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Introduction

Compare the loglikelihood from sva-limma-ash, setting \(\alpha=0\) and \(\alpha=1\), on real data.

library(vicar)
library(sva)
Loading required package: mgcv
Loading required package: nlme
This is mgcv 1.8-25. For overview type 'help("mgcv-package")'.
Loading required package: genefilter
Loading required package: BiocParallel
library(cate)
library(seqgendiff)
load('data/scde/scCD4.RData')
load('data/scde/scCD8.RData')
load('data/scde/scCD14.RData')
load('data/scde/scMB.RData')

CD4, CD8, CD14 and B cells. Look at number of genes and cells.

dim(CD4)
[1] 13713   709
dim(CD8)
[1] 13713   313
dim(CD14)
[1] 13713   432
dim(MB)
[1] 13713   342

CD4 vs MB cells.

Y = as.matrix(cbind(CD4,MB))

group_idx = c(rep(1,dim(CD4)[2]),rep(0,dim(MB)[2]))

# remove genes appearing in less than 10 cells

Y = Y[-which(rowSums(Y!=0)<10),]

X = model.matrix(~group_idx)
sva_sva = sva((Y),mod=X,mod0=X[,1],n.sv = 3)
Number of significant surrogate variables is:  3 
Iteration (out of 5 ):1  2  3  4  5  
X.sva <- cbind(X, sva_sva$sv)
lmout <- limma::lmFit(object = (Y), design = X.sva)
eout  <- limma::eBayes(lmout)
svaout           <- list()
svaout$betahat   <- lmout$coefficients[, 2]
svaout$sebetahat <- lmout$stdev.unscaled[, 2] * sqrt(eout$s2.post)
svaout$pvalues   <- eout$p.value[, 2]

# sva-limma-ash-alpha 0

sva_limma_ash0 = ashr::ash(svaout$betahat,svaout$sebetahat,alpha=0)
sva_limma_ash0$loglik
[1] 16134.95
# sva-limma-ash-alpha 1

sva_limma_ash1 = ashr::ash(svaout$betahat,svaout$sebetahat,alpha=1)
sva_limma_ash1$loglik
[1] 17052.65

Take log of Y

Y = log(Y+0.5)
sva_sva = sva((Y),mod=X,mod0=X[,1],n.sv = 3)
Number of significant surrogate variables is:  3 
Iteration (out of 5 ):1  2  3  4  5  
X.sva <- cbind(X, sva_sva$sv)
lmout <- limma::lmFit(object = (Y), design = X.sva)
eout  <- limma::eBayes(lmout)
svaout           <- list()
svaout$betahat   <- lmout$coefficients[, 2]
svaout$sebetahat <- lmout$stdev.unscaled[, 2] * sqrt(eout$s2.post)
svaout$pvalues   <- eout$p.value[, 2]

# sva-limma-ash-alpha 0

sva_limma_ash0 = ashr::ash(svaout$betahat,svaout$sebetahat,alpha=0)
sva_limma_ash0$loglik
[1] 16932.72
# sva-limma-ash-alpha 1

sva_limma_ash1 = ashr::ash(svaout$betahat,svaout$sebetahat,alpha=1)
sva_limma_ash1$loglik
[1] 17553.91

CD8 vs CD14 cells

Y = as.matrix(cbind(CD8,CD14))

group_idx = c(rep(1,dim(CD8)[2]),rep(0,dim(CD14)[2]))

# remove genes appearing in less than 10 cells

Y = Y[-which(rowSums(Y!=0)<10),]

X = model.matrix(~group_idx)
sva_sva = sva((Y),mod=X,mod0=X[,1],n.sv = 3)
Number of significant surrogate variables is:  3 
Iteration (out of 5 ):1  2  3  4  5  
X.sva <- cbind(X, sva_sva$sv)
lmout <- limma::lmFit(object = (Y), design = X.sva)
eout  <- limma::eBayes(lmout)
svaout           <- list()
svaout$betahat   <- lmout$coefficients[, 2]
svaout$sebetahat <- lmout$stdev.unscaled[, 2] * sqrt(eout$s2.post)
svaout$pvalues   <- eout$p.value[, 2]

# sva-limma-ash-alpha 0

sva_limma_ash0 = ashr::ash(svaout$betahat,svaout$sebetahat,alpha=0)
sva_limma_ash0$loglik
[1] 14146.63
# sva-limma-ash-alpha 1

sva_limma_ash1 = ashr::ash(svaout$betahat,svaout$sebetahat,alpha=1)
sva_limma_ash1$loglik
[1] 15013.91

Take log of Y

Y = log(Y+0.5)
sva_sva = sva((Y),mod=X,mod0=X[,1],n.sv = 3)
Number of significant surrogate variables is:  3 
Iteration (out of 5 ):1  2  3  4  5  
X.sva <- cbind(X, sva_sva$sv)
lmout <- limma::lmFit(object = (Y), design = X.sva)
eout  <- limma::eBayes(lmout)
svaout           <- list()
svaout$betahat   <- lmout$coefficients[, 2]
svaout$sebetahat <- lmout$stdev.unscaled[, 2] * sqrt(eout$s2.post)
svaout$pvalues   <- eout$p.value[, 2]

# sva-limma-ash-alpha 0

sva_limma_ash0 = ashr::ash(svaout$betahat,svaout$sebetahat,alpha=0)
sva_limma_ash0$loglik
[1] 16077.39
# sva-limma-ash-alpha 1

sva_limma_ash1 = ashr::ash(svaout$betahat,svaout$sebetahat,alpha=1)
sva_limma_ash1$loglik
[1] 16362.59

Simulate the easiest case…

library(ashr)
set.seed(12345)
beta = c(rep(0,100),rnorm(100))
sebetahat = abs(rnorm(200,0,1))
betahat = rnorm(200,beta,sebetahat)
beta.ash0 = ash(betahat, sebetahat,alpha=0)
beta.ash0$loglik
[1] -281.6105
beta.ash1 = ash(betahat, sebetahat,alpha=1)
beta.ash1$loglik
[1] -324.1801

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)

Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] ashr_2.2-39         seqgendiff_1.2.1    cate_1.0.4         
[4] sva_3.30.0          BiocParallel_1.16.0 genefilter_1.64.0  
[7] mgcv_1.8-25         nlme_3.1-137        vicar_0.1-10       

loaded via a namespace (and not attached):
 [1] Biobase_2.42.0       svd_0.4.1            foreach_1.4.4       
 [4] bit64_0.9-7          splines_3.5.1        assertthat_0.2.0    
 [7] mixsqp_0.2-2         stats4_3.5.1         blob_1.1.1          
[10] yaml_2.2.0           pillar_1.3.1         RSQLite_2.1.1       
[13] backports_1.1.2      lattice_0.20-38      glue_1.3.0          
[16] limma_3.38.2         digest_0.6.18        promises_1.0.1      
[19] colorspace_1.3-2     htmltools_0.3.6      httpuv_1.4.5        
[22] Matrix_1.2-15        plyr_1.8.4           XML_3.98-1.16       
[25] pkgconfig_2.0.2      esaBcv_1.2.1         purrr_0.3.2         
[28] xtable_1.8-3         corpcor_1.6.9        scales_1.0.0        
[31] whisker_0.3-2        later_0.7.5          git2r_0.26.1        
[34] tibble_2.1.1         annotate_1.60.0      IRanges_2.16.0      
[37] ggplot2_3.1.1        BiocGenerics_0.28.0  lazyeval_0.2.1      
[40] survival_2.43-1      magrittr_1.5         crayon_1.3.4        
[43] memoise_1.1.0        evaluate_0.12        fs_1.3.1            
[46] doParallel_1.0.14    MASS_7.3-51.1        truncnorm_1.0-8     
[49] tools_3.5.1          matrixStats_0.54.0   stringr_1.3.1       
[52] S4Vectors_0.20.1     munsell_0.5.0        AnnotationDbi_1.44.0
[55] compiler_3.5.1       rlang_0.4.0          grid_3.5.1          
[58] leapp_1.2            RCurl_1.95-4.11      iterators_1.0.10    
[61] bitops_1.0-6         rmarkdown_1.10       codetools_0.2-15    
[64] gtable_0.2.0         DBI_1.0.0            ruv_0.9.7           
[67] R6_2.3.0             gridExtra_2.3        knitr_1.20          
[70] dplyr_0.8.0.1        bit_1.1-14           workflowr_1.6.0     
[73] rprojroot_1.3-2      pscl_1.5.2           stringi_1.2.4       
[76] SQUAREM_2017.10-1    parallel_3.5.1       Rcpp_1.0.2          
[79] tidyselect_0.2.5