Defining Gene Sets and the Tested-Gene Universe

Why the Background Must Match the Analysis

A pathway enrichment analysis compares a selected collection of genes with genes assigned to a biological set. That comparison is only interpretable if the background represents genes that had a legitimate opportunity to be selected. In an RNA-seq experiment, a gene absent from the assay or excluded before differential-expression testing could not appear in the selected list. Counting it as an unselected background gene changes the reference set for reasons unrelated to the biological question.

The two inputs therefore need to be defined before enrichment is calculated: what counts as membership in the gene set? and which genes were eligible to be selected? These are data and analysis decisions, not merely labels attached to a pathway database. The earlier material on independent filtering is relevant here: genes removed from testing by a filter should not be treated as tested genes with non-significant results.

The intersection \(S \cap U\) is sometimes called the pathway genes in the background, or the effective pathway set for that analysis. A gene can be annotated to a pathway but not be eligible for the current analysis. Conversely, a gene can be in \(U\) without belonging to that pathway. The count of selected pathway genes is \(|D \cap S|\). Since \(D \subseteq U\), this is also \(|D \cap (S \cap U)|\): only genes both selected and eligible pathway members contribute.

Defining Membership and Eligibility

A gene-set definition needs a clear biological label and a reproducible membership rule. Record the source of the annotation, its release or retrieval date, the pathway or set identifier, and the identifier type used to represent genes. For example, a set might be defined as all unique Ensembl gene identifiers assigned to one specified pathway in a specified annotation release. A broad label such as “immune genes” is not sufficient unless the source and rule that determine membership are also given.

Identifiers require particular care. A pathway may use Entrez identifiers while an expression matrix uses Ensembl identifiers or gene symbols. Convert identifiers using a documented mapping and apply a consistent rule for unmapped or ambiguous entries. Gene symbols can change, and a single symbol may map to multiple records. If several probes or transcripts map to one gene, decide whether the analysis is at probe, transcript, or gene level, then use that same unit in the differential-expression results, pathway membership, and universe. Counting the same gene more than once can distort both membership and overlap.

The universe is analysis-specific. Begin with genes represented by the assay, then account for the mapping and quality-control steps, and finally identify the genes included in the tests that produced \(D\). In a gene-level RNA-seq analysis, the universe is typically the genes with usable counts that were actually tested after the stated filters. In a targeted panel, it is limited by panel coverage. In a microarray study, it is limited by the probes and the rules used to map probes to genes. A genome-wide annotation does not make every annotated gene eligible.

“Measured” and “tested” are related but not identical. A gene may have a recorded value yet be excluded from testing because it fails a pre-specified expression or quality filter. If the differential-expression procedure reports that gene as untested, it does not belong to \(U\). A gene that was tested and did not meet the selection threshold does belong to \(U\); it is an unselected gene, not an unmeasured one. Keep these categories distinct in the analysis records.

A Justification for Intersecting the Sets

Restricting pathway membership to \(U\) is not an arbitrary adjustment. It follows from the definition of the selected list. If \(D \subseteq U\), then every gene in \(D \cap S\) is necessarily in \(U\) as well. Thus \(D \cap S\) and \(D \cap (S \cap U)\) contain exactly the same genes:

The restriction changes the pathway’s eligible membership count from \(|S|\) to \(|S \cap U|\), and it changes the background from all annotated genes to the genes actually tested. The later calculation of enrichment uses these aligned inputs. This set identity does not, by itself, establish that an enrichment result is statistically significant; it establishes which genes are eligible to contribute to that calculation.

Filtering and the Meaning of “Untested”

The universe should correspond to the exact differential-expression results from which \(D\) was formed. If a filter removes genes before testing, the removed genes are outside \(U\). If a gene remains in the tests but has a p-value above the chosen cutoff, it remains inside \(U\), even though it is not in \(D\). This distinction matters whether selection is based on an adjusted p-value threshold, an effect-size threshold, or a combination: the selection rule defines \(D\), while the set of genes tested defines \(U\).

Keep filtering rules and selection rules separate in the analysis description. For example, a minimum-count rule might determine which genes are tested, while an adjusted p-value cutoff determines which tested genes are selected. The first changes \(U\); the second changes \(D\). When using a differential-expression result table, check whether it records filtered or untested genes, and do not infer that every omitted gene received a non-significant test result.

Checks, Alternatives, and Limitations

Before interpreting an enrichment result, verify that the selected list is a subset of the stated universe, that each gene is counted once at the chosen analysis level, and that the pathway membership is intersected with that universe. Also check that the annotation and identifier mapping are recorded well enough for another analyst to reconstruct the sets.

A useful alternative is to analyze a ranked list rather than first defining a selected list and a tested-gene universe for over-representation. Ranked-list methods use information across genes in a ranking, but they still require genes that can be matched to the assay and annotation. They do not justify including genes that could not be measured. For the over-representation approach, defining \(D\) and \(U\) explicitly is essential because the comparison is based on selected versus eligible genes.

No single background is correct for every study. Using all genes in an organism is usually inappropriate when the assay covered only a subset. Using all genes detected at any level can also be inappropriate if some detected genes were excluded from the actual tests. Even a carefully matched universe cannot fix poor annotation, ambiguous mappings, or biological and technical biases in which genes are more likely to be selected. Report the choices and interpret enrichment as a result conditional on the assay, filters, tests, and annotation used—not as evidence that the pathway caused the observed expression changes.