GTEx real data with mmbr commit 72ad394

Last updated: 2020-11-06

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Knit directory: mmbr-rss-dsc/

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In this version of mmbr, we simplified some computation, so the speed has improved. We fixed bug in prior scalar estimataion. We implemented ELBO for model with missing data. We computes ELBO for all models and the stopping criteria is based on changes in ELBO. (Without ELBO computation, the stopping criteria is based on changes in pip.)

Here is one gene identified in MASH paper that have different signs for brain vs non brain tissues.

# processing code
compute_maf <- function(geno){
  f <- mean(geno,na.rm = TRUE)/2
  return(min(f, 1-f))
}

compute_missing <- function(geno){
  miss <- sum(is.na(geno))/length(geno)
  return(miss)
}

mean_impute <- function(geno){
  f <- apply(geno, 2, function(x) mean(x,na.rm = TRUE))
  for (i in 1:length(f)) geno[,i][which(is.na(geno[,i]))] <- f[i]
  return(geno)
}

is_zero_variance <- function(x) {
  if (length(unique(x))==1) return(T)
  else return(F)
}

filter_X <- function(X, missing_rate_thresh, maf_thresh) {
  rm_col <- which(apply(X, 2, compute_missing) > missing_rate_thresh)
  if (length(rm_col)) X <- X[, -rm_col]
  rm_col <- which(apply(X, 2, compute_maf) < maf_thresh)
  if (length(rm_col)) X <- X[, -rm_col]
  rm_col <- which(apply(X, 2, is_zero_variance))
  if (length(rm_col)) X <- X[, -rm_col]
  return(mean_impute(X))
}

compute_cov_flash <- function(Y, error_cache = NULL){
  covar <- diag(ncol(Y))
  tryCatch({
    fl <- flashier::flash(Y, var.type = 2, prior.family = c(flashier::prior.normal(), flashier::prior.normal.scale.mix()), backfit = TRUE, verbose.lvl=0)
    if(fl$n.factors==0){
      covar <- diag(fl$residuals.sd^2)
    } else {
      fsd <- sapply(fl$fitted.g[[1]], '[[', "sd")
      covar <- diag(fl$residuals.sd^2) + crossprod(t(fl$flash.fit$EF[[2]]) * fsd)
    }
    if (nrow(covar) == 0) {
      covar <- diag(ncol(Y))
      stop("Computed covariance matrix has zero rows")
    }
  }, error = function(e) {
    if (!is.null(error_cache)) {
      saveRDS(list(data=Y, message=warning(e)), error_cache)
      warning("FLASH failed. Using Identity matrix instead.")
      warning(e)
    } else {
      stop(e)
    }
  })
  s <- apply(Y, 2, sd, na.rm=T)
  if (length(s)>1) s = diag(s)
  else s = matrix(s,1,1)
  covar <- s%*%cov2cor(covar)%*%s
  return(covar)
}

get_center <- function(k,n) {
  ## For given number k, get the range k surrounding n/2
  ## but have to make sure it does not go over the bounds
  if (is.null(k)) {
    return(1:n)
  }
  start = floor(n/2 - k/2)
  end = floor(n/2 + k/2)
  if (start<1) start = 1
  if (end>n) end = n
  return(start:end)
}

dat = readRDS('data/ENSG00000140265.12.Multi_Tissues.rds')
prior = 'data/FastQTLSumStats.mash.FL_PC3.rds'
cis = 500
U = readRDS(prior)$Ulist
weights = rep(1/length(U), length(U))
prior = mmbr::create_mash_prior(mixture_prior=list(weights=weights, matrices=U))
resid_Y = compute_cov_flash(dat$y_res)
X = filter_X(dat$X, 0.1, 0.05)
X = X[,get_center(cis, ncol(X))]
Y = dat$y_res

The covariance/correlation matrix of Y using pairwise complete observations:

library(corrplot)

corrplot 0.84 loaded

par(mfrow=c(1,2))
corrplot(cov(Y, use='pairwise.complete.obs'), method='color', type='upper', tl.col="black", tl.srt=45, is.corr = FALSE)
corrplot(cor(Y, use='pairwise.complete.obs'), method='color', type='upper', tl.col="black", tl.srt=45, is.corr = TRUE)

The covarince/correlation matrix of Y using FLASH:

colnames(resid_Y) = rownames(resid_Y) = colnames(Y)
par(mfrow=c(1,2))
corrplot(resid_Y, method='color', type='upper', tl.col="black", tl.srt=45, is.corr = FALSE)
corrplot(cov2cor(resid_Y), method='color', type='upper', tl.col="black", tl.srt=45, is.corr = TRUE)

Models with L = 10

We fit 3 models with L = 10:

model with exact computation;
model with approximate computation;
model with approximate computation using diagonal residual variance, which is equivalent to exact computation with diagonal residual variance.

stime <- proc.time()
res <- mmbr::msusie(X, Y, prior_variance=prior, residual_variance=resid_Y, approximate=FALSE, compute_objective = T)
etime <- proc.time()
time_res <- etime - stime
saveRDS(list(result = res, result_time = time_res), 'output/GTExprofile_res_elbo.rds')
rm(res)

stime <- proc.time()
res_approx <- mmbr::msusie(X, Y, prior_variance=prior, residual_variance=resid_Y, approximate=TRUE, compute_objective = T)
etime <- proc.time()
time_res_approx <- etime - stime
saveRDS(list(result = res_approx, result_time = time_res_approx), 'output/GTExprofile_resapprox_elbo.rds')
rm(res_approx)

stime <- proc.time()
res_approx_diag <- mmbr::msusie(X, Y, prior_variance=prior, residual_variance=diag(diag(resid_Y)), approximate=TRUE, compute_objective = T)
etime <- proc.time()
time_res_approx_diag <- etime - stime
saveRDS(list(result = res_approx_diag, result_time = time_res_approx_diag), 'output/GTExprofile_resapproxdiag_elbo.rds')
rm(res_approx_diag)

Load models:

library(mmbr)

Loading required package: mashr

Loading required package: ashr

Loading required package: susieR

res1 = readRDS('output/GTExprofile_res_elbo.rds')
res2 = readRDS('output/GTExprofile_resapprox_elbo.rds')
res3 = readRDS('output/GTExprofile_resapproxdiag_elbo.rds')

Model 1 credible sets:

susie_plot(res1$result, y='PIP', main=paste0('dense V, exact, ELBO=',round(res1$result$elbo[res1$result$niter], 2)))

Model 2 credible sets:

susie_plot(res2$result, y='PIP', main=paste0('dense V, approx, ELBO=', round(res2$result$elbo[res2$result$niter], 2)))

Model 3 credible sets:

susie_plot(res3$result, y='PIP', main=paste0('diagonal V, ELBO=', round(res3$result$elbo[res3$result$niter], 2)))

There is no overlapping between CSs. The blue CS in model 3 does not included in CSs from model 1 and 2.

	Total Time	Algorithm Time	# iterations
model 1	1008.105	753.656	15
model 2	724.233	701.838	15
model 3	2184.959	2163.417	56

Univariate Effects

p = mmbr::mmbr_plot(res1$result)
pdf('docs/assets/GRExProfile/GTExprofile_res_elbo.pdf', width = 60, height = 15)
print(p$plot)
dev.off()

Model 1 Effects

p = mmbr::mmbr_plot(res2$result)
pdf('docs/assets/GRExProfile/GTExprofile_resapprox_elbo.pdf', width = 60, height = 15)
print(p$plot)
dev.off()

Model 3 Effects

p = mmbr::mmbr_plot(res3$result)
pdf('docs/assets/GRExProfile/GTExprofile_resapproxdiag_elbo.pdf', width = 5, height = 15)
print(p$plot)
dev.off()

Model 4 result

Models with L = 3

stime <- proc.time()
res <- mmbr::msusie(X, Y, prior_variance=prior, residual_variance=resid_Y, approximate=FALSE, L=3, compute_objective = T)
etime <- proc.time()
time_res <- etime - stime
saveRDS(list(result = res, result_time = time_res), 'output/GTExprofile_resL3_elbo.rds')

stime <- proc.time()
res_approx <- mmbr::msusie(X, Y, prior_variance=prior, residual_variance=resid_Y, approximate=TRUE, L=3, compute_objective = T)
etime <- proc.time()
time_res_approx <- etime - stime
saveRDS(list(result = res_approx, result_time = time_res_approx), 'output/GTExprofile_resapproxL3_elbo.rds')

stime <- proc.time()
res_approx_diag <- mmbr::msusie(X, Y, prior_variance=prior, residual_variance=diag(diag(resid_Y)), approximate=TRUE, L=3, compute_objective = T)
etime <- proc.time()
time_res_approx_diag <- etime - stime
saveRDS(list(result = res_approx_diag, result_time = time_res_approx_diag), 'output/GTExprofile_resapproxdiagL3_elbo.rds')

res1_L3 = readRDS('output/GTExprofile_resL3_elbo.rds')
res2_L3 = readRDS('output/GTExprofile_resapproxL3_elbo.rds')
res3_L3 = readRDS('output/GTExprofile_resapproxdiagL3_elbo.rds')

Model 1 credible sets:

susie_plot(res1_L3$result, y='PIP', main=paste0('dense V, exact, ELBO=', round(res1_L3$result$elbo[res1_L3$result$niter], 2)))

Model 2 credible sets:

susie_plot(res2_L3$result, y='PIP', main=paste0('dense V, approx, ELBO=', round(res2_L3$result$elbo[res2_L3$result$niter], 2)))

Model 3 credible sets:

susie_plot(res3_L3$result, y='PIP', main=paste0('diagonal V, ELBO=', round(res3_L3$result$elbo[res3_L3$result$niter], 2)))

	Total Time	Algorithm Time	# iterations
model 1	692.535	449.446	25
model 2	502.582	482.78	25
model 3	569.317	540.502	25

p = mmbr::mmbr_plot(res1_L3$result)
pdf('docs/assets/GRExProfile/GTExprofile_resL3_elbo.pdf', width = 17, height = 15)
print(p$plot)
dev.off()

Model 1 L3 Effects

Models with L = 1

stime <- proc.time()
res <- mmbr::msusie(X, Y, prior_variance=prior, residual_variance=resid_Y, approximate=FALSE, L=1, compute_objective = T)
etime <- proc.time()
time_res <- etime - stime
saveRDS(list(result = res, result_time = time_res), 'output/GTExprofile_resL1_elbo.rds')

stime <- proc.time()
res_approx <- mmbr::msusie(X, Y, prior_variance=prior, residual_variance=resid_Y, approximate=TRUE, L=1, compute_objective = T)
etime <- proc.time()
time_res_approx <- etime - stime
saveRDS(list(result = res_approx, result_time = time_res_approx), 'output/GTExprofile_resapproxL1_elbo.rds')

stime <- proc.time()
res_approx_diag <- mmbr::msusie(X, Y, prior_variance=prior, residual_variance=diag(diag(resid_Y)), approximate=TRUE, L=1, compute_objective = T)
etime <- proc.time()
time_res_approx_diag <- etime - stime
saveRDS(list(result = res_approx_diag, result_time = time_res_approx_diag), 'output/GTExprofile_resapproxdiagL1_elbo.rds')

res1_L1 = readRDS('output/GTExprofile_resL1_elbo.rds')
res2_L1 = readRDS('output/GTExprofile_resapproxL1_elbo.rds')
res3_L1 = readRDS('output/GTExprofile_resapproxdiagL1_elbo.rds')

Model 1 credible sets:

susie_plot(res1_L1$result, y='PIP', main=paste0('dense V, exact, ELBO=', round(res1_L1$result$elbo[res1_L1$result$niter], 2)))

Model 2 credible sets:

susie_plot(res2_L1$result, y='PIP', main=paste0('dense V, approx, ELBO=', round(res2_L1$result$elbo[res2_L1$result$niter], 2)))

Model 3 credible sets:

susie_plot(res3_L1$result, y='PIP', main=paste0('diagonal V, ELBO=', round(res3_L1$result$elbo[res3_L1$result$niter], 2)))

The CS from model 3 does not overlap any CSs from model 1.

sessionInfo()

R version 3.6.3 (2020-02-29)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Catalina 10.15.7

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/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] mmbr_0.0.1.0305 susieR_0.9.26   mashr_0.2.40    ashr_2.2-51    
[5] corrplot_0.84   workflowr_1.6.2

loaded via a namespace (and not attached):
 [1] progress_1.2.2     tidyselect_1.1.0   xfun_0.19          purrr_0.3.4       
 [5] lattice_0.20-41    colorspace_1.4-1   vctrs_0.3.4        generics_0.1.0    
 [9] htmltools_0.5.0    yaml_2.2.1         rlang_0.4.8        mixsqp_0.3-46     
[13] later_1.1.0.1      pillar_1.4.6       glue_1.4.2         plyr_1.8.6        
[17] matrixStats_0.57.0 lifecycle_0.2.0    stringr_1.4.0      munsell_0.5.0     
[21] gtable_0.3.0       flashier_0.2.7     mvtnorm_1.1-1      evaluate_0.14     
[25] knitr_1.30         httpuv_1.5.4       invgamma_1.1       parallel_3.6.3    
[29] irlba_2.3.3        Rcpp_1.0.5         promises_1.1.1     backports_1.2.0   
[33] scales_1.1.1       rmeta_3.0          truncnorm_1.0-8    abind_1.4-5       
[37] fs_1.5.0           ggplot2_3.3.2      hms_0.5.3          digest_0.6.27     
[41] stringi_1.5.3      dplyr_1.0.2        ebnm_0.1-24        grid_3.6.3        
[45] rprojroot_1.3-2    tools_3.6.3        magrittr_1.5       tibble_3.0.4      
[49] crayon_1.3.4       whisker_0.4        pkgconfig_2.0.3    ellipsis_0.3.1    
[53] Matrix_1.2-18      SQUAREM_2020.5     prettyunits_1.1.1  assertthat_0.2.1  
[57] reshape_0.8.8      rmarkdown_2.5      rstudioapi_0.11    R6_2.5.0          
[61] git2r_0.27.1       compiler_3.6.3

GTEx real data with mmbr commit 72ad394

Yuxin Zou

11/5/2020

Models with L = 10

Models with L = 3

Models with L = 1