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

Introduction

This analysis compares the “OHF” FLASH fit to the “Top 20” FLASH fit. See here for fitting details.

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.

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/"
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)

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))
}

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)
}

Significant for OHF, not Top 20

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 here). 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.

# 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])
}

Significant for Top 20, not OHF

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.

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])
}

Different posterior means

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.

diff.pms <- c(8284, 6899, 12528, 2410)
for (i in 1:length(diff.pms)) {
  plot_it(diff.pms[i])
}

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