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The data are obtained from 5 vs 5 GTEx/Liver samples and 10K top expressed genes, and <span class="math inline">\(1000\)</span> independent simulation trials.</p> <p>Compare the numbers of false discoveries (by definition, all discoveries should be false) obtained by these four methods, using FDR <span class="math inline">\(\leq 0.05\)</span> and <span class="math inline">\(s\)</span>-value <span class="math inline">\(\leq 0.05\)</span> as cutoffs.</p> </div> <div id="simulation-p-values-for-bh-and-by-procedures-hatbeta-hatbeta-hat-s-hatbeta-hat-z-for-ash-and-truncash." class="section level2"> <h2>Simulation: <span class="math inline">\(p\)</span> values for <a href="https://www.jstor.org/stable/2346101">BH</a> and <a href="https://projecteuclid.org/euclid.aos/1013699998">BY</a> procedures; <span class="math inline">\(\hat\beta = \hat\beta\)</span>, <span class="math inline">\(\hat s = \hat\beta / \hat z\)</span>, for <code>ash</code> and <code>truncash</code>.</h2> <p><strong><span class="math inline">\(\hat\beta\)</span> obtained from <a href="nullpipeline.html">the <code>limma::lmFit</code> step of the pipeline</a>, <span class="math inline">\(\hat z\)</span> obtained from <a href="nullpipeline.html">the last step of the pipeline</a>.</strong></p> <pre class="r"><code>library(ashr) source("../code/truncash.R")</code></pre> <pre class="r"><code>p = read.table("../output/p_null_liver_777.txt") z = read.table("../output/z_null_liver_777.txt") betahat = read.table("../output/betahat_null_liver_777.txt") m = dim(p)[1] n = dim(p)[2] fd.bh = fd.by = fd.ash = fd.truncash = c() for (i in 1:m) { p_BH = p.adjust(p[i, ], method = "BH") fd.bh[i] = sum(p_BH <= 0.05) p_BY = p.adjust(p[i, ], method = "BY") fd.by[i] = sum(p_BY <= 0.05) betahat_trial = as.numeric(betahat[i, ]) sebetahat_trial = - betahat_trial / as.numeric(z[i, ]) fit.ash = ashr::ash(betahat_trial, sebetahat_trial, method = "fdr", mixcompdist = "normal") fd.ash[i] = sum(ashr::get_svalue(fit.ash) <= 0.05) fit.truncash = truncash(betahat_trial, sebetahat_trial, t = qnorm(0.975)) fd.truncash[i] = sum(get_svalue(fit.truncash) <= 0.05) }</code></pre> </div> <div id="result" class="section level2"> <h2>Result</h2> <p>Simulated under the global null, FWER <span class="math inline">\(=\)</span> FDR.</p> <div id="estimated-fwer-or-fdr-by-bh" class="section level3"> <h3>Estimated FWER or FDR by BH</h3> <pre class="r"><code>fdr.bh = mean(fd.bh >= 1) fdr.bh</code></pre> <pre><code>[1] 0.046</code></pre> <p>Estimated FWER or FDR by BY</p> <pre class="r"><code>fdr.by = mean(fd.by >= 1) fdr.by</code></pre> <pre><code>[1] 0.006</code></pre> <p>Estimated FWER or FDR by <code>ash</code></p> <pre class="r"><code>fdr.ash = mean(fd.ash >= 1) fdr.ash</code></pre> <pre><code>[1] 0.096</code></pre> <p>Estimated FWER or FDR by <code>truncash</code></p> <pre class="r"><code>fdr.truncash = mean(fd.truncash >= 1) fdr.truncash</code></pre> <pre><code>[1] 0.062</code></pre> </div> <div id="happenstance-of-false-discoveries-by-four-approaches" class="section level3"> <h3>Happenstance of false discoveries by four approaches</h3> <pre class="r"><code>maxcount = max(c(fd.bh, fd.by, fd.ash, fd.truncash)) xlim = c(0, maxcount) maxfreq = max(c(max(table(fd.bh)), max(table(fd.by)), max(table(fd.ash)), max(table(fd.truncash)))) ylim = c(0, maxfreq) plot(table(fd.bh), xlab = "Number of False Discoveries / 10K", ylab = "Frequency", main = "Benjamini - Hochberg 1995", xlim = xlim, ylim = ylim)</code></pre> <p><img src="figure/FDR_null_betahat.Rmd/unnamed-chunk-7-1.png" width="672" style="display: block; margin: auto;" /></p> <pre class="r"><code>plot(table(fd.by), xlab = "Number of False Discoveries / 10K", ylab = "Frequency", main = "Benjamini - Yekutieli 2001", xlim = xlim, ylim = ylim)</code></pre> <p><img src="figure/FDR_null_betahat.Rmd/unnamed-chunk-7-2.png" width="672" style="display: block; margin: auto;" /></p> <pre class="r"><code>plot(table(fd.ash), xlab = "Number of False Discoveries / 10K", ylab = "Frequency", main = "ash", xlim = xlim, ylim = ylim)</code></pre> <p><img src="figure/FDR_null_betahat.Rmd/unnamed-chunk-7-3.png" width="672" style="display: block; margin: auto;" /></p> <pre class="r"><code>plot(table(fd.truncash), xlab = "Number of False Discoveries / 10K", ylab = "Frequency", main = "truncash", xlim = xlim, ylim = ylim)</code></pre> <p><img src="figure/FDR_null_betahat.Rmd/unnamed-chunk-7-4.png" width="672" style="display: block; margin: auto;" /></p> </div> <div id="comparison-of-the-numbers-of-false-discoveries-by-four-approaches" class="section level3"> <h3>Comparison of the numbers of false discoveries by four approaches</h3> <pre class="r"><code>m = length(fd.bh) fd.ind = (1:m)[!((fd.bh == 0) & (fd.by == 0) & (fd.ash == 0) & (fd.truncash == 0))] plot(1:length(fd.ind), fd.bh[fd.ind], pch = 4, ylim = xlim, xlab = "Trials with False Discoveries", ylab = "Number of False Discoveries / 10K") points(1:length(fd.ind), fd.by[fd.ind], pch = 4, col = 2) points(1:length(fd.ind), fd.ash[fd.ind], pch = 4, col = 3) points(1:length(fd.ind), fd.truncash[fd.ind], pch = 4, col = 4) legend("topright", c("BH", "BY", "ash", "truncash"), col = 1:4, pch = 4)</code></pre> <p><img src="figure/FDR_null_betahat.Rmd/unnamed-chunk-8-1.png" width="672" style="display: block; margin: auto;" /></p> </div> </div> <div id="session-information" class="section level2"> <h2>Session Information</h2> <pre class="r"><code>sessionInfo()</code></pre> <pre><code>R version 3.3.2 (2016-10-31) Platform: x86_64-apple-darwin13.4.0 (64-bit) Running under: macOS Sierra 10.12.3 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] SQUAREM_2016.10-1 ashr_2.1.2 loaded via a namespace (and not attached): [1] Rcpp_0.12.9 knitr_1.15.1 magrittr_1.5 [4] workflowr_0.3.0 MASS_7.3-45 doParallel_1.0.10 [7] pscl_1.4.9 lattice_0.20-34 foreach_1.4.3 [10] stringr_1.1.0 tools_3.3.2 parallel_3.3.2 [13] grid_3.3.2 git2r_0.18.0 htmltools_0.3.5 [16] iterators_1.0.8 yaml_2.1.14 rprojroot_1.2 [19] digest_0.6.9 codetools_0.2-15 evaluate_0.10 [22] rmarkdown_1.3 stringi_1.1.2 backports_1.0.5 [25] truncnorm_1.0-7 </code></pre> </div> <hr> <p> This <a href="http://rmarkdown.rstudio.com">R Markdown</a> site was created with <a href="https://github.com/jdblischak/workflowr">workflowr</a> </p> <hr> <!-- To enable disqus, uncomment the section below and provide your disqus_shortname --> <!-- disqus <div id="disqus_thread"></div> <script type="text/javascript"> /* * * CONFIGURATION VARIABLES: EDIT BEFORE PASTING INTO YOUR WEBPAGE * * */ var disqus_shortname = 'rmarkdown'; 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