Last updated: 2018-08-03

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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]

plot_test <- function(n, lfsr, pm, method_name) {
  plot(strong[, n], pch=1, col="black", xlab="", ylab="", cex=0.6,
       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)
}

compare_methods <- function(lfsr1, lfsr2) {
  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)
  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))
}

# 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 of the more interesting examples follow.

ohf.v.top20 <- compare_methods(fl_lfsr, m_lfsr)

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")
}

Expand here to see past versions of ohf_not_mash-1.png:
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9867668 Jason Willwerscheid 2018-08-03

Expand here to see past versions of ohf_not_mash-2.png:
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9867668 Jason Willwerscheid 2018-08-03

Expand here to see past versions of ohf_not_mash-3.png:
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Expand here to see past versions of ohf_not_mash-4.png:
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9867668 Jason Willwerscheid 2018-08-03

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")
}

Expand here to see past versions of mash_not_ohf-1.png:
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9867668 Jason Willwerscheid 2018-08-03

Expand here to see past versions of mash_not_ohf-2.png:
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Expand here to see past versions of mash_not_ohf-3.png:
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Expand here to see past versions of mash_not_ohf-4.png:
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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        

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