS_7.3-47 codetools_0.2-15 backports_1.1.2
[34] scales_0.5.0 htmltools_0.3.6 splines_3.4.3
[37] colorspace_1.3-2 stringi_1.1.6 pscl_1.5.2
[40] lazyeval_0.2.1 munsell_0.4.3 doParallel_1.0.11
[43] truncnorm_1.0-7 SQUAREM_2017.10-1 R.oo_1.21.0 </code></pre>
<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 qvalue_2.10.0 edgeR_3.20.2 limma_3.34.4
loaded via a namespace (and not attached):
[1] Rcpp_0.12.16 compiler_3.4.3 pillar_1.0.1
[4] git2r_0.21.0 plyr_1.8.4 workflowr_1.0.1
[7] iterators_1.0.9 R.methodsS3_1.7.1 R.utils_2.6.0
[10] tools_3.4.3 digest_0.6.15 evaluate_0.10.1
[13] tibble_1.4.1 gtable_0.2.0 lattice_0.20-35
[16] rlang_0.1.6 foreach_1.4.4 Matrix_1.2-12
[19] parallel_3.4.3 yaml_2.1.18 stringr_1.3.0
[22] knitr_1.20 locfit_1.5-9.1 rprojroot_1.3-2
[25] grid_3.4.3 rmarkdown_1.9 ggplot2_2.2.1
[28] reshape2_1.4.3 magrittr_1.5 whisker_0.3-2
[31] MASS_7.3-47 codetools_0.2-15 backports_1.1.2
[34] scales_0.5.0 htmltools_0.3.6 splines_3.4.3
[37] colorspace_1.3-2 stringi_1.1.6 pscl_1.5.2
[40] lazyeval_0.2.1 munsell_0.4.3 doParallel_1.0.11
[43] truncnorm_1.0-7 SQUAREM_2017.10-1 R.oo_1.21.0 </code></pre>
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