Reporting Enriched Pathways as Testable Hypotheses

From an Enrichment Result to a Testable Hypothesis

A pathway-enrichment result is the outcome of a sequence of choices: which variants contribute, how variants are mapped to genes, which genes could have been tested, how pathways are represented, and what enrichment test is used. A report that gives only a pathway name and a small p-value hides those choices. It is difficult to assess, reproduce, or turn into a useful follow-up experiment.

The purpose of reporting is not to make an enrichment result sound definitive. It is to specify the statistical finding closely enough that readers can judge its scope and uncertainty, and to state what further evidence would be needed to evaluate the proposed biology. Enrichment is evidence about a defined collection of gene-level results relative to a defined comparison. By itself, it does not establish that every gene in the pathway is involved, identify a causal gene, or validate a mechanism.

What a Reproducible Report Needs to Specify

The tested universe is not simply “all genes.” A gene that could not receive a score, was excluded by an analysis filter, or had no usable pathway annotation may not have been eligible for the test. The report should give the number of genes in the universe and the rule defining membership in it. It should also state how many genes from each reported pathway were present in that universe. A pathway database can contain many genes that were not testable in the analysis; those genes should not silently enlarge the denominator.

Variant-to-gene mapping requires equally concrete description. State the mapping method, the data or annotations it uses, relevant thresholds, and how multiple variants or genes are handled. If mapping uncertainty was propagated into gene scores, say how; if a single mapping was used, say that too. The gene-level score should be described in terms of what it represents—for example, signed association evidence or an unsigned measure of association strength. These scores are not interchangeable, and the meaning of “higher” depends on the score and test.

For each pathway analysis, identify the pathway source and version, the gene-set definition, the enrichment estimand and test, and the family of tests used for multiplicity adjustment. A competitive test compares evidence in a set with evidence outside it; a self-contained test asks whether there is evidence within the set under its stated null. A reader needs to know which question was tested, not just the software name. For overlapping pathways, specify whether adjustment covers all pathways tested or a narrower declared family. Report the unadjusted p-value and the adjusted result, using the same adjustment convention throughout.

A useful result statement reports the pathway’s name and identifier, the number of genes tested in it, an effect estimate where available, its uncertainty, and the p-value and multiplicity-adjusted result. It should say what a positive or negative effect means for the chosen score. If the test yields only a ranking statistic or an enrichment score, explain its scale and direction rather than attaching an interpretation from a different model.

Report Direction and Uncertainty in the Right Terms

“Positive enrichment” is not a universal biological direction. If a pathway test uses unsigned association magnitudes, a positive enrichment statistic indicates that genes in the set tend to have stronger association evidence under that statistic. It does not mean that the trait increases expression of those genes, that the pathway is activated, or that the genes have effects in the same direction. If a test instead uses signed gene-level statistics, the sign must be interpreted relative to the allele or other direction convention used to create those statistics. Even then, the pathway-level sign does not establish a causal mechanism.

Where the method provides an interpretable effect estimate, report it with its scale, standard error, and confidence interval. A confidence interval describes the uncertainty of the estimate under the model and its assumptions; it is not a probability statement about the fixed parameter. P-values describe compatibility of the data with the specified null under the test assumptions, not the probability that the null is true. Multiplicity-adjusted results address a declared family of tests and should not be described as the probability that a particular pathway is a false discovery.

A short calculation explains why the interval is tied to the model rather than being a direct probability statement about the coefficient. Under the assumed normal approximation, repeated estimates satisfy approximately \((\hat{\beta}-\beta)/SE\sim N(0,1)\). Thus, the interval procedure covers the fixed coefficient \(\beta\) in about 95% of repetitions when its assumptions hold. For the observed data, the interval is an uncertainty summary; it does not assign a 95% probability to \(\beta\) lying between its endpoints.

Sensitivity Results Are Part of the Finding

Enrichment can depend on choices about mapping, gene-score construction, pathway membership, gene-level covariate adjustment, and the null procedure. A report should identify the important choices and summarize planned sensitivity analyses. For each, state what changed and give the result in comparable terms. If a result changes substantially, say so. Do not present only the version with the smallest p-value or treat agreement across analyses as independent replication when the analyses use the same underlying data.

Sensitivity results help distinguish a stable signal from one driven by a particular analytical choice. They do not remove uncertainty, and a result that survives several specifications is still an association-based enrichment result. Conversely, a result that weakens under an alternative mapping may still motivate a follow-up question, but the dependence on mapping should be visible in the report.

From Statistical Enrichment to Biological Follow-Up

An enriched pathway is a statistical summary of a gene set under a particular analysis. The result can be influenced by the genes’ scores, the pathway’s membership, annotation coverage, gene size or variant count, linkage disequilibrium, and overlap with other gene sets. Earlier material on enrichment diagnostics and sensitivity analysis addresses how these features can affect tests; a report should make clear which relevant controls or sensitivity checks were used.

Biological interpretation should therefore be framed as a hypothesis. Name the observed pattern and the proposed follow-up, but separate them: “genes assigned to this pathway showed stronger association evidence under the stated competitive test” is a statistical finding; “this pathway mediates the trait” is a mechanistic claim requiring additional evidence. Useful follow-up may test implicated genes or processes in independent data, relevant tissues or cell types, or experimental systems. Those studies can support or challenge the proposed mechanism; enrichment alone cannot validate it.

Common Reporting Pitfall

A common mistake is to report “the pathway was activated because its enrichment p-value was significant.” That conclusion does not follow from a small p-value: the test may use unsigned scores, and statistical enrichment does not establish expression change, activation, or causation. The correction is to state exactly what the statistic measures and in which direction, then describe biological activation as a hypothesis requiring evidence that directly addresses it.

Another mistake is to report a pathway’s database size without saying how many members were actually testable. The correction is to give both counts and define the tested universe. Together, these practices prevent a result from sounding more specific or conclusive than the analysis supports.