MASH v FLASH GTEx analysis: MASH v “Top 20”

Introduction

This analysis compares the MASH fit to the “Top 20” fit. See here for fitting details and here for an introduction to the plots.

library(mashr)

Loading required package: ashr

devtools::load_all("/Users/willwerscheid/GitHub/flashr/")

Loading flashr

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/"
m_final <- readRDS(paste0(fpath, "m.rds"))
fl_final <- readRDS(paste0(fpath, "Top20.rds"))

m_lfsr <- t(get_lfsr(m_final))
m_pm <- t(get_pm(m_final))

all_fl_lfsr <- readRDS(paste0(fpath, "fllfsr.rds"))
fl_lfsr <- all_fl_lfsr[[4]]
fl_pm <- flash_get_fitted_values(fl_final)

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))
}

Significant for Top 20, not MASH

As in the previous analysis, the most common case involves a combination of a small equal effect and a large unique effect. Some typical examples follow.

# mash.v.top20 <- compare_methods(fl_lfsr, m_lfsr, fl_pm, m_pm)

identical.plus.unique <- c(2184, 4752, 10000, 13684)

par(mfrow=c(1, 2))
for (n in identical.plus.unique) {
  plot_test(n, fl_lfsr, fl_pm, "Top 20")
  plot_test(n, m_lfsr, m_pm, "MASH")
}

Significant for MASH, not OHF

The most typical case here has MASH finding a significant equal effect, while FLASH finds a significant unique effect and an insignificant equal effect. In each of the following tests, there is a single outlying effect (with a raw \(z\)-score of around 4 or 5), which FLASH identifies as unique but which MASH “assigns” to the equal effect (or rather, to the data-driven covariance structure described in the previous analysis). Roughly, the other observations borrow strength from the outlying observation in MASH but not in FLASH.

par(mfrow=c(1, 2))

shrink.unique <- c(1115, 5174, 8578, 9928)

for (n in shrink.unique) {
  plot_test(n, fl_lfsr, fl_pm, "OHF")
  plot_test(n, m_lfsr, m_pm, "MASH")
}

Different posterior means

The following examples differ from the examples in the previous analysis in that all effect sizes are large. As a result, the MASH estimates do not coincide with the raw observations as neatly. Notice, for example, that in each case some of the MASH estimates are even larger than the observed effect sizes. This is because the posterior mixture weights are primarily concentrated on the ED_tPCA matrices rather than on the simple_het matrices (see here for a description of these matrices).

par(mfrow=c(1, 2))

diff.pms <- c(11467, 246, 6701)
for (n in diff.pms) {
  plot_test(n, fl_lfsr, fl_pm, "OHF")
  plot_test(n, m_lfsr, m_pm, "MASH")
}

Session information

sessionInfo()

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