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} </style> <div class="fluid-row" id="header"> <div class="btn-group pull-right"> <button type="button" class="btn btn-default btn-xs dropdown-toggle" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"><span>Code</span> <span class="caret"></span></button> <ul class="dropdown-menu" style="min-width: 50px;"> <li><a id="rmd-show-all-code" href="#">Show All Code</a></li> <li><a id="rmd-hide-all-code" href="#">Hide All Code</a></li> </ul> </div> <h1 class="title toc-ignore">MASH v FLASH GTEx analysis: OHF v “Top 20”</h1> </div> <p><strong>Last updated:</strong> 2018-08-04</p> <strong>workflowr checks:</strong> <small>(Click a bullet for more information)</small> <ul> <li> <p><details> <summary> <strong style="color:blue;">✔</strong> <strong>R Markdown file:</strong> up-to-date </summary></p> <p>Great! Since the R Markdown file has been committed to the Git repository, you know the exact version of the code that produced these results.</p> </details> </li> <li> <p><details> <summary> <strong style="color:blue;">✔</strong> <strong>Environment:</strong> empty </summary></p> <p>Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.</p> </details> </li> <li> <p><details> <summary> <strong style="color:blue;">✔</strong> <strong>Seed:</strong> <code>set.seed(20180609)</code> </summary></p> <p>The command <code>set.seed(20180609)</code> was run prior to running the code in the R Markdown file. 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The version displayed above was the version of the Git repository at the time these results were generated. <br><br> Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use <code>wflow_publish</code> or <code>wflow_git_commit</code>). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated: <pre><code> Ignored files: Ignored: .DS_Store Ignored: .Rhistory Ignored: .Rproj.user/ Ignored: data/ Ignored: docs/.DS_Store Ignored: docs/images/.DS_Store Ignored: docs/images/.Rapp.history Ignored: output/.DS_Store Ignored: output/.Rapp.history Ignored: output/MASHvFLASHgtex/.DS_Store Ignored: output/MASHvFLASHsims/.DS_Store Ignored: output/MASHvFLASHsims/backfit/.DS_Store Ignored: output/MASHvFLASHsims/backfit/.Rapp.history Unstaged changes: Modified: code/gtexanalysis.R </code></pre> Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes. </details> </li> </ul> <details> <summary> <small><strong>Expand here to see past versions:</strong></small> </summary> <ul> <table style="border-collapse:separate; border-spacing:5px;"> <thead> <tr> <th style="text-align:left;"> File </th> <th style="text-align:left;"> Version </th> <th style="text-align:left;"> Author </th> <th style="text-align:left;"> Date </th> <th style="text-align:left;"> Message </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> Rmd </td> <td style="text-align:left;"> <a href="https://github.com/willwerscheid/MASHvFLASH/blob/85bdd0b04af87cbe3a53d3fb242d8be700bac988/analysis/OHFvTop20.Rmd" target="_blank">85bdd0b</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> <td style="text-align:left;"> wflow_publish(c(“analysis/OHFvTop20.Rmd”, “analysis/index.Rmd”)) </td> </tr> <tr> <td style="text-align:left;"> html </td> <td style="text-align:left;"> <a href="https://cdn.rawgit.com/willwerscheid/MASHvFLASH/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/OHFvTop20.html" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> <td style="text-align:left;"> Build site. </td> </tr> <tr> <td style="text-align:left;"> Rmd </td> <td style="text-align:left;"> <a href="https://github.com/willwerscheid/MASHvFLASH/blob/312476b990c8ec8b600434b175e84da2fb500c8b/analysis/OHFvTop20.Rmd" target="_blank">312476b</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> <td style="text-align:left;"> wflow_publish(c(“analysis/OHFvTop20.Rmd”, “analysis/MASHvOHF.Rmd”, </td> </tr> </tbody> </table> </ul> <p></details></p> <hr /> <div id="introduction" class="section level2"> <h2>Introduction</h2> <p>This analysis compares the “OHF” FLASH fit to the “Top 20” FLASH fit. See <a href="MASHvFLASHgtex2.html">here</a> for fitting details.</p> <p>In general, differences among FLASH fits are much subtler than differences between the MASH fit and any given FLASH fit. To interpret the differences, I introduce a new plotting tool that compares loadings. Bar heights correspond to normalized absolute values of loadings, with loadings for the OHF method displayed above the x-axis and loadings for the “Top 20” method displayed below. The leftmost black bar corresponds to the “equal effects” loading; the colored bars correspond to unique effects; and the rightmost numbered bars correspond to data-driven loadings.</p> <pre class="r"><code>library(mashr)</code></pre> <pre><code>Loading required package: ashr</code></pre> <pre class="r"><code>devtools::load_all("/Users/willwerscheid/GitHub/flashr/")</code></pre> <pre><code>Loading flashr</code></pre> <pre class="r"><code>gtex <- readRDS(gzcon(url("https://github.com/stephenslab/gtexresults/blob/master/data/MatrixEQTLSumStats.Portable.Z.rds?raw=TRUE"))) strong <- t(gtex$strong.z) fpath <- "./output/MASHvFLASHgtex2/" ohf_final <- readRDS(paste0(fpath, "ohf.rds")) top20_final <- readRDS(paste0(fpath, "top20.rds")) all_fl_lfsr <- readRDS(paste0(fpath, "fllfsr.rds")) ohf_lfsr <- all_fl_lfsr[[1]] top20_lfsr <- all_fl_lfsr[[4]] ohf_pm <- flash_get_fitted_values(ohf_final) top20_pm <- flash_get_fitted_values(top20_final)</code></pre> <pre class="r"><code>missing.tissues <- c(7, 8, 19, 20, 24, 25, 31, 34, 37) gtex.colors <- read.table("https://github.com/stephenslab/gtexresults/blob/master/data/GTExColors.txt?raw=TRUE", sep = '\t', comment.char = '')[-missing.tissues, 2] OHF.colors <- c("tan4", "tan3") zero.colors <- c("black", gray.colors(19, 0.2, 0.9), gray.colors(17, 0.95, 1)) plot_test <- function(n, lfsr, pm, method_name) { plot(strong[, n], pch=1, col="black", xlab="", ylab="", cex=0.6, ylim=c(min(c(strong[, n], 0)), max(c(strong[, n], 0))), main=paste0("Test #", n, "; ", method_name)) size = rep(0.6, 44) shape = rep(15, 44) signif <- lfsr[, n] <= .05 shape[signif] <- 17 size[signif] <- 1.35 - 15 * lfsr[signif, n] size <- pmin(size, 1.2) points(pm[, n], pch=shape, col=as.character(gtex.colors), cex=size) abline(0, 0) } plot_ohf_v_ohl_loadings <- function(n, ohf_fit, ohl_fit, ohl_name, legend_pos = "bottomright") { ohf <- abs(ohf_fit$EF[n, ] * apply(abs(ohf_fit$EL), 2, max)) ohl <- -abs(ohl_fit$EF[n, ] * apply(abs(ohl_fit$EL), 2, max)) data <- rbind(c(ohf, rep(0, length(ohl) - 45)), c(ohl[1:45], rep(0, length(ohf) - 45), ohl[46:length(ohl)])) colors <- c("black", as.character(gtex.colors), OHF.colors, zero.colors[1:(length(ohl) - 45)]) x <- barplot(data, beside=T, col=rep(colors, each=2), main=paste0("Test #", n, " loadings"), legend.text = c("OHF", ohl_name), args.legend = list(x = legend_pos, bty = "n", pch="+-", fill=NULL, border="white")) text(x[2*(46:47) - 1], min(data) / 10, labels=as.character(1:2), cex=0.4) text(x[2*(48:ncol(data))], max(data) / 10, labels=as.character(1:(length(ohl) - 45)), cex=0.4) } compare_methods <- function(lfsr1, lfsr2, pm1, pm2) { res <- list() res$first_not_second <- find_A_not_B(lfsr1, lfsr2) res$lg_first_not_second <- find_large_A_not_B(lfsr1, lfsr2) res$second_not_first <- find_A_not_B(lfsr2, lfsr1) res$lg_second_not_first <- find_large_A_not_B(lfsr2, lfsr1) res$diff_pms <- find_overall_pm_diff(pm1, pm2) return(res) } # Find tests where many conditions are significant according to # method A but not according to method B. find_A_not_B <- function(lfsrA, lfsrB) { select_tests(colSums(lfsrA <= 0.05 & lfsrB > 0.05)) } # Find tests where many conditions are highly significant according to # method A but are not significant according to method B. find_large_A_not_B <- function(lfsrA, lfsrB) { select_tests(colSums(lfsrA <= 0.01 & lfsrB > 0.05)) } find_overall_pm_diff <- function(pmA, pmB, n = 4) { pm_diff <- colSums((pmA - pmB)^2) return(order(pm_diff, decreasing = TRUE)[1:4]) } # Get at least four (or min_n) "top" tests. select_tests <- function(colsums, min_n = 4) { n <- 45 n_tests <- 0 while (n_tests < min_n && n > 0) { n <- n - 1 n_tests <- sum(colsums >= n) } return(which(colsums >= n)) }</code></pre> <pre class="r"><code>plot_it <- function(n, legend.pos = "bottomright") { par(mfrow=c(1, 2)) plot_test(n, ohf_lfsr, ohf_pm, "OHF") plot_test(n, top20_lfsr, top20_pm, "Top 20") par(mfrow=c(1, 1)) plot_ohf_v_ohl_loadings(n, ohf_final, top20_final, "Top 20", legend.pos) }</code></pre> </div> <div id="significant-for-ohf-not-top-20" class="section level2"> <h2>Significant for OHF, not Top 20</h2> <p>The fact that the OHF fit only has two data-driven loadings can constrain its estimates to follow the patterns prescribed by those loadings (depicted <a href="MASHvFLASHgtex2.html#data-driven_loadings_(step_1)">here</a>). Typically, when estimates are deemed significant by OHF but not by the “Top 20” method, OHF places a large weight on a single data-driven loading, whereas the “Top 20” method disperses weight across several data-driven loadings. The following examples are typical.</p> <pre class="r"><code># ohf.v.top20 <- compare_methods(ohf_lfsr, top20_lfsr, ohf_pm, top20_pm) ohl.first.loading <- c(2180, 3727, 5746) legend.pos <- c("topleft", "bottomright", "topleft") for (i in 1:length(ohl.first.loading)) { plot_it(ohl.first.loading[i], legend.pos[i]) }</code></pre> <p><img src="figure/OHFvTop20.Rmd/ohf_not_mash-1.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of ohf_not_mash-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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/ohf_not_mash-1.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/ohf_not_mash-2.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of ohf_not_mash-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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/ohf_not_mash-2.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/ohf_not_mash-3.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of ohf_not_mash-3.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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/ohf_not_mash-3.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/ohf_not_mash-4.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of ohf_not_mash-4.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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/ohf_not_mash-4.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/ohf_not_mash-5.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of ohf_not_mash-5.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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/ohf_not_mash-5.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/ohf_not_mash-6.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of ohf_not_mash-6.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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/ohf_not_mash-6.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details></p> </div> <div id="significant-for-top-20-not-ohf" class="section level2"> <h2>Significant for Top 20, not OHF</h2> <p>Another consequence of the fact that the OHF fit only has two data-driven loadings is that it will fail to find any patterns that are not prescribed by those loadings. In the following examples, OHF places virtually no weight on its data-driven loadings, whereas the “Top 20” method places moderate to large weights on at least a few data-driven loadings.</p> <pre class="r"><code>ohf.no.dd <- c(2072, 14689, 10205) legend.pos <- c("topright", "topleft", "topright") for (i in 1:length(ohf.no.dd)) { plot_it(ohf.no.dd[i], legend.pos[i]) }</code></pre> <p><img src="figure/OHFvTop20.Rmd/mash_not_ohf-1.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of mash_not_ohf-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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/mash_not_ohf-1.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/mash_not_ohf-2.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of mash_not_ohf-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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/mash_not_ohf-2.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/mash_not_ohf-3.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of mash_not_ohf-3.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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/mash_not_ohf-3.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/mash_not_ohf-4.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of mash_not_ohf-4.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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/mash_not_ohf-4.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/mash_not_ohf-5.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of mash_not_ohf-5.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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/mash_not_ohf-5.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/mash_not_ohf-6.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of mash_not_ohf-6.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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/mash_not_ohf-6.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details></p> </div> <div id="different-posterior-means" class="section level2"> <h2>Different posterior means</h2> <p>This category of tests is perhaps the most intriguing of the three. In each of the following examples, the “Top 20” method assigns much larger weights to many unique effects, so that there is in general less shrinkage for the largest effects. As a result, it is also able to shrink the relatively smaller effects more aggressively.</p> <pre class="r"><code>diff.pms <- c(8284, 6899, 12528, 2410) for (i in 1:length(diff.pms)) { plot_it(diff.pms[i]) }</code></pre> <p><img src="figure/OHFvTop20.Rmd/diff_pms-1.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of diff_pms-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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/diff_pms-1.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/diff_pms-2.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of diff_pms-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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/diff_pms-2.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/diff_pms-3.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of diff_pms-3.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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/diff_pms-3.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/diff_pms-4.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of diff_pms-4.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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/diff_pms-4.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/diff_pms-5.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of diff_pms-5.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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/diff_pms-5.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/diff_pms-6.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of diff_pms-6.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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/diff_pms-6.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/diff_pms-7.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of diff_pms-7.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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/diff_pms-7.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details> <img src="figure/OHFvTop20.Rmd/diff_pms-8.png" width="672" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of diff_pms-8.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/willwerscheid/MASHvFLASH/blob/7758c2fa8cdbef8c26874e7c6efec2c45908259b/docs/figure/OHFvTop20.Rmd/diff_pms-8.png" target="_blank">7758c2f</a> </td> <td style="text-align:left;"> Jason Willwerscheid </td> <td style="text-align:left;"> 2018-08-04 </td> </tr> </tbody> </table> <p></details></p> </div> <div id="session-information" class="section level2"> <h2>Session information</h2> <pre class="r"><code>sessionInfo()</code></pre> <pre><code>R version 3.4.3 (2017-11-30) 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/3.4/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] flashr_0.5-12 mashr_0.2-7 ashr_2.2-10 loaded via a namespace (and not attached): [1] Rcpp_0.12.17 pillar_1.2.1 compiler_3.4.3 [4] git2r_0.21.0 plyr_1.8.4 workflowr_1.0.1 [7] R.methodsS3_1.7.1 R.utils_2.6.0 iterators_1.0.9 [10] tools_3.4.3 testthat_2.0.0 digest_0.6.15 [13] tibble_1.4.2 gtable_0.2.0 evaluate_0.10.1 [16] memoise_1.1.0 lattice_0.20-35 rlang_0.2.0 [19] Matrix_1.2-12 foreach_1.4.4 commonmark_1.4 [22] yaml_2.1.17 parallel_3.4.3 ebnm_0.1-12 [25] mvtnorm_1.0-7 xml2_1.2.0 withr_2.1.1.9000 [28] stringr_1.3.0 knitr_1.20 roxygen2_6.0.1.9000 [31] devtools_1.13.4 rprojroot_1.3-2 grid_3.4.3 [34] R6_2.2.2 rmarkdown_1.8 rmeta_3.0 [37] ggplot2_2.2.1 magrittr_1.5 whisker_0.3-2 [40] scales_0.5.0 backports_1.1.2 codetools_0.2-15 [43] htmltools_0.3.6 MASS_7.3-48 assertthat_0.2.0 [46] softImpute_1.4 colorspace_1.3-2 stringi_1.1.6 [49] lazyeval_0.2.1 munsell_0.4.3 doParallel_1.0.11 [52] pscl_1.5.2 truncnorm_1.0-8 SQUAREM_2017.10-1 [55] R.oo_1.21.0 </code></pre> </div> <!-- Adjust MathJax settings so that all math formulae are shown using TeX fonts only; 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