mashr_application1

Last updated: 2020-01-14

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Knit directory: mash-single-cell-rnaseq/

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Remarks:

Used data from “Shared genetic effects on chromatin and gene expression indicate a role for enhancer priming in immune response” https://doi.org/10.1038/s41588-018-0046-7. eQTLs from 4 conditions downloaded from https://zenodo.org/record/1158560#.Xgjl5BdKhp8.
For selecting strong signals: we first filter with the criteria p-value <0.05. Then, take the top signals (the most significant SNP for each gene) in naive condition, and filter gene-SNP pairs in other conditions based on top signals in naive condition. The resulting “top_snps.RData” contains 15678 significant Gene-SNP pairs in 4 conditions.
The 4 conditions are: naive/ IF/ IF+SL/ SL. (IF, SL are two drug treatments)
1. Use strong signals to learn data-driven covariance patterns. (2) Fit models on the random subset of data, to learn weights for data-driven covariance matrix + canonical covariance matrix.
Ways to assess the model fit.
Compared the log-likelihood with/without ED step: extremely similar.

library(ashr)
library(mashr)

Format data to mashr format

load("/Users/nicholeyang/Desktop/Rotation/mash-single-cell-rnaseq/data/top_snps.RData")
load("/Users/nicholeyang/Desktop/Rotation/mash-single-cell-rnaseq/data/random_snps.RData")

dt_beta_top <- top_snps[,c("beta_naive", "beta_IF", "beta_IFSL", "beta_SL")]
dt_pval_top <- top_snps[,c("p_nominal_naive", "p_nominal_IF", "p_nominal_IFSL", "p_nominal_SL")]


dt_beta_random <- random_snps[,c("beta_naive", "beta_IF", "beta_IFSL", "beta_SL")]
dt_pval_random <- random_snps[,c("p_nominal_naive", "p_nominal_IF", "p_nominal_IFSL", "p_nominal_SL")]

dt_beta_top = as.matrix(dt_beta_top)
dt_pval_top = as.matrix(dt_pval_top)

dt_beta_random = as.matrix(dt_beta_random)
dt_pval_random = as.matrix(dt_pval_random)

Correlation structure

data.temp = mash_set_data(dt_beta_random, Shat = NULL, pval = dt_pval_random)
Vhat = estimate_null_correlation_simple(data.temp)
rm(data.temp)

data.strong = mash_set_data(dt_beta_top, Shat = NULL, pval = dt_pval_top, V=Vhat)
data.random = mash_set_data(dt_beta_random, Shat = NULL, pval = dt_pval_random, V=Vhat)

Data driven covariance

U.pca = cov_pca(data.strong,4)
U.ed = cov_ed(data.strong, U.pca)

Fit mashr model with both canonical & data-driven covariance structure

U.c = cov_canonical(data.random)
m = mash(data.random, Ulist = c(U.ed,U.c))

 - Computing 40000 x 393 likelihood matrix.
 - Likelihood calculations took 10.09 seconds.
 - Fitting model with 393 mixture components.
 - Model fitting took 83.44 seconds.
 - Computing posterior matrices.
 - Computation allocated took 139.36 seconds.

## Use learned weights to gain posterior estimation for strong signals
m2 = mash(data.strong, g=get_fitted_g(m), fixg=TRUE)

 - Computing 15678 x 393 likelihood matrix.
 - Likelihood calculations took 3.83 seconds.
 - Computing posterior matrices.
 - Computation allocated took 19.45 seconds.

Estimate data driven covariance

U.pca = cov_pca(data.strong,4)
U.ed = cov_ed(data.strong, U.pca)

Fit mashr model with both canonical & data-driven covariance structure

U.c = cov_canonical(data.random)
m = mash(data.random, Ulist = c(U.ed,U.c))

 - Computing 40000 x 393 likelihood matrix.
 - Likelihood calculations took 9.21 seconds.
 - Fitting model with 393 mixture components.
 - Model fitting took 85.87 seconds.
 - Computing posterior matrices.
 - Computation allocated took 150.04 seconds.

## Use learned weights to gain posterior estimation for strong signals
m2 = mash(data.strong, g=get_fitted_g(m), fixg=TRUE)

 - Computing 15678 x 393 likelihood matrix.
 - Likelihood calculations took 3.71 seconds.
 - Computing posterior matrices.
 - Computation allocated took 20.70 seconds.

print(get_loglik(m))

[1] 205233

print(get_estimated_pi(m))

         null      ED_PCA_1      ED_PCA_2      ED_PCA_3      ED_PCA_4 
 3.865163e-01  5.281307e-03  1.511466e-04  0.000000e+00  3.692821e-02 
      ED_tPCA      identity    beta_naive       beta_IF     beta_IFSL 
 2.683872e-04  3.302612e-05  0.000000e+00  0.000000e+00  0.000000e+00 
      beta_SL equal_effects  simple_het_1  simple_het_2  simple_het_3 
 0.000000e+00  5.530311e-01  0.000000e+00  2.458072e-04  1.754470e-02

barplot(get_estimated_pi(m),las = 2)

Version	Author	Date
f74b3e4	Nicholeyang0215	2020-01-04

mash_plot_meta(m,get_significant_results(m)[1])

Version	Author	Date
f74b3e4	Nicholeyang0215	2020-01-04

Effect Size Comparison

Posterior Mean VS. Original Effect

Conditions 1-4 are: naive/ IF/ IF+SL/ SL. (IF, SL are two drug treatments)

random signal posterior comparison

par(mfrow = c(2,2))

for (i in c(1:4)){
  
  plot(data.random$Bhat[,i], get_pm(m)[,i], pch = 20, ylab = "Posterior Mean", xlab = "Original Effect", main = paste('Condition_',i, sep = ""))
  abline(coef = c(0,1), col = "red")
  
}

Scaled by standard deviation: Posterior Mean VS. Original Effect

par(mfrow = c(2,2))
for ( i in c(1:4)){
  
  plot(data.random$Bhat[,i]/data.random$Shat[,i], get_pm(m)[,i]/get_psd(m)[,i], pch = 20, ylab = "Posterior Mean", xlab = "Original Effect", main = paste('Condition_',i, sep = ""))
  abline(coef = c(0,1), col = "red")
  
}

strong signal posterior comparison

par(mfrow = c(2,2))

for (i in c(1:4)){
  
  plot(data.strong$Bhat[,i], get_pm(m2)[,i], pch = 20, ylab = "Posterior Mean", xlab = "Original Effect", main = paste('Condition_',i, sep = ""))
  abline(coef = c(0,1), col = "red")
  
}

Scaled by standard deviation: Posterior Mean VS. Original Effect

par(mfrow = c(2,2))
for ( i in c(1:4)){
  
  plot(data.strong$Bhat[,i]/data.strong$Shat[,i], get_pm(m2)[,i]/get_psd(m2)[,i], pch = 20, ylab = "Posterior Mean", xlab = "Original Effect", main = paste('Condition_',i, sep = ""))
  abline(coef = c(0,1), col = "red")
  
}

Run mashr without ED step: loglikelihood are very close.

Data driven covariance

U.pca = cov_pca(data.strong,4)
U.c = cov_canonical(data.random)
m3 = mash(data.random, Ulist = c(U.pca,U.c))

 - Computing 40000 x 393 likelihood matrix.
 - Likelihood calculations took 10.04 seconds.
 - Fitting model with 393 mixture components.
 - Model fitting took 86.23 seconds.
 - Computing posterior matrices.
 - Computation allocated took 155.79 seconds.

print(get_loglik(m))

[1] 205233

print(get_loglik(m3))

[1] 205232.7

barplot(get_estimated_pi(m3),las = 2)

sessionInfo()

R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.15

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] mashr_0.2.21.0641 ashr_2.2-38      

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.2        plyr_1.8.4        compiler_3.5.1   
 [4] later_1.0.0       git2r_0.26.1      highr_0.7        
 [7] workflowr_1.5.0   iterators_1.0.12  tools_3.5.1      
[10] digest_0.6.18     evaluate_0.13     lattice_0.20-38  
[13] rlang_0.4.0       Matrix_1.2-15     foreach_1.4.7    
[16] yaml_2.2.0        parallel_3.5.1    mvtnorm_1.0-11   
[19] xfun_0.4          stringr_1.4.0     knitr_1.21       
[22] fs_1.3.1          rprojroot_1.3-2   grid_3.5.1       
[25] glue_1.3.0        R6_2.4.0          rmarkdown_1.11   
[28] mixsqp_0.1-97     rmeta_3.0         magrittr_1.5     
[31] whisker_0.3-2     backports_1.1.3   promises_1.1.0   
[34] codetools_0.2-16  htmltools_0.4.0   MASS_7.3-51.1    
[37] assertthat_0.2.1  abind_1.4-5       httpuv_1.5.2     
[40] stringi_1.3.1     doParallel_1.0.15 pscl_1.5.2       
[43] truncnorm_1.0-8   SQUAREM_2017.10-1

mashr_application1

Yunqi Yang

12/8/2019

Format data to mashr format

Correlation structure

Data driven covariance

Fit mashr model with both canonical & data-driven covariance structure

Estimate data driven covariance

Fit mashr model with both canonical & data-driven covariance structure

Effect Size Comparison

Posterior Mean VS. Original Effect

random signal posterior comparison

Scaled by standard deviation: Posterior Mean VS. Original Effect

strong signal posterior comparison

Scaled by standard deviation: Posterior Mean VS. Original Effect

Run mashr without ED step: loglikelihood are very close.

Data driven covariance