Last updated: 2021-10-11

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Knit directory: single-cell-topics/analysis/

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Rmd e2577f1 Peter Carbonetto 2021-10-11 Working on the data simulation step in the de_analysis_detailed_look
html cd17ccf Peter Carbonetto 2021-10-09 Initial build of the de_analysis_detailed_look workflowr page.
Rmd b8e1fe8 Peter Carbonetto 2021-10-09 workflowr::wflow_publish(“de_analysis_detailed_look.Rmd”)
Rmd 888ea7d Peter Carbonetto 2021-10-08 I have an initial implementation of function simulate_twotopic_scrnaseq_data used to evaluate the de_analysis methods in fastTopics.

Add summary of the analysis here.

Load the packages used in the analysis below, and some additional functions for simulating the data.

library(Matrix)
library(fastTopics)
library(MCMCpack)
library(ggplot2)
library(cowplot)
source("../code/de_eval_functions.R")

Simulate UMI counts

We begin by simulating counts intended to “mimic” UMI count data from a single-cell RNA sequencing experiment. In particular, we simulate counts \(x_{ij}\) from a Poisson NMF model \(x_{ij} \sim \mathrm{Poisson}(\lambda_{ij})\), such that \(\lambda_{ij} = \sum_{k=1}^K l_{ik} f_{jk}\). For now we focus our attention on the case of \(K = 2\) topics (e.g., two cell types or two cell states) to simplify the analysis; comparing gene expression between three or topics brings some additional complications which aren’t necessary for vunderstanding the properties of the new DE methods.

set.seed(1)
dat <- simulate_twotopic_umi_data()
X <- dat$X

The multinomial sample sizes (the total count in each cell) were simulated to be normally distributed on the (base-10) log scale with mean 3.2 and s.d. 0.2:

s <- rowSums(X)
ggplot(data.frame(s = log10(s)),aes(x = s)) +
  geom_histogram(color = "white",fill = "black",bins = 32) +
  labs(x = "log10 size",y = "cells") +
  theme_cowplot()

mean(log10(s))
sd(log10(s))
# [1] 3.25348
# [1] 0.1849638

We have simulated the expression rates so that they are normally distributed on the log scale:

ggplot(data.frame(f = as.vector(dat$F)),aes(x = log10(f))) +
  geom_histogram(color = "white",fill = "black",bins = 32) +
  labs(x = "log10 expression rate",y = "genes") +
  theme_cowplot()

The log-fold changes (LFCs) in expression are simulated to be roughly t-distibuted with 1.7 degrees of freedom, \(\mathrm{lfc\)} 0.7t_{1.7}$:

lfc <- log2(dat$F[,1]/dat$F[,2])
mean(lfc == 0)
ggplot(data.frame(lfc = lfc[lfc != 0]),aes(x = lfc)) +
geom_histogram(color = "white",fill = "black",bins = 32) +
  theme_cowplot()

# [1] 0.5002

sessionInfo()
# R version 3.6.2 (2019-12-12)
# 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] cowplot_1.0.0     ggplot2_3.3.5     MCMCpack_1.4-5    MASS_7.3-51.4    
# [5] coda_0.19-3       fastTopics_0.6-70 Matrix_1.2-18    
# 
# loaded via a namespace (and not attached):
#  [1] httr_1.4.2         tidyr_1.1.3        jsonlite_1.7.2     viridisLite_0.3.0 
#  [5] RcppParallel_4.4.2 assertthat_0.2.1   mixsqp_0.3-46      yaml_2.2.0        
#  [9] progress_1.2.2     ggrepel_0.9.1      pillar_1.6.2       backports_1.1.5   
# [13] lattice_0.20-38    quantreg_5.54      glue_1.4.2         quadprog_1.5-8    
# [17] digest_0.6.23      promises_1.1.0     colorspace_1.4-1   htmltools_0.4.0   
# [21] httpuv_1.5.2       pkgconfig_2.0.3    invgamma_1.1       SparseM_1.78      
# [25] purrr_0.3.4        scales_1.1.0       whisker_0.4        later_1.0.0       
# [29] Rtsne_0.15         MatrixModels_0.4-1 git2r_0.26.1       tibble_3.1.3      
# [33] farver_2.0.1       generics_0.0.2     ellipsis_0.3.2     withr_2.4.2       
# [37] ashr_2.2-51        lazyeval_0.2.2     magrittr_2.0.1     crayon_1.4.1      
# [41] mcmc_0.9-6         evaluate_0.14      fs_1.3.1           fansi_0.4.0       
# [45] truncnorm_1.0-8    tools_3.6.2        data.table_1.12.8  prettyunits_1.1.1 
# [49] hms_1.1.0          lifecycle_1.0.0    stringr_1.4.0      plotly_4.9.2      
# [53] munsell_0.5.0      irlba_2.3.3        compiler_3.6.2     rlang_0.4.11      
# [57] grid_3.6.2         htmlwidgets_1.5.1  labeling_0.3       rmarkdown_2.3     
# [61] gtable_0.3.0       DBI_1.1.0          R6_2.4.1           knitr_1.26        
# [65] dplyr_1.0.7        utf8_1.1.4         workflowr_1.6.2    rprojroot_1.3-2   
# [69] stringi_1.4.3      parallel_3.6.2     SQUAREM_2017.10-1  Rcpp_1.0.7        
# [73] vctrs_0.3.8        tidyselect_1.1.1   xfun_0.11