LD Reference Mismatch in Colocalization

Why LD Reference Choice Matters

Fine-mapping-informed colocalization asks whether genetic evidence for two traits supports a shared causal variant. The association statistics alone do not identify the causal variant when nearby variants are correlated: several variants can show similar signals because they are in linkage disequilibrium (LD). Fine-mapping uses an LD structure to distinguish a causal variant from correlated alternatives. If that structure comes from a reference panel that does not represent the study samples, the fine-mapping model may interpret the observed association pattern incorrectly, and colocalization evidence can change as a result.

This is not merely a technical issue about choosing a convenient genotype dataset. LD can differ across ancestry groups, and reference panels can also be unsuitable because they are small, poorly matched, or do not capture the study’s local population structure. A credible set or colocalization posterior calculated under the wrong LD structure may look precise while being poorly calibrated for the data at hand.

How LD Enters Fine-Mapping-Informed Colocalization

For \(m\) variants, an LD matrix \(R\) contains pairwise genotype correlations: its entry \(r_{jk}\) is the correlation between genotypes at variants \(j\) and \(k\), under the population and genotype coding used to calculate it. Fine-mapping methods use \(R\), together with association evidence and a model for causal signals, to evaluate which variants could explain the observed pattern. In multi-signal colocalization, fine-mapping results for each trait contribute to the assessment of whether the traits share a causal variant or have distinct causal variants.

The key issue is that association statistics observed in the study reflect the study’s LD, not the reference panel’s LD. If the model is supplied a different correlation pattern, it can predict the wrong association pattern under each candidate causal variant. This can change variant-level posterior inclusion probabilities (PIPs), credible sets, signal pairing, and ultimately the posterior probabilities assigned to the colocalization hypotheses. It does not follow that every mismatch produces a false result in the same direction: it may weaken, inflate, or redirect support.

A simple derivation makes the dependence concrete. Suppose a single causal genotype \(G_j\) and a tested genotype \(G_k\) are standardized to have mean zero and variance one in the study population. Let the quantitative trait satisfy \(Y=\beta G_j+\varepsilon\), where \(\varepsilon\) is independent of the genotypes, has mean zero, and has variance \(\sigma_\varepsilon^2\). Write \(r_{kj}=\operatorname{Corr}(G_k,G_j)\). The population marginal regression slope of \(Y\) on \(G_k\) is \(\operatorname{Cov}(G_k,Y)=r_{kj}\beta\). The residual from that marginal regression is \(Y-r_{kj}\beta G_k=\beta(G_j-r_{kj}G_k)+\varepsilon\), with variance \(\beta^2(1-r_{kj}^2)+\sigma_\varepsilon^2\). Thus, for large \(n\), the marginal \(Z\)-statistic has approximate mean

The denominator includes the residual contribution from the part of the causal genotype not predicted by \(G_k\). It is not generally just \(\sigma_\varepsilon\). A reference panel with a different \(r_{kj}\) therefore gives a different expected relationship between a candidate causal variant and nearby marginal association statistics. The approximation assumes a correctly specified marginal linear regression, standardized genotypes in the study population, independent homoskedastic errors, and sufficiently large \(n\); it describes the expected statistic, not an exact value for any particular sample.

Diagnosing a Mismatch

An ancestry label alone is not enough to establish that a reference panel is appropriate. The relevant question is whether the LD among the analyzed variants is reasonably representative of the association samples in the locus. When individual-level study genotypes are available, LD can be estimated directly in an appropriate subset, subject to adequate sample size and quality. With summary statistics only, direct comparison may not be possible; the analyst should then compare plausible reference panels and state that LD mismatch cannot be ruled out.

Any comparison requires care. Use the same set of variants in each matrix and ensure genotype coding is consistent. The treatment of variant alleles and allele alignment is a separate technical requirement; assume here that the association data and LD matrices have already been made consistent. A different variant set can create an apparent LD discrepancy simply because different pairs are being compared. Small reference samples also yield noisy correlation estimates, so a difference in estimated LD need not reflect a true population difference.

A simple summary diagnostic is the root mean squared difference between the off-diagonal correlations in two matrices. For \(m\) variants, one version is

This is a descriptive measure, not a universal pass/fail threshold. A modest average discrepancy can conceal a large difference for a variant pair that drives fine-mapping, while a larger discrepancy among weakly associated variants may have little practical effect. Inspect important pairs and local blocks as well as an overall summary.

Assessing Colocalization Robustness

A useful robustness analysis compares results under the best-supported matched panel with results under other plausible panels. Keep the association data, analyzed variants, fine-mapping specifications, priors, and other modeling choices fixed wherever possible. Change the LD input deliberately, record the panel’s ancestry and sample size, and rerun the fine-mapping and colocalization steps that use that LD. If multiple association studies have different ancestry compositions, assess the LD suitability for each study rather than assuming that one panel represents both.

Compare more than a single colocalization posterior. Examine changes in PIPs, credible-set membership, signal-level pairings, and the posterior probabilities for shared versus distinct causal variants. Check whether the same variants or closely related signals continue to drive the result. A high posterior under one panel and a substantially lower posterior under another indicates sensitivity to LD choice; it does not by itself establish which panel is correct or which hypothesis is true.

What Robustness Can and Cannot Establish

Agreement across several appropriate panels increases confidence that the conclusion is not being driven by one particular LD estimate. It does not prove that the LD is perfectly represented, eliminate other model limitations, or convert colocalization evidence into a causal claim about a molecular mechanism. Conversely, disagreement is informative: it identifies a dependence that should be explained and may motivate using study-specific LD or improving the reference data.

A sensitivity analysis is strongest when the compared panels are plausible representations of the study samples and when the same variants and model settings are used. Comparing an appropriate panel with an obviously unrelated one can demonstrate that the method responds to LD, but cannot quantify realistic uncertainty. If results change only when using implausible references, that is different from instability across several credible alternatives.

Common Mistakes

• Treating a reference panel as a neutral substitute for study LD. A panel’s correlations are estimates from its own samples; ancestry or sampling differences can make them unsuitable for the association data.
• Attributing every change in colocalization posterior to biological differences. A change may arise because the supplied LD alters fine-mapping, not because the traits truly have different causal variants.
• Using a single global discrepancy as a definitive quality test. An average can hide a consequential mismatch at the variants driving the signal, and there is no universal threshold that guarantees validity.
• Reporting only the most favorable panel result. If plausible panels lead to materially different evidence, that sensitivity belongs in the interpretation.
• Assuming ancestry matching guarantees a good LD reference. Sample size, variant availability, local population structure, and data quality also affect how representative the estimated matrix is.