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
)

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")

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 4.4.0 beta (2024-04-15 r86425)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 22.04.4 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.19-bioc/R/lib/libRblas.so 
## LAPACK: /var/cache/basilisk/1.15.5/pareg/1.7.0/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_1.7.0           tfprobability_0.15.1  tensorflow_2.16.0    
##  [4] enrichplot_1.23.2     ComplexHeatmap_2.19.0 lubridate_1.9.3      
##  [7] forcats_1.0.0         stringr_1.5.1         dplyr_1.1.4          
## [10] purrr_1.0.2           readr_2.1.5           tidyr_1.3.1          
## [13] tibble_3.2.1          tidyverse_2.0.0       ggraph_2.2.1         
## [16] ggplot2_3.5.0         BiocStyle_2.31.0     
## 
## loaded via a namespace (and not attached):
##   [1] splines_4.4.0           later_1.3.2             ggplotify_0.1.2        
##   [4] filelock_1.0.3          polyclip_1.10-6         basilisk.utils_1.15.2  
##   [7] lifecycle_1.0.4         doParallel_1.0.17       globals_0.16.3         
##  [10] lattice_0.22-6          MASS_7.3-60.2           magrittr_2.0.3         
##  [13] sass_0.4.9              rmarkdown_2.26          jquerylib_0.1.4        
##  [16] yaml_2.3.8              remotes_2.5.0           httpuv_1.6.15          
##  [19] doRNG_1.8.6             sessioninfo_1.2.2       pkgbuild_1.4.4         
##  [22] reticulate_1.36.0       cowplot_1.1.3           DBI_1.2.2              
##  [25] RColorBrewer_1.1-3      keras_2.13.0            pkgload_1.3.4          
##  [28] zlibbioc_1.49.3         BiocGenerics_0.49.1     yulab.utils_0.1.4      
##  [31] tweenr_2.0.3            circlize_0.4.16         GenomeInfoDbData_1.2.12
##  [34] IRanges_2.37.1          S4Vectors_0.41.6        ggrepel_0.9.5          
##  [37] listenv_0.9.1           tidytree_0.4.6          parallelly_1.37.1      
##  [40] codetools_0.2-20        DOSE_3.29.2             ggforce_0.4.2          
##  [43] tidyselect_1.2.1        shape_1.4.6.1           aplot_0.2.2            
##  [46] UCSC.utils_0.99.7       farver_2.1.1            viridis_0.6.5          
##  [49] doFuture_1.0.1          matrixStats_1.3.0       stats4_4.4.0           
##  [52] base64enc_0.1-3         jsonlite_1.8.8          GetoptLong_1.0.5       
##  [55] ellipsis_0.3.2          tidygraph_1.3.1         iterators_1.0.14       
##  [58] foreach_1.5.2           ggnewscale_0.4.10       progress_1.2.3         
##  [61] tools_4.4.0             treeio_1.27.1           Rcpp_1.0.12            
##  [64] glue_1.7.0              gridExtra_2.3           tfruns_1.5.2           
##  [67] xfun_0.43               qvalue_2.35.0           usethis_2.2.3          
##  [70] GenomeInfoDb_1.39.14    withr_3.0.0             BiocManager_1.30.22    
##  [73] fastmap_1.1.1           basilisk_1.15.5         fansi_1.0.6            
##  [76] digest_0.6.35           timechange_0.3.0        R6_2.5.1               
##  [79] mime_0.12               gridGraphics_0.5-1      colorspace_2.1-0       
##  [82] Cairo_1.6-2             GO.db_3.19.0            RSQLite_2.3.6          
##  [85] utf8_1.2.4              generics_0.1.3          data.table_1.15.4      
##  [88] prettyunits_1.2.0       graphlayouts_1.1.1      httr_1.4.7             
##  [91] htmlwidgets_1.6.4       scatterpie_0.2.2        whisker_0.4.1          
##  [94] pkgconfig_2.0.3         gtable_0.3.4            blob_1.2.4             
##  [97] XVector_0.43.1          shadowtext_0.1.3        htmltools_0.5.8.1      
## [100] profvis_0.3.8           bookdown_0.39           fgsea_1.29.0           
## [103] clue_0.3-65             scales_1.3.0            Biobase_2.63.1         
## [106] png_0.1-8               ggfun_0.1.4             knitr_1.46             
## [109] tzdb_0.4.0              reshape2_1.4.4          rjson_0.2.21           
## [112] nloptr_2.0.3            nlme_3.1-164            proxy_0.4-27           
## [115] cachem_1.0.8            GlobalOptions_0.1.2     parallel_4.4.0         
## [118] miniUI_0.1.1.1          HDO.db_0.99.1           AnnotationDbi_1.65.2   
## [121] logger_0.3.0            pillar_1.9.0            vctrs_0.6.5            
## [124] urlchecker_1.0.1        promises_1.3.0          xtable_1.8-4           
## [127] cluster_2.1.6           evaluate_0.23           magick_2.8.3           
## [130] tinytex_0.50            zeallot_0.1.0           cli_3.6.2              
## [133] compiler_4.4.0          rngtools_1.5.2          rlang_1.1.3            
## [136] crayon_1.5.2            future.apply_1.11.2     labeling_0.4.3         
## [139] plyr_1.8.9              fs_1.6.3                stringi_1.8.3          
## [142] viridisLite_0.4.2       BiocParallel_1.37.1     munsell_0.5.1          
## [145] Biostrings_2.71.5       lazyeval_0.2.2          devtools_2.4.5         
## [148] GOSemSim_2.29.2         Matrix_1.7-0            dir.expiry_1.11.0      
## [151] hms_1.1.3               patchwork_1.2.0         bit64_4.0.5            
## [154] future_1.33.2           KEGGREST_1.43.0         shiny_1.8.1.1          
## [157] highr_0.10              igraph_2.0.3            memoise_2.0.1          
## [160] bslib_0.7.0             ggtree_3.11.2           fastmatch_1.1-4        
## [163] bit_4.0.5               ape_5.8

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.