Contents

1 Overview

This vignette is an introduction to the usage of pareg. It estimates pathway enrichment scores by regressing differential expression p-values of all genes considered in an experiment on their membership to a set of biological pathways. These scores are computed using a regularized generalized linear model with LASSO and network regularization terms. The network regularization term is based on a pathway similarity matrix (e.g., defined by Jaccard similarity) and thus classifies this method as a modular enrichment analysis tool (Huang, Sherman, and Lempicki 2009).

2 Installation

if (!require("BiocManager", quietly = TRUE)) {
  install.packages("BiocManager")
}
BiocManager::install("pareg")

3 Load required packages

We start our analysis by loading the pareg package and other required libraries.

library(ggraph)
library(tidyverse)
library(ComplexHeatmap)
library(enrichplot)

library(pareg)

set.seed(42)

4 Introductory example

4.1 Generate pathway database

For the sake of this introductory example, we generate a synthetic pathway database with a pronounced clustering of pathways.

group_num <- 2
pathways_from_group <- 10

gene_groups <- purrr::map(seq(1, group_num), function(group_idx) {
  glue::glue("g{group_idx}_gene_{seq_len(15)}")
})
genes_bg <- paste0("bg_gene_", seq(1, 50))

df_terms <- purrr::imap_dfr(
  gene_groups,
  function(current_gene_list, gene_list_idx) {
    purrr::map_dfr(seq_len(pathways_from_group), function(pathway_idx) {
      data.frame(
        term = paste0("g", gene_list_idx, "_term_", pathway_idx),
        gene = c(
          sample(current_gene_list, 10, replace = FALSE),
          sample(genes_bg, 10, replace = FALSE)
        )
      )
    })
  }
)

df_terms %>%
  sample_n(5)
##        term       gene
## 1 g1_term_9 g1_gene_12
## 2 g1_term_5  g1_gene_7
## 3 g2_term_2  g2_gene_2
## 4 g1_term_3 bg_gene_47
## 5 g1_term_8  g1_gene_1

4.2 Term similarities

Before starting the actual enrichment estimation, we compute pairwise pathway similarities with pareg’s helper function.

mat_similarities <- compute_term_similarities(
  df_terms,
  similarity_function = jaccard
)

hist(mat_similarities, xlab = "Term similarity")

We can see a clear clustering of pathways.

Heatmap(
  mat_similarities,
  name = "Similarity",
  col = circlize::colorRamp2(c(0, 1), c("white", "black"))
)

4.3 Create synthetic study

We then select a subset of pathways to be activated. In a performance evaluation, these would be considered to be true positives.

active_terms <- similarity_sample(mat_similarities, 5)
active_terms
## [1] "g2_term_6" "g2_term_3" "g2_term_3" "g2_term_2" "g2_term_8"

The genes contained in the union of active pathways are considered to be differentially expressed.

de_genes <- df_terms %>%
  filter(term %in% active_terms) %>%
  distinct(gene) %>%
  pull(gene)

other_genes <- df_terms %>%
  distinct(gene) %>%
  pull(gene) %>%
  setdiff(de_genes)

The p-values of genes considered to be differentially expressed are sampled from a Beta distribution centered at \(0\). The p-values for all other genes are drawn from a Uniform distribution.

df_study <- data.frame(
  gene = c(de_genes, other_genes),
  pvalue = c(rbeta(length(de_genes), 0.1, 1), rbeta(length(other_genes), 1, 1)),
  in_study = c(
    rep(TRUE, length(de_genes)),
    rep(FALSE, length(other_genes))
  )
)

table(
  df_study$pvalue <= 0.05,
  df_study$in_study, dnn = c("sig. p-value", "in study")
)
##             in study
## sig. p-value FALSE TRUE
##        FALSE    34   17
##        TRUE      1   28

4.4 Enrichment analysis

Finally, we compute pathway enrichment scores.

fit <- pareg(
  df_study %>% select(gene, pvalue),
  df_terms,
  network_param = 1, term_network = mat_similarities
)
## + '/home/biocbuild/.cache/R/basilisk/1.12.1/0/bin/conda' 'create' '--yes' '--prefix' '/home/biocbuild/.cache/R/basilisk/1.12.1/pareg/1.4.1/pareg' 'python=3.8.13' '--quiet' '-c' 'anaconda'
## + '/home/biocbuild/.cache/R/basilisk/1.12.1/0/bin/conda' 'install' '--yes' '--prefix' '/home/biocbuild/.cache/R/basilisk/1.12.1/pareg/1.4.1/pareg' 'python=3.8.13'
## + '/home/biocbuild/.cache/R/basilisk/1.12.1/0/bin/conda' 'install' '--yes' '--prefix' '/home/biocbuild/.cache/R/basilisk/1.12.1/pareg/1.4.1/pareg' '-c' 'anaconda' 'python=3.8.13' 'tensorflow=2.10.0' 'tensorflow-probability=0.14.0'

The results can be exported to a dataframe for further processing…

fit %>%
  as.data.frame() %>%
  arrange(desc(abs(enrichment))) %>%
  head() %>%
  knitr::kable()
term enrichment
g2_term_6 -0.6759553
g2_term_3 -0.6003887
g2_term_2 -0.5817953
g2_term_4 -0.4232832
g2_term_8 -0.4122331
g1_term_2 0.3979995

…and also visualized in a pathway network view.

plot(fit, min_similarity = 0.1)

To provide a wider range of visualization options, the result can be transformed into an object which is understood by the functions of the enrichplot package.

obj <- as_enrichplot_object(fit)

dotplot(obj) +
  scale_colour_continuous(name = "Enrichment Score")
## Scale for colour is already present.
## Adding another scale for colour, which will replace the existing scale.

treeplot(obj) +
  scale_colour_continuous(name = "Enrichment Score")
## Scale for colour is already present.
## Adding another scale for colour, which will replace the existing scale.

4.5 Session information

sessionInfo()
## R version 4.3.1 (2023-06-16)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 22.04.2 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.17-bioc/R/lib/libRblas.so 
## LAPACK: /home/biocbuild/.cache/R/basilisk/1.12.1/pareg/1.4.1/pareg/lib/libmkl_rt.so.1;  LAPACK version 3.9.0
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_GB              LC_COLLATE=C              
##  [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       
## 
## time zone: America/New_York
## tzcode source: system (glibc)
## 
## attached base packages:
## [1] grid      stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] pareg_1.4.1           tfprobability_0.15.1  tensorflow_2.11.0    
##  [4] enrichplot_1.20.0     ComplexHeatmap_2.16.0 lubridate_1.9.2      
##  [7] forcats_1.0.0         stringr_1.5.0         dplyr_1.1.2          
## [10] purrr_1.0.1           readr_2.1.4           tidyr_1.3.0          
## [13] tibble_3.2.1          tidyverse_2.0.0       ggraph_2.1.0         
## [16] ggplot2_3.4.2         BiocStyle_2.28.0     
## 
## loaded via a namespace (and not attached):
##   [1] splines_4.3.1           later_1.3.1             bitops_1.0-7           
##   [4] ggplotify_0.1.1         filelock_1.0.2          polyclip_1.10-4        
##   [7] basilisk.utils_1.12.1   lifecycle_1.0.3         rprojroot_2.0.3        
##  [10] doParallel_1.0.17       globals_0.16.2          processx_3.8.2         
##  [13] lattice_0.21-8          MASS_7.3-60             magrittr_2.0.3         
##  [16] sass_0.4.6              rmarkdown_2.23          jquerylib_0.1.4        
##  [19] yaml_2.3.7              remotes_2.4.2           httpuv_1.6.11          
##  [22] doRNG_1.8.6             sessioninfo_1.2.2       pkgbuild_1.4.2         
##  [25] reticulate_1.30         cowplot_1.1.1           DBI_1.1.3              
##  [28] RColorBrewer_1.1-3      keras_2.11.1            pkgload_1.3.2.1        
##  [31] zlibbioc_1.46.0         BiocGenerics_0.46.0     RCurl_1.98-1.12        
##  [34] yulab.utils_0.0.6       tweenr_2.0.2            circlize_0.4.15        
##  [37] GenomeInfoDbData_1.2.10 IRanges_2.34.1          S4Vectors_0.38.1       
##  [40] ggrepel_0.9.3           listenv_0.9.0           tidytree_0.4.2         
##  [43] parallelly_1.36.0       codetools_0.2-19        DOSE_3.26.1            
##  [46] ggforce_0.4.1           tidyselect_1.2.0        shape_1.4.6            
##  [49] aplot_0.1.10            farver_2.1.1            viridis_0.6.3          
##  [52] doFuture_1.0.0          matrixStats_1.0.0       stats4_4.3.1           
##  [55] base64enc_0.1-3         jsonlite_1.8.7          GetoptLong_1.0.5       
##  [58] ellipsis_0.3.2          tidygraph_1.2.3         iterators_1.0.14       
##  [61] foreach_1.5.2           ggnewscale_0.4.9        progress_1.2.2         
##  [64] tools_4.3.1             treeio_1.24.1           Rcpp_1.0.11            
##  [67] glue_1.6.2              gridExtra_2.3           tfruns_1.5.1           
##  [70] here_1.0.1              xfun_0.39               usethis_2.2.2          
##  [73] qvalue_2.32.0           GenomeInfoDb_1.36.1     withr_2.5.0            
##  [76] BiocManager_1.30.21     fastmap_1.1.1           basilisk_1.12.1        
##  [79] fansi_1.0.4             callr_3.7.3             digest_0.6.33          
##  [82] timechange_0.2.0        R6_2.5.1                mime_0.12              
##  [85] gridGraphics_0.5-1      colorspace_2.1-0        Cairo_1.6-0            
##  [88] GO.db_3.17.0            RSQLite_2.3.1           utf8_1.2.3             
##  [91] generics_0.1.3          data.table_1.14.8       prettyunits_1.1.1      
##  [94] graphlayouts_1.0.0      httr_1.4.6              htmlwidgets_1.6.2      
##  [97] scatterpie_0.2.1        whisker_0.4.1           pkgconfig_2.0.3        
## [100] gtable_0.3.3            blob_1.2.4              XVector_0.40.0         
## [103] shadowtext_0.1.2        htmltools_0.5.5         profvis_0.3.8          
## [106] bookdown_0.34           fgsea_1.26.0            clue_0.3-64            
## [109] scales_1.2.1            Biobase_2.60.0          png_0.1-8              
## [112] ggfun_0.1.1             knitr_1.43              tzdb_0.4.0             
## [115] reshape2_1.4.4          rjson_0.2.21            nloptr_2.0.3           
## [118] nlme_3.1-162            proxy_0.4-27            cachem_1.0.8           
## [121] GlobalOptions_0.1.2     parallel_4.3.1          miniUI_0.1.1.1         
## [124] HDO.db_0.99.1           AnnotationDbi_1.62.2    logger_0.2.2           
## [127] pillar_1.9.0            vctrs_0.6.3             urlchecker_1.0.1       
## [130] promises_1.2.0.1        xtable_1.8-4            cluster_2.1.4          
## [133] evaluate_0.21           magick_2.7.4            zeallot_0.1.0          
## [136] cli_3.6.1               compiler_4.3.1          rngtools_1.5.2         
## [139] rlang_1.1.1             crayon_1.5.2            future.apply_1.11.0    
## [142] labeling_0.4.2          ps_1.7.5                plyr_1.8.8             
## [145] fs_1.6.2                stringi_1.7.12          viridisLite_0.4.2      
## [148] BiocParallel_1.34.2     munsell_0.5.0           Biostrings_2.68.1      
## [151] lazyeval_0.2.2          devtools_2.4.5          GOSemSim_2.26.1        
## [154] Matrix_1.6-0            dir.expiry_1.8.0        hms_1.1.3              
## [157] patchwork_1.1.2         future_1.33.0           bit64_4.0.5            
## [160] KEGGREST_1.40.0         shiny_1.7.4.1           highr_0.10             
## [163] igraph_1.5.0            memoise_2.0.1           bslib_0.5.0            
## [166] ggtree_3.8.0            fastmatch_1.1-3         bit_4.0.5              
## [169] ape_5.7-1

References

Huang, Da Wei, Brad T Sherman, and Richard A Lempicki. 2009. “Bioinformatics Enrichment Tools: Paths Toward the Comprehensive Functional Analysis of Large Gene Lists.” Nucleic Acids Research 37 (1): 1–13.