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| value is around 3.1. Since lfsr and lfdr are both more conservative than q values, 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)

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)

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

mash increases power, because it considers the sharing among conditions. We 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, main = 'Estiamted pi')

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, main='Estimated pi with threshold (0.01) in scale')

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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