Last updated: 2018-08-30

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library(mashr)
Loading required package: ashr
library(knitr)
library(kableExtra)
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)
  }
}

There are two random sets in the GTEx summary data set. 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()
data 1 18189
data 2 25718 
barplot(get_estimated_pi(model), las=2, cex.names = 0.7)

Expand here to see past versions of unnamed-chunk-5-1.png:
Version Author Date
e9f5a34 zouyuxin 2018-08-30

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 for the grid less than the threshold are merged into null part.

barplot(get_estimated_pi(model, thres = 0.01), las=2, cex.names = 0.7)

Expand here to see past versions of unnamed-chunk-6-1.png:
Version Author Date
e9f5a34 zouyuxin 2018-08-30

The correlation for the ED_tPCA is

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

Expand here to see past versions of unnamed-chunk-7-1.png:
Version Author Date
e9f5a34 zouyuxin 2018-08-30

There are 483 significant samples in data 1.

Permute samples in each condition to break the sharing

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

Sample size:

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()
data 1 18189
data 2 25718 
barplot(get_estimated_pi(model), las=2, cex.names = 0.7)

Expand here to see past versions of unnamed-chunk-10-1.png:
Version Author Date
e9f5a34 zouyuxin 2018-08-30 

barplot(get_estimated_pi(model, thres = 0.01), las=2, cex.names = 0.7)

Expand here to see past versions of unnamed-chunk-11-1.png:
Version Author Date
e9f5a34 zouyuxin 2018-08-30

There are 44 significant samples in data 1.

There is no overfitting issue.

Session information

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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