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
)
## Loaded Tensorflow version 2.3.0

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 -0.6760687
g2_term_3 -0.6005415
g2_term_2 -0.5818557
g2_term_4 -0.4233026
g2_term_8 -0.4123425
g1_term_2 0.3978593

…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 4.2.0 RC (2022-04-19 r82224)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04.4 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.15-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.15-bioc/R/lib/libRlapack.so
## 
## 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       
## 
## attached base packages:
## [1] grid      stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] pareg_1.0.0           tfprobability_0.15.0  tensorflow_2.8.0     
##  [4] enrichplot_1.16.0     ComplexHeatmap_2.12.0 forcats_0.5.1        
##  [7] stringr_1.4.0         dplyr_1.0.8           purrr_0.3.4          
## [10] readr_2.1.2           tidyr_1.2.0           tibble_3.1.6         
## [13] tidyverse_1.3.1       ggraph_2.0.5          ggplot2_3.3.5        
## [16] BiocStyle_2.24.0     
## 
## loaded via a namespace (and not attached):
##   [1] utf8_1.2.2             reticulate_1.24        tidyselect_1.1.2      
##   [4] RSQLite_2.2.12         AnnotationDbi_1.58.0   BiocParallel_1.30.0   
##   [7] scatterpie_0.1.7       munsell_0.5.0          codetools_0.2-18      
##  [10] future_1.25.0          withr_2.5.0            keras_2.8.0           
##  [13] colorspace_2.0-3       GOSemSim_2.22.0        Biobase_2.56.0        
##  [16] highr_0.9              knitr_1.38             rstudioapi_0.13       
##  [19] stats4_4.2.0           DOSE_3.22.0            listenv_0.8.0         
##  [22] labeling_0.4.2         GenomeInfoDbData_1.2.8 matrixLaplacian_1.0   
##  [25] polyclip_1.10-0        bit64_4.0.5            farver_2.1.0          
##  [28] rprojroot_2.0.3        parallelly_1.31.1      vctrs_0.4.1           
##  [31] treeio_1.20.0          generics_0.1.2         xfun_0.30             
##  [34] R6_2.5.1               doParallel_1.0.17      GenomeInfoDb_1.32.0   
##  [37] clue_0.3-60            graphlayouts_0.8.0     bitops_1.0-7          
##  [40] cachem_1.0.6           fgsea_1.22.0           gridGraphics_0.5-1    
##  [43] assertthat_0.2.1       scales_1.2.0           gtable_0.3.0          
##  [46] Cairo_1.5-15           globals_0.14.0         tidygraph_1.2.1       
##  [49] rlang_1.0.2            zeallot_0.1.0          scatterplot3d_0.3-41  
##  [52] GlobalOptions_0.1.2    splines_4.2.0          lazyeval_0.2.2        
##  [55] broom_0.8.0            BiocManager_1.30.17    yaml_2.3.5            
##  [58] reshape2_1.4.4         modelr_0.1.8           backports_1.4.1       
##  [61] qvalue_2.28.0          tools_4.2.0            bookdown_0.26         
##  [64] ggplotify_0.1.0        ellipsis_0.3.2         jquerylib_0.1.4       
##  [67] RColorBrewer_1.1-3     proxy_0.4-26           BiocGenerics_0.42.0   
##  [70] Rcpp_1.0.8.3           plyr_1.8.7             base64enc_0.1-3       
##  [73] progress_1.2.2         zlibbioc_1.42.0        RCurl_1.98-1.6        
##  [76] prettyunits_1.1.1      GetoptLong_1.0.5       viridis_0.6.2         
##  [79] S4Vectors_0.34.0       haven_2.5.0            ggrepel_0.9.1         
##  [82] cluster_2.1.3          here_1.0.1             fs_1.5.2              
##  [85] furrr_0.2.3            magrittr_2.0.3         magick_2.7.3          
##  [88] data.table_1.14.2      DO.db_2.9              circlize_0.4.14       
##  [91] reprex_2.0.1           whisker_0.4            ggnewscale_0.4.7      
##  [94] matrixStats_0.62.0     hms_1.1.1              patchwork_1.1.1       
##  [97] evaluate_0.15          readxl_1.4.0           IRanges_2.30.0        
## [100] gridExtra_2.3          shape_1.4.6            tfruns_1.5.0          
## [103] compiler_4.2.0         crayon_1.5.1           shadowtext_0.1.2      
## [106] htmltools_0.5.2        ggfun_0.0.6            tzdb_0.3.0            
## [109] aplot_0.1.3            lubridate_1.8.0        DBI_1.1.2             
## [112] tweenr_1.0.2           dbplyr_2.1.1           rappdirs_0.3.3        
## [115] MASS_7.3-57            Matrix_1.4-1           cli_3.3.0             
## [118] parallel_4.2.0         igraph_1.3.1           pkgconfig_2.0.3       
## [121] xml2_1.3.3             foreach_1.5.2          ggtree_3.4.0          
## [124] bslib_0.3.1            XVector_0.36.0         rvest_1.0.2           
## [127] yulab.utils_0.0.4      digest_0.6.29          Biostrings_2.64.0     
## [130] rmarkdown_2.14         cellranger_1.1.0       fastmatch_1.1-3       
## [133] tidytree_0.3.9         rjson_0.2.21           nloptr_2.0.0          
## [136] lifecycle_1.0.1        nlme_3.1-157           jsonlite_1.8.0        
## [139] viridisLite_0.4.0      fansi_1.0.3            pillar_1.7.0          
## [142] lattice_0.20-45        KEGGREST_1.36.0        fastmap_1.1.0         
## [145] httr_1.4.2             GO.db_3.15.0           glue_1.6.2            
## [148] png_0.1-7              iterators_1.0.14       bit_4.0.4             
## [151] ggforce_0.3.3          stringi_1.7.6          sass_0.4.1            
## [154] blob_1.2.3             memoise_2.0.1          ape_5.6-2

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.