Conditional And Fine-Mapping-Based Colocalization

Why separate signals before colocalization?

At a locus, a trait can be associated with more than one causal variant. If one signal affects a phenotype and another affects gene expression, a single-signal colocalization analysis may mix their evidence: it can mistake a shared signal plus a distinct signal for one ambiguous association pattern. The central task here is to separate the signals in each trait, then compare the resulting signal-specific evidence for sharing.

Two broad strategies are useful. Conditional analysis adjusts association estimates for one or more selected variants, often in a sequence. Fine-mapping-based analysis uses a model of multiple causal variants to estimate which variants, or signal-specific variant configurations, are supported by the data. Both can prepare inputs for signal-level colocalization, but they answer different questions and rely on different assumptions.

Colocalization asks whether the association signals for two traits are consistent with a shared causal variant rather than distinct causal variants. Here, the focus is how to obtain and compare signal-specific evidence when either trait may have multiple signals. Signal separation does not itself establish sharing, and a shared genomic position does not by itself establish a shared causal variant.

Conditional analysis: adjust for selected variants

In conditional analysis, association for a candidate variant is tested after adjusting for one or more other variants. With individual-level data, this is ordinary regression including the conditioning genotypes as covariates. With summary statistics, conditional effects can be reconstructed using a linkage disequilibrium (LD) correlation matrix, provided the summary statistics and LD information are compatible.

For a simple two-variant illustration, suppose genotypes \(X_1\) and \(X_2\) are standardized to mean zero and variance one, their correlation is \(r\), and the phenotype model is \(Y=\beta_1X_1+\beta_2X_2+\epsilon\), with errors uncorrelated with both genotypes. The marginal regression coefficients are not generally the two model coefficients: each can reflect the other variant’s effect through LD. In this setting, the conditional coefficient for \(X_2\) after adjusting for \(X_1\) is:

The denominator accounts for the remaining variance in \(X_2\) after removing its linear association with \(X_1\). In larger analyses the corresponding operation uses the LD matrix for all included variants, and uncertainty must also be calculated for the conditional estimate. A conditional test produces an adjusted effect estimate and uncertainty, or an adjusted test statistic and p-value. It does not, by itself, produce a posterior probability that a variant is causal.

A sequential procedure may identify a lead variant, condition on it, and search the residual association pattern for another signal. This can be efficient and interpretable when the signals are well separated and the conditioning variants are reliable. But a lead variant is a selected proxy, not necessarily the causal variant. If it only imperfectly tags the causal allele, conditioning on it may leave residual association from that same signal; conditioning on an inappropriate or weakly supported variant can also distort the residual pattern.

Fine-mapping-based separation

Fine-mapping models use the association evidence and LD to distribute support across candidate causal variants. A multi-signal model allows more than one causal effect in the locus, rather than forcing all association into a single variant. For each modeled signal, a method may report posterior inclusion probabilities (PIPs), a credible set, or other signal-level posterior summaries. A credible set is a collection of variants intended to contain the causal variant for a particular signal at a stated posterior coverage under the model; it is not a list of equally likely variants, nor a guarantee that the true variant is included.

Fine-mapping-based colocalization can compare the signal-specific variant support for the two traits. In a simple signal-pair formulation, let \(BF_{Ai}\) and \(BF_{Bi}\) denote evidence for variant \(i\) as the causal variant for the respective signals, and let \(\pi_i\) be the prior probability assigned to variant \(i\) within a signal. Under a shared-variant hypothesis \(H_4\), the two traits use the same variant; under a distinct-variant hypothesis \(H_3\), they use different variants. Their evidence, up to the prior mass assigned to each hypothesis, has the form:

This simplified expression assumes one causal variant per signal and the stated prior structure. Multi-signal implementations may use richer models, but the key idea remains: compare evidence for the same variant against evidence for distinct variants. Simply observing that two credible sets overlap is not this comparison. The overlap discards information about how support is distributed within each set and does not account for the hypothesis priors.

What the two strategies assume and report

Neither strategy is assumption-free. Both need compatible trait definitions, genome build, variant identifiers, and effect-allele alignment. Both depend on LD information that represents the analyzed population and variant set well enough for the intended analysis. Differences in ancestry, imputation, variant coverage, or LD estimation can change the apparent number and strength of signals. If the traits’ association estimates are not comparable, signal separation cannot repair the underlying mismatch.

Conditional analysis is often attractive when individual-level data permit direct regression, or when a well-supported conditioning set is available and the goal is to test whether association remains after adjustment. Fine-mapping-based methods are useful when uncertainty about which variants generate each signal is central and when signal-specific posterior summaries are needed. They are not competing answers to exactly the same question: conditioning asks what association remains after adjustment; fine-mapping asks how the data and model distribute causal-variant support.

In either approach, a signal-specific comparison must match the signals being compared. If a locus has two GWAS signals and one expression signal, for example, each plausible signal pair should be considered rather than treating the locus as one undifferentiated association. Report which signals were paired, how they were separated, and the assumptions and inputs that define the reported comparison.

Derivation and an LD failure mode

The two-variant conditional formula follows from residualizing \(X_2\) against \(X_1\). The residual genotype is \(X_2-rX_1\), whose variance is \(1-r^2\). Its covariance with \(Y\) is the marginal covariance of \(X_2\) with \(Y\) minus \(r\) times the marginal covariance of \(X_1\) with \(Y\). Dividing that covariance by the residual variance gives the coefficient of \(X_2\) in a regression that also includes \(X_1\):

This also exposes a diagnostic: as \(|r|\) approaches one, little genotype variation remains to distinguish the variants. Conditional estimates become unstable, and small errors in LD or marginal estimates can cause substantial changes. Fine-mapping faces a related identification problem: highly correlated variants can have similar likelihoods, so posterior support may be spread across them. A method can represent uncertainty across correlated variants without resolving which one is causal.

Diagnostics, limitations, and common mistakes

Useful checks are specific to the separation strategy. For conditional analysis, inspect residual association after each conditioning step, check that the conditioning variants are supported and correctly aligned, and verify that the LD matrix comes from an appropriate population and variant set. A residual peak may indicate another signal, but it may also arise because the conditioning variant is an imperfect proxy or because the LD calculation is inaccurate. Sequential selection can be sensitive to the order of entry and to the threshold used to declare another signal.

For fine-mapping, inspect the number of modeled signals, signal-specific PIPs and credible sets, and sensitivity to reasonable prior or model choices. Diffuse posterior support is a result, not a reason to report only the top variant. Check that the variants contributing to the comparison are observed or adequately imputed in both traits and represented in the LD information. Fine-mapping cannot recover a causal variant absent from the analyzed candidate set, and a misspecified number of signals can merge distinct effects or divide one effect into unstable components.

A common mistake is to conclude, “The credible sets overlap, so the traits colocalize.” Overlap says only that some variants appear in both sets; it ignores the relative evidence for the variants and does not compare shared against distinct causal configurations. The correction is to use a signal-level colocalization model or another explicit comparison of shared-variant and distinct-variant evidence, and report uncertainty and priors.

A second mistake is to treat conditioning on a lead variant as if it removed a causal signal exactly. It removes the component represented by that conditioning genotype under the model. When LD is imperfect, or the conditioning set is misspecified, residual association can remain. Conversely, conditioning on correlated variants can inflate uncertainty and obscure a real second signal. Neither strategy establishes that a shared genetic signal mediates a relationship between traits; the conclusion is about statistical evidence for shared genetic association, not a causal pathway between phenotypes.