Last updated: 2019-05-08

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Rmd eafe173 Joyce Hsiao 2019-05-08 downstream effects of data transformation methods in null datasets: initial assessment

Introduction

Applying data transformation methods to single-cell gene expression count and computing type I error rate in null datasets.

Notations:

\(X_{ig}\): gene expression count in cell \(i\) from gene \(g\)

\(X_{i+}\): gene expression count in cell \(i\), i.e., \(X_{i+} = \sum_g X_{ig}\)

\(S_i\): library size normalization factor for cell \(i\)

\(p\): a positive pseudo-count added to expression matrix; traditionally it is used to ensure log-transformation of the expression matrix is well-defined. For now we use pseudo-count of 1.

Data transformation compared:

  1. log2_none_p1: \(log2(X_{ig} + p)\) where \(p=1\).

  2. log2_libsum_p1: \(log2(X_{ig}/X_{i+} + p)\) where \(p=1\)

  3. log2_libscale_TMM_p1: \(log2(X_{ig}/S_{i} + p)\) where \(p=1\) using edgeR TMM method to estimate \(S_i\).

  4. log2_libscale_RLE_p1: \(log2(X_{ig}/S_{i} + p)\) where \(p=1\) using DESeq2 RLE method to estimate \(S_i\).

  5. counts_pearsons: Pearson’s residuals of expression counts, derived using sctransform (Hafemeister and Satija, 2019).

Pipeline compared:

More about counts_pearson:

For a given gene \(g\), use the sum of all molecules assigned to a cell as a proxy for sequencing depth, and use this cell attribute in a regression model with negative binomial distribution and log link function. Thus, let \(X_g\) be the vector of UMI counts assigned to gene \(g\), and \(m\) be the vector of molecules assigned to the cells, i.e., \(m_i = \sum_i X_{ig}\). For a given \(g\), we have

\(log(E(X_g)) = \beta_0 + \beta_1 log10 m\)

Using the NB parametrization with mean \(\mu\) and variance \(\mu + \mu^2/\theta\),

Pearson’s residuals are defined as:

\(z_{ig} = (X_{ig}-\mu_{ig})/\sigma_{ig}\)

where

\(\mu_{ig} = exp(\beta_{0g} + \beta_{1g}log10 m_i)\),

\(\sigma_{ig} = \sqrt(\mu_{ig} + \mu^2_{ig}/\theta_{g})\)

Data simulation parameters:

Required packages

knitr::opts_chunk$set(warning=F, message=F)

library(dscrutils)
library(tidyverse)
── Attaching packages ───────────────────────────────────────────────────────── tidyverse 1.2.1 ──
✔ ggplot2 3.1.0       ✔ purrr   0.3.2  
✔ tibble  2.1.1       ✔ dplyr   0.8.0.1
✔ tidyr   0.8.3       ✔ stringr 1.3.1  
✔ readr   1.3.1       ✔ forcats 0.3.0  
── Conflicts ──────────────────────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()

Simulate data and run methods

#methods <- c("limma_voom", "sva_ttest", "t_test")

library(seqgendiff)
library(sctransform)
#source("dsc/modules/poisthin.R")
source("dsc/modules/filter_genes.R")
source("dsc/modules/transform_data.R")
source("dsc/modules/t_test.R")
source("dsc/modules/wilcoxon.R")
source("dsc/modules/limma_voom.R")
source("dsc/modules/edger.R")
source("dsc/modules/deseq2.R")

counts <- readRDS("dsc/data/pbmc_counts.rds")
nsamp <- 100
ngene <- 1000
prop_null <- 0
libsize_factor <- 0
signal_fun <- function(n) rep(libsize_factor, n)
signal_params <- list()
#pvals_thres <- .001
nsim <- 50
for (i in 1:nsim) {
  set.seed(i)
  data_obj <- poisthin(t(counts), nsamp=nsamp, ngene=ngene, 
                       signal_params=signal_params, signal_fun=signal_fun, 
                       prop_null = prop_null)
  saveRDS(data_obj, file = paste0("output/transform_null.Rmd/data_obj_",i,".rds"))
}


nsim <- 50    
transform_methods_list <- c("log2_none_p1", "log2_libsum_p1", "log2_libscale_TMM_p1", 
                            "log2_libscale_RLE_p1", "counts_pearsons")
de_methods_list <- c("edger", "deseq2", "limma_voom", "t_test")

transform_methods_list <- c("log2_none_p1")
de_methods_list <- c("t_test")

out <- do.call(rbind, lapply(1:nsim, function(i) {

  data_obj <- readRDS(file = paste0("output/transform_null.Rmd/data_obj_",i,".rds"))
  Y <- t(data_obj$Y)
  X <- data_obj$X
  keep_genes <- filter_genes(Y, min_cell_detected=5)
  Y <- Y[keep_genes,]
  
  foo_m <- do.call(rbind, lapply(1:length(de_methods_list), function(j) {

  if (de_methods_list[j] == "edger") {
      res <- edger(Y=Y, X=X)
      pvals <- res$pval
      return(data.frame(type1error_01=mean(pvals < .01, na.rm=TRUE),
                        type1error_005=mean(pvals < .005, na.rm=TRUE),
                        type1error_001=mean(pvals < .001, na.rm=TRUE),
                        transform_method = de_methods_list[j],
                        de_method = de_methods_list[j],
                        nsim = i))
  } 
  if (de_methods_list[j] == "deseq2") {
      res <- deseq2(Y=Y, X=X)
      pvals <- res$pval
      return(data.frame(type1error_01=mean(pvals < .01, na.rm=TRUE),
                        type1error_005=mean(pvals < .005, na.rm=TRUE),
                        type1error_001=mean(pvals < .001, na.rm=TRUE),
                        transform_method = de_methods_list[j],
                        de_method = de_methods_list[j],
                        nsim = i))
  } 
  if (de_methods_list[j] == "limma_voom") {
      res <- limma_voom(Y=Y, X=X)
      pvals <- res$pval
      return(data.frame(type1error_01=mean(pvals < .01, na.rm=TRUE),
                        type1error_005=mean(pvals < .005, na.rm=TRUE),
                        type1error_001=mean(pvals < .001, na.rm=TRUE),
                        transform_method = de_methods_list[j],
                        de_method = de_methods_list[j],
                        nsim = i))
  } 

  if (de_methods_list[j] == "t_test") {
      foo_t <- do.call(rbind, lapply(1:length(transform_methods_list), function(k) {
          if (transform_methods_list[k] == "log2_none_p1") {
          transformed_Y <- transform_data(Y, libscale_method = "none", 
                                          log="log2", pseudo_count=1)
          }
          if (transform_methods_list[k] == "log2_libsum_p1") {
          transformed_Y <- transform_data(Y, libscale_method = "sum", 
                                          log="log2", pseudo_count=1)
          }
          if (transform_methods_list[k] == "log2_libscale_TMM_p1") {
          transformed_Y <- transform_data(Y, libscale_method = "TMM", 
                                          log="log2", pseudo_count=1)
          }
          if (transform_methods_list[k] == "log2_libscale_RLE_p1") {
          transformed_Y <- transform_data(Y, libscale_method = "RLE", 
                                          log="log2", pseudo_count=1)
          }
          if (transform_methods_list[k] == "counts_pearsons") {
          transformed_Y <- transform_data(Y, libscale_method = "pearsons_residual", 
                                          log="none", pseudo_count=1)
          }
          res <- t_test(transformed_Y, X)
          pvals <- res[2,]
          return(data.frame(type1error_01=mean(pvals < .01, na.rm=TRUE),
                            type1error_005=mean(pvals < .005, na.rm=TRUE),
                            type1error_001=mean(pvals < .001, na.rm=TRUE),
                            transform_method = transform_methods_list[k],
                            de_method = de_methods_list[j],
                            nsim = i))
      }) )
      return(foo_t)      
    }
  }) )
   return(foo_m)
}))


saveRDS(out, file = "output/transform_null.Rmd/type1error.rds")

Analysis

#alpha <- .001
out <- readRDS(file = "output/transform_null.Rmd/type1error.rds")

levels(out$transform_method)
[1] "edger"                "deseq2"               "limma_voom"          
[4] "log2_none_p1"         "log2_libsum_p1"       "log2_libscale_TMM_p1"
[7] "log2_libscale_RLE_p1" "counts_pearsons"     
labels_methods <- c("edger", "deseq2", "limma_voom", "ttest_log2_none_p1",
            "ttest_log2_libsum_p1", "ttest_log2_libscale_TMM_p1", 
            "ttest_log2_libscale_RLE_p1", "ttest_counts_pearsons")


out %>% #filter(n1==50) %>% 
    group_by(de_method, transform_method) %>%
    ggplot(., aes(x=transform_method, y=type1error_001, col=transform_method)) +
#        facet_wrap(~de_method) +
        geom_boxplot() + geom_point() + xlab("Type 1 error at alpha < .001") +
        geom_hline(yintercept = .001, col="gray50") +
        ylab("Type I error") +
      scale_x_discrete(position = "top",
                       labels=labels_methods) +
       theme(axis.text.x=element_text(angle = 20, vjust = -.3, hjust=.1)) +
       stat_summary(fun.y=mean, geom="point", shape=4, size=4, col="black")

Version Author Date
a4c5501 Joyce Hsiao 2019-05-08 
out %>% #filter(n1==50) %>% 
    group_by(de_method, transform_method) %>%
    ggplot(., aes(x=transform_method, y=type1error_01, col=transform_method)) +
#        facet_wrap(~de_method) +
        geom_boxplot() + geom_point() + xlab("Type 1 error at alpha < .01") +
        geom_hline(yintercept = .01, col="gray50") +
        ylab("Type I error") +
      scale_x_discrete(position = "top",
                       labels=labels_methods) +
       theme(axis.text.x=element_text(angle = 20, vjust = -.3, hjust=.1)) +
       stat_summary(fun.y=mean, geom="point", shape=4, size=4, col="black")

Version Author Date
a4c5501 Joyce Hsiao 2019-05-08 

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] forcats_0.3.0   stringr_1.3.1   dplyr_0.8.0.1   purrr_0.3.2    
 [5] readr_1.3.1     tidyr_0.8.3     tibble_2.1.1    ggplot2_3.1.0  
 [9] tidyverse_1.2.1 dscrutils_0.3.8

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.1       cellranger_1.1.0 plyr_1.8.4       compiler_3.5.1  
 [5] pillar_1.3.1     git2r_0.23.0     workflowr_1.3.0  tools_3.5.1     
 [9] digest_0.6.18    lubridate_1.7.4  jsonlite_1.6     evaluate_0.12   
[13] nlme_3.1-137     gtable_0.2.0     lattice_0.20-38  pkgconfig_2.0.2 
[17] rlang_0.3.4      cli_1.0.1        rstudioapi_0.10  yaml_2.2.0      
[21] haven_1.1.2      withr_2.1.2      xml2_1.2.0       httr_1.3.1      
[25] knitr_1.20       hms_0.4.2        generics_0.0.2   fs_1.2.6        
[29] rprojroot_1.3-2  grid_3.5.1       tidyselect_0.2.5 glue_1.3.0      
[33] R6_2.4.0         readxl_1.1.0     rmarkdown_1.10   modelr_0.1.2    
[37] magrittr_1.5     whisker_0.3-2    backports_1.1.2  scales_1.0.0    
[41] htmltools_0.3.6  rvest_0.3.2      assertthat_0.2.0 colorspace_1.3-2
[45] labeling_0.3     stringi_1.2.4    lazyeval_0.2.1   munsell_0.5.0   
[49] broom_0.5.1      crayon_1.3.4