What Does It Mean for Two Signals to Colocalize?
A genome-wide association study (GWAS) tests genetic variants for association with a trait, such as disease risk. An expression quantitative trait locus (eQTL) analysis tests variants for association with the expression level of a particular gene, often in a specified tissue or cell type. When both analyses report association in the same genomic region, it is tempting to say that the trait and expression signals “overlap.” But overlapping association is not the question colocalization is intended to answer.
The central question is whether the GWAS association and the eQTL association are attributable to the same causal genetic variant. A different possibility is that two distinct causal variants happen to be near each other and are correlated because of linkage disequilibrium (LD). In either case, several variants in the region may show association in the observed data.
Here, “causal variant” means a variant that generates the association signal in the statistical model being considered. The term alone does not establish a biological mechanism. Even if the same variant affects both a trait and expression, that result does not prove that the expression change mediates the trait effect. The variant could affect both through separate pathways, or the relevant mechanism could involve another molecular feature.
Why Nearby Association Peaks Can Mislead
Variants in LD tend to be inherited together. As a result, a variant that is correlated with the causal variant can show association even when it has no direct effect on the trait or expression. A regional association plot therefore displays association patterns, not a direct label identifying the causal variant.
A simple linear model shows why. Suppose genotypes are standardized to mean zero and variance one. For one phenotype \(Y\), assume that a single causal genotype \(X_a\) affects the phenotype:
Assume the residual \(\varepsilon\) has mean zero and is uncorrelated with the genotypes in the region. The marginal regression coefficient for another standardized genotype \(X_j\) is its covariance with \(Y\). Therefore,
The final equality uses the standardization of both genotypes and the assumption that \(X_j\) is uncorrelated with \(\varepsilon\). Thus, a noncausal variant \(j\) can have a substantial marginal association when its LD correlation with the causal variant \(a\) is high. The same reasoning applies separately to an eQTL phenotype. If the GWAS and eQTL have different causal variants in strong LD, each can tag the other’s signal.
This calculation is a single-causal-variant illustration. Real regions may contain multiple causal variants, and population structure, imputation quality, sample composition, or model misspecification can also affect association patterns. The calculation establishes the key point without implying that every region follows this simplified model.
Worked Example: Different Causal Variants With Overlapping Peaks
Consider two standardized variants, A and B, with LD correlation \(r_{AB}=0.90\). In a hypothetical region, suppose A is causal for a standardized GWAS trait, with effect \(\beta_A=0.20\), while B is causal for standardized expression of a gene, with effect \(\beta_B=0.30\). Assume one causal variant per phenotype and that the residuals are uncorrelated with both genotypes.
For the GWAS trait, the marginal coefficients at A and B are expected to be
For expression, B is causal, so the corresponding marginal coefficients are
Both variants can therefore appear associated in both analyses, and both regional patterns can look similar. Nevertheless, the assumed causal variants are different: A for the GWAS trait and B for expression. The calculation gives expected marginal coefficients; it does not supply sample sizes or standard errors, so it cannot determine which variant will have the smallest p-value in a particular data set. The example shows why overlapping peaks alone cannot establish a shared causal variant.
Fine-Mapping Helps, but Resolution Matters
Fine-mapping uses the association data and an LD model to assess which variants are plausible causes of a signal. A credible set is a set of variants intended to contain the causal variant with a stated posterior probability under the fine-mapping model and its assumptions. For colocalization, fine-mapping is useful because the relevant comparison is between the variants that could explain each signal, not simply between the two lead variants.
If the plausible causal variants for the GWAS signal and the eQTL signal are well resolved and point to the same variant, that is more informative than coincident lead markers. If each signal has a broad credible set, especially one containing several highly correlated variants, the data may not distinguish a shared causal variant from two different variants in the same LD block. Overlap between credible sets is therefore not itself proof of colocalization.
Worked Example: Overlapping Credible Sets Do Not Identify a Shared Variant
Suppose a hypothetical GWAS fine-mapping analysis gives a 95% credible set \(\{v_1,v_2\}\), and an eQTL analysis for one gene in one tissue also gives a 95% credible set \(\{v_1,v_2\}\). Assume the variants are in very strong LD, so the data have limited ability to distinguish them.
The shared set tells us that both analyses retain the same two candidates. It does not tell us whether both signals are caused by \(v_1\), both by \(v_2\), or whether the GWAS signal is caused by \(v_1\) while the eQTL signal is caused by \(v_2\). Each of those possibilities is compatible with the set membership alone.
The conclusion is therefore limited: the analyses have not resolved whether the causal variants are shared. More precise fine-mapping, better-matched LD information, or additional independent data may help, but if the variants are statistically indistinguishable in the available data, stronger wording is not justified.
Assumptions and Practical Checks
A meaningful shared-variant comparison requires that the two analyses refer to comparable variant identities and genomic positions. They must also concern the intended gene and expression context: an eQTL for one gene in one tissue is not automatically evidence about expression in another tissue. Variant matching, allele alignment, genome build, and summary-statistic harmonization require careful treatment; the important point here is that a comparison cannot be interpreted if the two analyses are not referring to the same genetic variants.
The association signals also need to be adequately characterized. A weak or absent eQTL signal may reflect limited power rather than evidence that expression is unrelated to the region. Conversely, a strong eQTL and a strong GWAS association do not, on their own, show that the variants are shared. LD estimates should be appropriate for the populations underlying the association data, since differences in LD can alter which variants tag a signal.
A useful diagnostic sequence is to ask whether each analysis has a credible association signal, whether its plausible causal variants are sufficiently resolved, and whether the two variant-level patterns support the same causal candidate rather than merely a shared LD neighborhood. If the answer to the resolution question is no, the appropriate result is uncertainty, not a forced shared-versus-distinct conclusion.
Specify the GWAS trait, the gene, the expression tissue or cell type, and the genomic region under study.
Assess whether the GWAS and eQTL evidence is adequate for evaluating causal variants, rather than relying only on a reported lead association.
Ask whether the evidence points to the same variant or whether distinct variants in LD remain plausible explanations.
Report shared-variant evidence as such; do not convert it into a claim of expression-mediated causation without separate evidence.
Colocalization and Other Ways to Compare Signals
Several simpler comparisons are useful as exploratory descriptions, but they answer different questions. The table summarizes the distinction.
| Approach | What it compares | What it cannot establish by itself |
|---|---|---|
| Lead-variant overlap | Whether the strongest reported marker is the same in both analyses | Whether that marker, rather than a correlated variant, is causal for both signals |
| Physical proximity | Whether association peaks occur near one another along the genome | Whether their causal variants are shared |
| Credible-set overlap | Whether fine-mapped candidate sets have variants in common | Whether the causal variant is the same when multiple variants remain plausible |
| Colocalization question | Whether both associations are attributable to the same causal variant | Whether expression mediates the trait effect or identifies the full biological mechanism |
The introductory material on fine-mapping and credible sets provides the context for interpreting variant-level uncertainty. Colocalization adds a comparison across two association signals, while retaining that uncertainty. It should not be treated as a substitute for fine-mapping, nor should it be reduced to matching two lead-variant labels.
Common Pitfalls and Limits
- Calling nearby peaks colocalized. Physical proximity is not evidence that the underlying causal variant is shared. Distinct causal variants can be correlated through LD and produce similar regional patterns.
- Treating a shared lead variant as proof. A lead variant is the strongest observed association in an analysis, not necessarily the causal variant. Another correlated variant may drive the signal.
- Over-interpreting overlapping credible sets. A shared set may reflect unresolved LD rather than a shared causal variant. The width and composition of each set matter.
- Confusing shared genetic cause with mediation. A shared variant can affect both expression and a trait without the expression change causing the trait effect. Colocalization alone does not establish the direction or pathway of molecular mediation.
- Treating weak evidence as evidence of absence. If an eQTL analysis is underpowered or expression is poorly measured, failure to detect association does not show that no relevant eQTL exists.
The main limitation is that colocalization is only as informative as the association data, variant resolution, LD information, and causal model used to represent the signals. When the data cannot distinguish two correlated candidates, reporting that unresolved status is more accurate than claiming either a shared or a distinct causal variant.
Check Your Understanding
Answer each question, then compare with the solutions below.
- A GWAS and an eQTL analysis have lead variants 2 kb apart. Does this establish colocalization? Explain.
- Two standardized variants have \(r=0.80\). A GWAS causal effect at variant A is \(0.10\). Under the single-causal-variant model, what marginal coefficient is expected at variant B?
- Both analyses have credible sets containing variants \(u\) and \(v\), which are highly correlated. What conclusion is justified, and what conclusion is not justified?
- If the same variant is supported as causal for a trait and for gene expression, does that prove expression mediates the trait effect? Why or why not?
Solutions. (1) No. A distance of 2 kb describes physical proximity, not causal identity; distinct variants in LD could generate the two signals. (2) The expected marginal coefficient is \(r\beta_A=0.80(0.10)=0.080\). This is the expected association at B under the stated model, not proof that B is causal. (3) It is justified to say that the candidate sets overlap but the causal variant is unresolved. It is not justified to assert that both signals are caused by \(u\), by \(v\), or by one shared variant. (4) No. A shared variant supports a shared genetic cause for the two associations, but it does not establish that the expression change mediates the trait effect; the variant could affect both through separate mechanisms.