5.4 Part 1 — Over-Representation Analysis (ORA) | Introduction to Transcriptomics

5.4 Part 1 — Over-Representation Analysis (ORA)

What is ORA?

ORA asks: “Are my significant DE genes enriched in any pathway more than expected by chance?”

It uses a hypergeometric test (equivalent to a one-sided Fisher’s exact test):

Query set — significant DE genes (padj < 0.05, |LFC| >= 1), converted to gene symbols
Background — all genes tested by DESeq2, converted to gene symbols
Gene sets — KEGG pathways
FDR correction — empirical FDR (eFDR) via resampling, which accounts for interdependence between gene sets

Key assumption: ORA treats all significant genes equally — it ignores magnitude or direction of fold change. This is why we also run GSEA (Part 2), which uses the full ranked list.

5.4.1 Prepare Input

sig_genes <- res_sig_sym$gene
all_genes  <- res_df_sym$gene

cat("Query set (significant genes) :", length(sig_genes), "\n")

## Query set (significant genes) : 646

cat("Pool (all tested genes)        :", length(all_genes), "\n")

## Pool (all tested genes)        : 3698

cat("Overlap with first pathway     :",
    length(intersect(sig_genes, kegg_gmt$list_of_values[[1]])), "genes\n")

## Overlap with first pathway     : 7 genes

Tip: Always use all tested genes as the background, not the full genome. DESeq2 already filtered to expressed genes, so res_df_sym is the correct pool. Using the full genome inflates the background and produces over-optimistic p-values.

5.4.2 Run ORA

set.seed(42)

ora_model <- ora(
  gmt                       = kegg_gmt,
  element_names             = sig_genes,
  background_element_names  = all_genes,
  p_value_adjustment_method = "eFDR",
  number_of_permutations    = 1000
)

ora_results <- mulea::run_test(ora_model)

cat("Pathways tested          :", nrow(ora_results), "\n")

## Pathways tested          : 121

cat("Significant (eFDR < 0.05):", sum(ora_results$eFDR < 0.05, na.rm = TRUE), "\n")

## Significant (eFDR < 0.05): 12

5.4.3 Filter and Inspect Significant Pathways

ora_sig <- ora_results %>%
  filter(eFDR < 0.05) %>%
  arrange(eFDR)

cat("Significant ORA pathways:", nrow(ora_sig), "\n")

## Significant ORA pathways: 12

DT::datatable(
  ora_sig %>%
    select(ontology_id, ontology_name, nr_common_with_tested_elements,
           nr_common_with_background_elements, p_value, eFDR) %>%
    mutate(across(where(is.numeric), \(x) round(x, 4))),
  rownames   = FALSE,
  colnames   = c("KEGG ID", "Pathway", "Hits in query",
                 "Hits in background", "p-value", "eFDR"),
  extensions = c("Buttons", "Scroller"),
  options    = list(
    dom      = "Bfrtip",
    buttons  = c("copy", "csv"),
    scrollX  = TRUE,
    scrollY  = 300,
    scroller = TRUE
  ),
  caption = "Significant ORA pathways — treatment vs control (eFDR < 0.05)"
)

Visualise ORA Results

5.4.4 Bar Plot — Enriched Pathways

ora_bar <- ora_sig %>%
  slice_min(eFDR, n = 20) %>%
  mutate(ontology_name = fct_reorder(ontology_name, -log10(eFDR)))

ora_barplot <- ggplot(ora_bar,
                      aes(x    = -log10(eFDR),
                          y    = ontology_name,
                          fill = -log10(eFDR))) +
  geom_col(width = 0.7) +
  geom_vline(xintercept = -log10(0.05), linetype = "dashed",
             color = "black", linewidth = 0.5) +
  scale_fill_gradient(low = "#92C5DE", high = "#CA0020") +
  theme_bw() +
  theme(legend.position = "none") +
  labs(
    title    = "ORA — Enriched KEGG Pathways (eFDR < 0.05)",
    subtitle = "Treatment vs Control | E. coli MG1655",
    x        = "-log10(eFDR)",
    y        = NULL
  )

ora_barplot

ggplotly(ora_barplot)

5.4.5 Lollipop Plot — Gene Hits per Pathway

ora_lollipop <- ggplot(ora_bar,
                       aes(x     = nr_common_with_tested_elements,
                           y     = ontology_name,
                           color = eFDR)) +
  geom_segment(aes(x    = 0,
                   xend = nr_common_with_tested_elements,
                   yend = ontology_name),
               linewidth = 0.8, color = "grey70") +
  geom_point(size = 4) +
  scale_color_gradient(low = "#CA0020", high = "#92C5DE", name = "eFDR") +
  theme_bw() +
  labs(
    title    = "ORA — Gene Hits per Pathway",
    subtitle = "Point colour = eFDR",
    x        = "Number of DE genes in pathway",
    y        = NULL
  )

ora_lollipop

ggplotly(ora_lollipop)