Last updated: 2018-05-10

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    Rmd fc22b3f zouyuxin 2018-05-10 wflow_publish(“analysis/MashCommonbaseline.Rmd”)

Last updated: 2018-05-10

Code version: fc22b3f

library(limma); library(mashr); library(mclust); library(plyr);
Loading required package: ashr
Package 'mclust' version 5.4
Type 'citation("mclust")' for citing this R package in publications.

Attaching package: 'mclust'
The following object is masked from 'package:ashr':

    dens
library(flashr); library(colorRamps); library(corrplot)
corrplot 0.84 loaded

Implement mash on John’s data at time point 18.

data = readRDS('data/results/Microarray_compiledGLM.rds')

Mash

The standard errors in the data are from t distribution with df 733. Since pt(-abs(Bhat/Shat), df) is very close to zero, it is hard to obtain the standard error from the normal distribution. The degree of freedom is large here, we use the original standard error.

mash.data = mash_set_data(Bhat = data$Chat, Shat = data$SE)
L = diag(ncol(data$Chat))
# the 4th col is CTL
L[,4] = -1
row.names(L) = colnames(data$Chat)
L = L[-4,]
mash.data.diff = mash_set_data_contrast(mash.data, L)

Top genes:

# find strong genes
m.1by1 = mash_1by1(mash.data.diff, alpha=0)
strong = get_significant_results(m.1by1)
Z = mash.data.diff$Bhat/mash.data.diff$Shat
Z.strong = Z[strong,]
# center
Z.center = apply(Z.strong, 2, function(x) x - mean(x))

Estimate covariance structures:

Data Driven:

Flash:

flash.data = flash_set_data(Z.center)
fmodel = flash(flash.data, greedy = TRUE, backfit = TRUE)
fitting factor/loading 1
fitting factor/loading 2
fitting factor/loading 3
fitting factor/loading 4
factors = flash_get_ldf(fmodel)$f
row.names(factors) = row.names(L)
pve.order = order(flash_get_pve(fmodel), decreasing = TRUE)

par(mfrow=c(1,3))
for(i in pve.order){
  barplot(factors[,i], main=paste0('Factor ',i, ' pve= ', round(flash_get_pve(fmodel)[i],3)), las=2, cex.names = 0.7)
}

par(mfrow=c(1,1))

flash on the loading:

loading = fmodel$EL[,1:3]
colnames(loading) = paste0('Factor',seq(1,3))
flash.loading = flash_set_data(loading)
flmodel = flash(flash.loading, greedy = TRUE, backfit = TRUE)
fitting factor/loading 1

The flash prefers the rank 0 model. There is no hidden structure in the loading matrix.

Cluster loadings:

mod = Mclust(loading)
summary(mod$BIC)
Best BIC values:
             VVI,9         VVE,9       VVV,9
BIC      -39480.53 -39486.265635 -39619.0773
BIC diff      0.00     -5.738225   -138.5499

Using clustering result to fit mash:

\[l_{i}\sim \sum_{j=1}^{m}N(\mu_{j}, \Sigma_{j})\] We estimate the covariance as \(F(\Sigma_j + \mu_{j}\mu_{j}')F'\).

U_list = alply(mod$parameters$variance$sigma,3)
mu_list = alply(mod$parameters$mean,2)
ll = list()
for (i in 1:length(U_list)){
  ll[[i]] = U_list[[i]] + mu_list[[i]] %*% t(mu_list[[i]])
}

Factors = fmodel$EF[,1:3]
U.loading = lapply(ll, function(U){Factors %*% (U %*% t(Factors))})
names(U.loading) = paste0('Load', "_", (1:length(U.loading)))

# rank 1
Flash_res = flash_get_lf(fmodel)
U.Flash = c(mashr::cov_from_factors(t(as.matrix(factors)), "Flash"), 
            list("tFlash" = t(Flash_res) %*% Flash_res / nrow(Z.center)))

PCA:

U.pca = cov_pca(mash_set_data(Z.center), 3)

Canonical

U.c = cov_canonical(mash_set_data(Z.center))

Extreme Deconvolution

U.dd = c(U.pca, U.loading, U.Flash, list('XX' = t(Z.center) %*% Z.center / nrow(Z.center)))

mash.data.ed = mash.data.diff
mash.data.ed$Bhat = mash.data.diff$Bhat[strong,]
mash.data.ed$Shat = mash.data.diff$Shat[strong,]
mash.data.ed$Shat_alpha = mash.data.diff$Shat_alpha[strong,]
saveRDS(cov_ed(mash.data.ed, U.dd), 'output/MashCB_EE_Cov.rds')

Mash model:

U.ed = readRDS('output/MashCB_EE_Cov.rds')
saveRDS(mash(mash.data.diff, c(U.c, U.ed), algorithm.version = 'R'), 'output/MashCB_model_EE.rds')

Result

mash.model = readRDS('output/MashCB_model_EE.rds')

The log-likelihood of fit is

get_loglik(mash.model)
[1] 63723.63

Here is a plot of weights learned:

options(repr.plot.width=12, repr.plot.height=4)
barplot(get_estimated_pi(mash.model), las = 2, cex.names = 0.7)

Check tPCA covariance matrix

x           <- mash.model$fitted_g$Ulist[["ED_tPCA"]]
colnames(x) <- row.names(L)
rownames(x) <- colnames(x)
corrplot(x, method='color', cl.lim=c(-0.1,1), type='upper', addCoef.col = "black", tl.col="black", tl.srt=45, col=colorRampPalette(c("blue","white","red"))(200))

layout(matrix(c(1,2,3,4), 2, 2, byrow=TRUE))
svd.out = svd(mash.model$fitted_g$Ulist[["ED_tPCA"]])
v = svd.out$v
colnames(v) = row.names(L)
rownames(v) = colnames(v)
options(repr.plot.width=10, repr.plot.height=5)
for (j in 1:4)
  barplot(v[,j]/v[,j][which.max(abs(v[,j]))], cex.names = 0.7,
          las = 2, main = paste0("EigenVector ", j, " for tPCA"))

Check Load 9 covariance matrix

x           <- mash.model$fitted_g$Ulist[["ED_Load_9"]]
colnames(x) <- row.names(L)
rownames(x) <- colnames(x)
corrplot(x, method='color', cl.lim=c(-0.2,1), type='upper', addCoef.col = "black", tl.col="black", tl.srt=45, col=colorRampPalette(c("blue","white","red"))(200))

layout(matrix(c(1,2,3,4), 2, 2, byrow=TRUE))
svd.out = svd(mash.model$fitted_g$Ulist[["ED_Load_9"]])
v = svd.out$v
colnames(v) = row.names(L)
rownames(v) = colnames(v)
options(repr.plot.width=10, repr.plot.height=5)
for (j in 1:4)
  barplot(v[,j]/v[,j][which.max(abs(v[,j]))], cex.names = 0.7,
          las = 2, main = paste0("EigenVector ", j, " for Load 9"))

Check Load 8 covariance matrix

x           <- mash.model$fitted_g$Ulist[["ED_Load_8"]]
colnames(x) <- row.names(L)
rownames(x) <- colnames(x)
corrplot(x, method='color', cl.lim=c(-0.2,1), type='upper', addCoef.col = "black", tl.col="black", tl.srt=45, col=colorRampPalette(c("blue","white","red"))(200))

layout(matrix(c(1,2,3,4), 2, 2, byrow=TRUE))
svd.out = svd(mash.model$fitted_g$Ulist[["ED_Load_8"]])
v = svd.out$v
colnames(v) = row.names(L)
rownames(v) = colnames(v)
options(repr.plot.width=10, repr.plot.height=5)
for (j in 1:4)
  barplot(v[,j]/v[,j][which.max(abs(v[,j]))], cex.names = 0.7,
          las = 2, main = paste0("EigenVector ", j, " for Load 8"))

Check PCA1 covariance matrix

x           <- mash.model$fitted_g$Ulist[["ED_PCA_1"]]
colnames(x) <- row.names(L)
rownames(x) <- colnames(x)
corrplot(x, method='color', cl.lim=c(-0.2,1), type='upper', addCoef.col = "black", tl.col="black", tl.srt=45, col=colorRampPalette(c("blue","white","red"))(200))

layout(matrix(c(1,2,3,4), 2, 2, byrow=TRUE))
svd.out = svd(mash.model$fitted_g$Ulist[["ED_PCA_1"]])
v = svd.out$v
colnames(v) = row.names(L)
rownames(v) = colnames(v)
options(repr.plot.width=10, repr.plot.height=5)
for (j in 1:4)
  barplot(v[,j]/v[,j][which.max(abs(v[,j]))], cex.names = 0.7,
          las = 2, main = paste0("EigenVector ", j, " for PCA 1"))

There are 5187 diferentially expressed genes.

Check pairwise sharing by magnitude and sign:

x = get_pairwise_sharing(mash.model)
x[x > 1]    <- 1
x[x < -1]   <- -1
colnames(x) <- row.names(L)
rownames(x) <- colnames(x)
corrplot.mixed(x, tl.pos="d",upper='color', cl.lim=c(0,1), upper.col=colorRampPalette(rev(c("#D73027","#FC8D59","#FEE090","#FFFFBF",
                               "#E0F3F8","#91BFDB","#4575B4")))(40),
               tl.cex=1.2)

Check pairwise sharing by sign:

x = get_pairwise_sharing(mash.model, factor=0)
x[x > 1]    <- 1
x[x < -1]   <- -1
colnames(x) <- row.names(L)
rownames(x) <- colnames(x)
corrplot.mixed(x, tl.pos="d",upper='color', cl.lim=c(0,1), upper.col=colorRampPalette(rev(c("#D73027","#FC8D59","#FEE090","#FFFFBF",
                               "#E0F3F8","#91BFDB","#4575B4")))(40),
               tl.cex=1.2)

Session information

sessionInfo()
R version 3.4.4 (2018-03-15)
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] corrplot_0.84  colorRamps_2.3 flashr_0.5-6   plyr_1.8.4    
[5] mclust_5.4     mashr_0.2-6    ashr_2.2-7     limma_3.34.9  

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.16      pillar_1.2.2      compiler_3.4.4   
 [4] git2r_0.21.0      workflowr_1.0.1   R.methodsS3_1.7.1
 [7] R.utils_2.6.0     iterators_1.0.9   tools_3.4.4      
[10] digest_0.6.15     tibble_1.4.2      gtable_0.2.0     
[13] evaluate_0.10.1   lattice_0.20-35   rlang_0.2.0      
[16] Matrix_1.2-14     foreach_1.4.4     yaml_2.1.19      
[19] parallel_3.4.4    mvtnorm_1.0-7     ebnm_0.1-11      
[22] stringr_1.3.0     knitr_1.20        REBayes_1.3      
[25] rprojroot_1.3-2   grid_3.4.4        rmarkdown_1.9    
[28] rmeta_3.0         ggplot2_2.2.1     magrittr_1.5     
[31] whisker_0.3-2     scales_0.5.0      backports_1.1.2  
[34] codetools_0.2-15  htmltools_0.3.6   MASS_7.3-50      
[37] assertthat_0.2.0  softImpute_1.4    colorspace_1.3-2 
[40] stringi_1.2.2     Rmosek_8.0.69     lazyeval_0.2.1   
[43] munsell_0.4.3     doParallel_1.0.11 pscl_1.5.2       
[46] truncnorm_1.0-8   SQUAREM_2017.10-1 R.oo_1.22.0

Session information

sessionInfo()
R version 3.4.4 (2018-03-15)
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] corrplot_0.84  colorRamps_2.3 flashr_0.5-6   plyr_1.8.4    
[5] mclust_5.4     mashr_0.2-6    ashr_2.2-7     limma_3.34.9  

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.16      pillar_1.2.2      compiler_3.4.4   
 [4] git2r_0.21.0      workflowr_1.0.1   R.methodsS3_1.7.1
 [7] R.utils_2.6.0     iterators_1.0.9   tools_3.4.4      
[10] digest_0.6.15     tibble_1.4.2      gtable_0.2.0     
[13] evaluate_0.10.1   lattice_0.20-35   rlang_0.2.0      
[16] Matrix_1.2-14     foreach_1.4.4     yaml_2.1.19      
[19] parallel_3.4.4    mvtnorm_1.0-7     ebnm_0.1-11      
[22] stringr_1.3.0     knitr_1.20        REBayes_1.3      
[25] rprojroot_1.3-2   grid_3.4.4        rmarkdown_1.9    
[28] rmeta_3.0         ggplot2_2.2.1     magrittr_1.5     
[31] whisker_0.3-2     scales_0.5.0      backports_1.1.2  
[34] codetools_0.2-15  htmltools_0.3.6   MASS_7.3-50      
[37] assertthat_0.2.0  softImpute_1.4    colorspace_1.3-2 
[40] stringi_1.2.2     Rmosek_8.0.69     lazyeval_0.2.1   
[43] munsell_0.4.3     doParallel_1.0.11 pscl_1.5.2       
[46] truncnorm_1.0-8   SQUAREM_2017.10-1 R.oo_1.22.0

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