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<title>Voom on null data - multiple examples</title>

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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>

</div>


<p><strong>Last updated:</strong> 2017-11-07</p>
<p><strong>Code version:</strong> 2c05d59a58ecc268f0c8a6026611face486e327e</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(&quot;../data/Liver.csv&quot;)
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=&quot;histogram of effect tests&quot;)
  qqnorm(z[[i]])
  abline(a=0,b=1,col=1)
}</code></pre>
<p><img src="figure/voom_null.Rmd/unnamed-chunk-3-1.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-2.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-3.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-4.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-5.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-6.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-7.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-8.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-9.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-10.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-11.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-12.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-13.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-14.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-15.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-16.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-17.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-18.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-19.png" width="672" style="display: block; margin: auto;" /><img src="figure/voom_null.Rmd/unnamed-chunk-3-20.png" width="672" style="display: block; margin: auto;" /></p>
<div id="session-information" class="section level2">
<h2>Session information</h2>
<pre class="r"><code>sessionInfo()</code></pre>
<pre><code>R version 3.4.2 (2017-09-28)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Sierra 10.12.6

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_2.1-27   qvalue_2.10.0 edgeR_3.20.1  limma_3.34.0 

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.13      compiler_3.4.2    git2r_0.19.0     
 [4] plyr_1.8.4        iterators_1.0.8   tools_3.4.2      
 [7] digest_0.6.12     evaluate_0.10.1   tibble_1.3.4     
[10] gtable_0.2.0      lattice_0.20-35   rlang_0.1.4      
[13] Matrix_1.2-11     foreach_1.4.3     yaml_2.1.14      
[16] parallel_3.4.2    stringr_1.2.0     knitr_1.17       
[19] locfit_1.5-9.1    rprojroot_1.2     grid_3.4.2       
[22] rmarkdown_1.6     ggplot2_2.2.1     reshape2_1.4.2   
[25] magrittr_1.5      backports_1.1.1   scales_0.5.0     
[28] codetools_0.2-15  htmltools_0.3.6   splines_3.4.2    
[31] MASS_7.3-47       colorspace_1.3-2  stringi_1.1.5    
[34] lazyeval_0.2.1    munsell_0.4.3     doParallel_1.0.11
[37] pscl_1.5.2        truncnorm_1.0-7   SQUAREM_2017.10-1</code></pre>
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