Worked Pathway Analysis from Locus Results to Enrichment

From Locus Results to a Pathway Test

A pathway analysis is only as interpretable as the chain of decisions that produces it. A locus association is evidence about variants, not automatically evidence about a particular gene or pathway. Variants may map to several plausible genes; gene scores can be affected by how many variants are tested and how correlated those variants are; and pathway membership is tested relative to a defined background. A defensible analysis makes these steps explicit and checks whether the result survives reasonable alternatives.

This tutorial follows a hypothetical analysis from locus-level variant statistics to a competitive pathway test. The example is deliberately small enough to calculate by hand. In a real study, the gene universe, LD reference, pathway collection, and resampling scheme would be much larger, but the logic is the same.

The mapping weights need not be mutually exclusive: one variant can have nonzero weights for multiple genes. They are not automatically causal probabilities. Their meaning depends on how the mapping procedure constructed them, and uncertainty in those weights should be reflected in sensitivity analysis or in the gene-score calculation.

Map Variants and Construct Gene Scores

Suppose a locus has variant-level association statistics \(z_v\). One simple evidence score uses \(z_v^2\), so evidence in either association direction contributes positively. For a gene \(g\), a weighted sum is

This score is a summary, not by itself a calibrated gene-level test statistic. In particular, the sum can increase with the number of mapped variants, and correlated variants can contribute redundant evidence. A gene with a large \(Q_g\) should not be compared with another gene as if the two scores had the same null distribution unless that comparability has been justified.

A practical analysis can calibrate each raw gene score against a null distribution that reflects the gene’s variant count, LD, and the scoring procedure. For example, generate null variant statistics using an appropriate LD reference, apply the same variant-to-gene mapping and scoring steps, and record the resulting scores for each gene. If the null mean and standard deviation for gene \(g\) are \(\mu_{0g}\) and \(\sigma_{0g}\), respectively, a standardized score is

This standardization expresses a gene’s observed score relative to its own null distribution. It does not remove every possible source of bias: the null simulations, mapping, and gene universe must still be appropriate. In particular, an LD reference that poorly represents the study population can yield misleading calibration.

Define the Gene Universe and Control Technical Differences

Before testing a pathway, define the gene universe: the genes eligible to appear in the analysis. It should reflect the genes that could have received a score under the study’s variant coverage, annotation, and mapping rules. Comparing pathway genes with all annotated genes when many of those genes could not have been scored creates an inappropriate reference group.

Gene size and variant count matter because larger genes tend to contain more assayed variants and may have more opportunities to accumulate association evidence. LD matters because correlated variants do not provide the same amount of independent information as equally numerous uncorrelated variants. Functional annotation coverage can also differ across genes. A pathway test that ignores these features can mistake technical differences for pathway enrichment.

There are several possible controls, including a covariate-adjusted regression, matched-gene comparisons, or a permutation scheme that preserves relevant features and LD structure. The method should match the test’s estimand and data structure. The example below uses matched comparisons so that the adjustment and its assumptions are visible.

Test a Pathway and Correct for Multiplicity

Consider five matched pairs of genes. In each pair, one gene belongs to a prespecified pathway and the other is a matched nonmember. Suppose the pairs lie in independent LD blocks, and the matching has made pathway membership exchangeable within each pair under the null. Let \(U_{i,\mathrm{in}}\) and \(U_{i,\mathrm{out}}\) denote the standardized scores for the pathway member and matched nonmember in pair \(i\). A simple one-sided competitive statistic is the average paired difference:

where \(m\) is the number of matched pairs. Large positive values indicate stronger scores among pathway members. Under the matched null, the member and nonmember labels can be swapped within each pair. With \(m\) independent pairs, there are \(2^m\) label assignments. The permutation p-value is the proportion of assignments whose statistic is at least as large as the observed statistic. If the test is two-sided, the comparison instead uses the absolute statistic; the direction should be chosen before examining the results.

Usually, many pathways are tested. Their p-values require a multiplicity procedure appropriate to the testing family and dependence among pathways. For example, the Benjamini–Hochberg procedure controls the false discovery rate under its standard conditions: sort the \(K\) p-values from smallest to largest, then compare the \(i\)th value with \(i\alpha/K\), applying the procedure’s step-up rule. Overlapping pathways can yield dependent tests, so the dependence and the chosen correction should be considered rather than assumed away.

In the toy example, suppose three pathway tests yield p-values \(0.03125\), \(0.125\), and \(0.500\). Applying Benjamini–Hochberg to these three values gives adjusted values \(0.09375\), \(0.1875\), and \(0.500\), respectively. For the smallest p-value, the unadjusted calculation is \(0.03125 \times 3/1=0.09375\); the other two are \(0.125 \times 3/2=0.1875\) and \(0.500 \times 3/3=0.500\). Thus, the smallest adjusted value is \(0.09375\), not below \(0.05\). The pathway is suggestive in this hypothetical analysis, but it does not meet a 5% false-discovery-rate threshold under this correction.

Check Sensitivity Before Drawing a Conclusion

A pathway result can depend on uncertain mapping, score construction, the gene universe, matching, the LD reference, and pathway definitions. Sensitivity analysis asks whether the main conclusion is stable under plausible alternatives. It does not mean selecting whichever analysis gives the smallest p-value. The alternatives and the reason for considering them should be reported clearly.

Common Mistakes and the Full Analysis Logic

• Treating mapped genes as certain. A variant near a gene, or assigned a nonzero mapping weight, does not establish that the gene mediates the association. Retain mapping uncertainty in the score or check plausible alternatives.
• Counting correlated variants as independent evidence. A sum of variant statistics can be inflated or miscalibrated when LD is ignored. Use an LD-aware null or resampling procedure that reflects the correlations in the data.
• Ignoring the gene universe. A pathway comparison is defined relative to eligible genes, not an arbitrary list of all annotated genes. Specify how coverage and mapping determine eligibility.
• Assuming gene-size correction is automatic. A standardized gene score or a pathway p-value does not, by itself, prove that gene size and variant count have been controlled. State how those features enter the null, matching, or model.
• Calling an unadjusted result significant after testing many pathways. The relevant evidence must account for the testing family and the dependence structure. A small raw p-value can fail the multiplicity-adjusted criterion.

The end-to-end logic is therefore: define the locus evidence and gene universe; map variants to genes while retaining uncertainty; construct and calibrate gene scores using LD-aware information; compare pathway members with a suitable competitive reference that controls technical differences; adjust for the full set of pathways tested; and check whether the conclusion survives reasonable analytic alternatives. Each step limits a different source of misleading enrichment. A stable pathway result is evidence of a pattern in the association data, not proof of a causal mechanism.