Last updated: 2018-05-15

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    html 242b122 LSun 2017-02-22 pihat0

Last updated: 2018-05-15

Code version: 388e65e

Introduction

Using correlated global null data simulated from GTEx/Liver, \(\hat\pi_0\) is estimated by truncash and ashr. Ideally the estimates should be close to \(1\).

Simulation

In truncash, the threshold is \(T = 1.96\).

library(ashr)
source("../code/truncash.R")
p = read.table("../output/p_null_liver_777.txt")
z = read.table("../output/z_null_liver_777.txt")
betahat = read.table("../output/betahat_null_liver_777.txt")

m = dim(p)[1]
n = dim(p)[2]
pihat0.ash = pihat0.truncash = c()

for (i in 1:m) {
  betahat_trial = as.numeric(betahat[i, ])
  sebetahat_trial = - betahat_trial / as.numeric(z[i, ])
  fit.ash = ashr::ash(betahat_trial, sebetahat_trial, method = "fdr", mixcompdist = "normal")
  pihat0.ash[i] = get_pi0(fit.ash)
  fit.truncash = truncash(betahat_trial, sebetahat_trial, t = qnorm(0.975))
  pihat0.truncash[i] = get_pi0(fit.truncash)
}

Result

False positive rate by ash

mean(pihat0.ash < 1)
[1] 0.287

False positive rate by truncash

mean(pihat0.truncash < 1)
[1] 0.202

Compare \(\hat\pi_0\) estimated by ash and truncash

xlim = c(min(c(pihat0.ash, pihat0.truncash)), 1)
plot(pihat0.ash, pihat0.truncash, xlim = xlim, ylim = xlim, xlab = "ash", ylab = "truncash", main = expression(hat(pi)[0]))
abline(0, 1, lty = 2, col = "blue")
abline(v = 1, lty = 3, col = "red")
abline(h = 1, lty = 3, col = "red")

Expand here to see past versions of unnamed-chunk-5-1.png:
Version Author Date
0f36d99 LSun 2017-12-21
242b122 LSun 2017-02-22 
boxplot(pihat0.ash, pihat0.truncash, main = expression(hat(pi)[0]), names = c("ash", "truncash"))
abline(h = 1, lty = 2, col = "red")

Expand here to see past versions of unnamed-chunk-5-2.png:
Version Author Date
0f36d99 LSun 2017-12-21
242b122 LSun 2017-02-22

Session Information

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 10.13.4

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] SQUAREM_2017.10-1 ashr_2.2-2       

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.16      knitr_1.20        whisker_0.3-2    
 [4] magrittr_1.5      workflowr_1.0.1   MASS_7.3-47      
 [7] pscl_1.5.2        doParallel_1.0.11 lattice_0.20-35  
[10] foreach_1.4.4     stringr_1.3.0     tools_3.4.3      
[13] parallel_3.4.3    grid_3.4.3        R.oo_1.21.0      
[16] git2r_0.21.0      htmltools_0.3.6   iterators_1.0.9  
[19] yaml_2.1.18       rprojroot_1.3-2   digest_0.6.15    
[22] Matrix_1.2-12     codetools_0.2-15  R.utils_2.6.0    
[25] evaluate_0.10.1   rmarkdown_1.9     stringi_1.1.6    
[28] compiler_3.4.3    backports_1.1.2   R.methodsS3_1.7.1
[31] truncnorm_1.0-7

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