Enrichment Analysis

Basics

Enrichment analysis = to analyze whether specific biological pathways or functions are over-represented (enriched) in large-scale omics data, e.g. genes or proteins.

Core idea

input: a gene/protein list, or a ranked gene/protein list
question: whether some biological pathways, functions, or gene groups appear more than expected
output: enriched pathways/functions/gene sets for interpretation

Important idea

Enrichment analysis is usually not about one gene. It is about whether a group of genes points to a biological function, pathway, or process.

Key terms

Foreground
= the selected/presented genes or proteins

Background
= the genes/proteins existing in the whole genome, or the reference set used for comparison

Warning

Background choice matters. A bad background can make the enrichment result misleading. It should match the experiment, not always the whole genome.

Gene set
= a predefined group of genes that share something, e.g. same pathway, same biological function, same cellular location, or same regulation pattern

Ranked gene list
= genes ordered by a score, e.g. fold change, test statistic, correlation, or other measurement

Enriched
= a gene set/pathway/function appears more strongly than expected by chance

Enrichment scores
= a number that summarizes how strongly a gene/protein set is enriched in the input data.
It is often based on:

overlap between a selected list and a gene set
position of gene set members in a ranked list
statistical evidence that the observed pattern is unlikely by chance, related to p-value reasoning

Tip

Different methods calculate enrichment scores differently. So the score should be interpreted together with the method/tool that produced it. See below.

Main Types

Overview and Comparison

graph LR
    A[Enrichment Analysis] --> B[Over-Representation Analysis ORA]
    A --> C[Gene Set Enrichment Analysis GSEA]
    A --> D[Functional Enrichment Analysis]
    D --> E[GO Enrichment]
    D --> F[Pathway Enrichment]
    E --> G[GO Biological Process]
    E --> H[GO Molecular Function]
    E --> I[GO Cellular Component]

Method	Input	Main question	When to use	Gene set presented
ORA	selected foreground + background	is this gene set over-represented in the selected genes?	when there is a clear selected gene/protein list	any predefined gene set
GSEA	ranked gene list	are genes from this gene set concentrated at the top/bottom of the ranking?	when cutoff for selecting genes is unclear	any predefined gene set
GO enrichment	gene list/ranked list + GO database	enrichment (by ORA or GSEA) using GO terms	functional interpretation	functions/processes/locations
Pathway enrichment	gene list/ranked list + pathway database	enrichment (by ORA or GSEA) using pathway gene sets	pathway interpretation	biological pathways or interaction routes

Over-Representation Analysis (ORA)

= tests whether a gene set is over-represented in a selected foreground list compared with a background list

How it works

start with a foreground gene list, e.g. differentially expressed genes from differential analysis
choose a background gene set, e.g. all measured genes
check each pathway/function/gene set
ask: does this gene set contain more foreground genes than expected?

Input

foreground gene list
background gene list
gene set database

Output

gene sets/pathways/functions with enrichment scores or p-values

Enrichment scores & stats

In ORA, the score/statistics are based on overlap between:

foreground genes
background genes
genes inside one gene set/pathway/function

Notation:

$N$ = total number of background genes
$n$ = number of selected foreground genes
$K$ = number of genes in the gene set, within the background
$k$ = observed overlap between the foreground and the gene set

Contingency table (related idea: contingency table tests):

	In gene set	Not in gene set	Total
Foreground	$k$	$n - k$	$n$
Not foreground	$K - k$	$N - K - n + k$	$N - n$
Background total	$K$	$N - K$	$N$

Gene ratio

= proportion of foreground genes in the gene set

gene ratio = k / n

Background ratio

= proportion of background genes in the gene set

background ratio = K / N

Fold enrichment

= how much more common the gene set is in the foreground than in the background.

fold enrichment = gene ratio / background ratio
                = (k / n) / (K / N)

Meaning:

fold enrichment > 1: gene set is more common in the foreground than expected
fold enrichment = 1: gene set appears at the expected background rate
fold enrichment < 1: gene set is less common in the foreground than expected

P-value

P-value comes from a random sampling model with tests:

hypergeometric test, a discrete probability model related to Random Variables & Probability distributions
Fisher's exact test
Hypergeometric probability:

P(X = k) = [C(K, k) * C(N-K, n-k)] / C(N, n)

For enrichment, the p-value is usually:

p-value = P(X >= observed k)

Meaning:

small p-value: this much overlap would be unlikely by random sampling
large p-value: this overlap could easily happen by random sampling

Adjusted p-value / FDR

ORA tests many gene sets at once, so tools correct p-values for multiple testing. Adjusted p-value / FDR provides corrected significance after considering that many gene sets were tested. See Adjusting p-values in Statistical analysis.

Gene Set Enrichment Analysis (GSEA)

= tests whether genes from a gene set tend to appear near the top or bottom of a ranked gene list.

How it works

start with all genes ranked by a score
do not need to first cut genes into significant/non-significant groups
for each gene set, check whether its genes are concentrated at one end of the ranked list

Input

ranked gene list
gene set database

Output

gene sets enriched near the top or bottom of the ranking

Enrichment scores & stats

In GSEA, the score/statistics are based on where gene set members appear in a ranked gene list.

GSEA Enrichment Score

GSEA walks down the ranked list:

if the gene is in the gene set: running score goes up
if the gene is not in the gene set: running score goes down

Simplified unweighted idea:

genes inside the gene set add positive weight
genes outside the gene set add negative weight
the running score starts at 0 and ends at 0

The enrichment score is the largest deviation from zero.

Enrichment Score = maximum running-score deviation from 0

Meaning:

positive ES: gene set is concentrated near the top of the ranking
negative ES: gene set is concentrated near the bottom of the ranking
ES near 0: gene set is spread more randomly across the ranking

Note

In real GSEA, the increase can be weighted by the ranking score, so highly ranked genes may contribute more strongly.

NES

= normalized enrichment score.

Why normalize:

different gene sets have different sizes
raw ES values are not always directly comparable

So GSEA often normalizes ES to make gene sets more comparable.

P-value

GSEA p-value usually comes from permutation/randomization, which is also a sampling/randomization idea (see Data Sampling).

Simplified idea:

calculate the real ES
shuffle gene labels or rankings many times
calculate ES again for each random version
ask how often a random ES is as strong as the real ES
p-value = fraction of random/permuted results with ES as strong as observed ES

Functional enrichment analysis

= general name for enrichment analysis that interprets a gene/protein list by biological functions.

Analyzes whether certain biological functions, pathways, or gene sets are statistically over-represented (enriched) in a list of genes/proteins/metabolites of interest.
how it works
1. take a list of significant genes or proteins
2. compare them to known biological pathways or function sets
3. statistically test whether any functions or pathways appear more often than expected

GO enrichment

= enrichment analysis using Gene Ontology terms as the gene sets. It is not a different statistical idea by itself - it means the enrichment result is interpreted through GO terms.

Gene Ontology (GO) = a structured vocabulary for describing gene functions.

Main GO categories

GO category	Meaning
GO Biological Process (BP)	biological programs/processes, e.g. cell cycle
GO Molecular Function (MF)	molecular activity, e.g. binding or enzyme activity
GO Cellular Component (CC)	where gene products are located, e.g. nucleus or membrane

How it works

use GO terms as predefined gene sets
run ORA or GSEA-like analysis
output enriched GO terms

Pathway enrichment

= enrichment analysis using pathway databases as gene sets.

Examples of pathway-style interpretation

signaling pathways
metabolic pathways
disease-related pathways

Common workflow

get gene/protein measurements from omics data
for protein, usually first map proteins to gene IDs / annotations; see Proteomics Analysis and Modeling
define input
- ORA: foreground + background
- GSEA: ranked gene list
choose gene sets/database
- GO terms
- pathways
- other curated gene sets
run enrichment test
correct for multiple testing (Adjusting p-values in Statistical analysis)
interpret enriched terms carefully

Things to be careful about

gene identifiers need to match the database; for proteins, check platform/protein identifiers in Proteomics Analysis and Modeling#What proteomics data looks like
enrichment does not prove causality
similar GO terms can be redundant
large gene sets may be easier to detect but less specific
small gene sets may be specific but unstable
multiple testing correction is needed because many gene sets are tested (Adjusting p-values in Statistical analysis)