MASH Null – Real Data (GTEx random set)

Last updated: 2018-08-31

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library(mashr)

Loading required package: ashr

library(knitr)
library(kableExtra)

There are two random sets in the GTEx summary data set. We don’t know the null in the real data. If we have the individual level data, we can do a permutation to generate null. With the summary statistics, we select the null set using threshold on z scores.

Using qvalues 0.05 as the threshold, the corresponding non-significant |z| values are less than 3.5. We select the samples with \(\max_{r} |Z_{jr}| < 3.5\) from each data set as the null set. We estimate data driven covariance matrices from data 1, estimate noise correlation from data 2, fit mash model on data 2 and calculate posterior on data 1.

data = readRDS('../output/GTEx_3.5_nullData.rds')
model = readRDS('../output/GTEx_3.5_nullModel.rds')

Sample size:

samplesize = matrix(c(nrow(data$m.data1.null$Bhat), nrow(data$m.data2.null$Bhat)))
row.names(samplesize) = c('data 1', 'data 2')
samplesize %>% kable() %>% kable_styling()

The estimated weights from data 2 is

barplot(get_estimated_pi(model), las=2, cex.names = 0.7)

The estimated weights \(\hat{\pi}\) on null part is not large. The weight on the other covariance structures may concentrate on the small grid (small \(\omega_{l}\)). So they are very close to null, but we cannot view it in the plot. I modified the get_estimated_pi function to have a threshold for grid. The weights on the grid less than the threshold are merged into the null part.

get_estimated_pi = function(m, dimension = c("cov", "grid", "all"), thres = NULL){
  dimension = match.arg(dimension)
  if (dimension == "all") {
      get_estimated_pi_no_collapse(m)
  }
  else {
      g = get_fitted_g(m)
      pihat = g$pi
      pihat_names = NULL
      pi_null = NULL
      if (g$usepointmass) {
        pihat_names = c("null", pihat_names)
        pi_null = pihat[1]
        pihat = pihat[-1]
      }
      pihat = matrix(pihat, nrow = length(g$Ulist))
      if(!is.null(thres)){
        pi_null = sum(pihat[, g$grid <= thres]) + pi_null
        pihat = pihat[, g$grid > thres]
      }
      if (dimension == "cov"){
        pihat = rowSums(pihat)
        pihat_names = c(pihat_names, names(g$Ulist))
      }
      else if (dimension == "grid") {
        pihat = colSums(pihat)
        pihat_names = c(pihat_names, 1:length(g$grid))
      }
      pihat = c(pi_null, pihat)
      names(pihat) = pihat_names
      return(pihat)
  }
}

barplot(get_estimated_pi(model, thres = 0.01), las=2, cex.names = 0.7, main='Estimated pi with threshold (0.01) in grid')

The correlation for the ED_tPCA is

corrplot::corrplot(cov2cor(model$fitted_g$Ulist[['ED_tPCA']]))

There are 483 significant samples in data 1.

data = readRDS('../output/GTEx_3.5_nullPermData.rds')
model = readRDS('../output/GTEx_3.5_nullPermModel.rds')

samplesize = matrix(c(nrow(data$m.data1.p.null$Bhat), nrow(data$m.data2.p.null$Bhat)))
row.names(samplesize) = c('data 1', 'data 2')
samplesize %>% kable() %>% kable_styling()

barplot(get_estimated_pi(model), las=2, cex.names = 0.7, main = 'Estiamted pi')

barplot(get_estimated_pi(model, thres = 0.01), las=2, cex.names = 0.7, main='Estimated pi with threshold (0.01) in grid')

sessionInfo()

R version 3.5.1 (2018-07-02)
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/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/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] kableExtra_0.9.0 knitr_1.20       mashr_0.2-11     ashr_2.2-10     

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.18      highr_0.7         pillar_1.3.0     
 [4] compiler_3.5.1    git2r_0.23.0      plyr_1.8.4       
 [7] workflowr_1.1.1   R.methodsS3_1.7.1 R.utils_2.6.0    
[10] iterators_1.0.10  tools_3.5.1       corrplot_0.84    
[13] digest_0.6.15     viridisLite_0.3.0 tibble_1.4.2     
[16] evaluate_0.11     lattice_0.20-35   pkgconfig_2.0.2  
[19] rlang_0.2.2       Matrix_1.2-14     foreach_1.4.4    
[22] rstudioapi_0.7    yaml_2.2.0        parallel_3.5.1   
[25] mvtnorm_1.0-8     xml2_1.2.0        httr_1.3.1       
[28] stringr_1.3.1     hms_0.4.2         rprojroot_1.3-2  
[31] grid_3.5.1        R6_2.2.2          rmarkdown_1.10   
[34] rmeta_3.0         readr_1.1.1       magrittr_1.5     
[37] whisker_0.3-2     scales_1.0.0      backports_1.1.2  
[40] codetools_0.2-15  htmltools_0.3.6   MASS_7.3-50      
[43] rvest_0.3.2       assertthat_0.2.0  colorspace_1.3-2 
[46] stringi_1.2.4     munsell_0.5.0     doParallel_1.0.11
[49] pscl_1.5.2        truncnorm_1.0-8   SQUAREM_2017.10-1
[52] crayon_1.3.4      R.oo_1.22.0      

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