Interpreting Correlated Variants at an Associated Locus

From an Association Signal to a Set of Correlated Variants

An association analysis may identify a variant whose genotype is associated with a trait. That variant is often called the lead marker: usually, it is the variant with the smallest p-value among those tested in the region. The label describes the result of a statistical comparison, not a biological conclusion. A nearby variant may have a similar association because the two variants are inherited together often enough that one can act as a marker for the other.

Interpreting such a locus requires keeping three ideas separate: the variant tested, the pattern of linkage disequilibrium (LD) between variants, and the variant that—if any—has a causal effect on the trait. Haplotype frequencies and LD measures describe how alleles co-occur in the sampled population. They can show why multiple variants may carry similar association information, but they do not by themselves identify which variant affects the trait.

Here, \(C\) is simply a label for a second variant under consideration; the notation does not imply that it is causal. \(D>0\) means the two coded alleles occur together more often than expected under independence, while \(D<0\) means they occur together less often. The \(r^2\) measure ranges from zero to one and describes the strength of allelic correlation without its direction. The sign of \(D\), together with the allele coding, is needed to interpret which allele at one variant tends to accompany which allele at the other.

A large \(r^2\) indicates that the allele at one variant predicts the allele at the other relatively well in the population and sample being described. It does not mean that the variants are identical, that both affect the trait, or that either has a causal effect. The frequencies and LD may differ across populations, and an estimated LD measure is subject to sampling uncertainty.

What a Lead Marker Does—and Does Not—Tell Us

An association test evaluates a specified variant, usually by comparing trait outcomes across its genotype dosages under a chosen model. A lead marker is the tested variant that ranks most strongly by the selected criterion, commonly the smallest p-value. It is not necessarily the variant with the largest biological effect: p-values also depend on allele frequency, sample size, standard error, imputation quality, and the analysis model.

When two variants are correlated, their genotype dosages can contain overlapping information. If a causal variant is not directly measured, a correlated marker may still be associated with the trait because people carrying the marker allele are more likely to carry the causal allele. The marker then provides statistical evidence about the region, but the association does not show that changing the marker itself would change the trait.

The following relationship makes the relevant assumption explicit. Let \(G_M\) and \(G_C\) be the allele dosages (0, 1, or 2) for the coded alleles at \(M\) and \(C\). Suppose haplotypes are paired independently to form individuals, both loci are biallelic, and the dosages are standardized to \(Z_M\) and \(Z_C\), each with mean zero and variance one. Under this random-pairing assumption, the correlation between standardized dosages equals the allelic correlation \(r\). If the trait follows an additive model with \(C\) as the causal variant, the marginal association at \(M\) is then related to LD as follows.

In this model, \(\gamma\) is the expected change in the outcome per one-standard-deviation increase in the causal-variant dosage, and \(\beta_M\) is the marginal change per one-standard-deviation increase in marker dosage. This relation is not a universal conversion from haplotype \(r\) to an association effect. It relies on the stated random pairing, additive model, dosage standardization, and error condition. Without those assumptions, haplotype-level \(r^2\) alone does not determine the genotype-dosage correlation or the marker’s regression slope.

Why Several Variants Can Share One Signal

An associated locus often contains a group of correlated variants. If one member of that group is related to the trait, alleles at other members may track it through LD. Consequently, several variants can each have small p-values even though the analysis has not shown that each one has an independent effect. Their test results are correlated, not a set of independent confirmations.

Association statistics for correlated variants need not be exactly equal. Differences can arise from imperfect LD, allele frequencies, missingness, imputation quality, standard errors, or details of the test. A variant with the smallest p-value is therefore the lead marker for that analysis, not automatically the causal variant. The association pattern identifies statistical evidence in the region; distinguishing among correlated candidates generally requires evidence beyond the LD pattern alone.

LD Is Not a Causal Test

LD describes co-occurrence of alleles, whereas causality concerns what would happen to the trait if a variant were changed while relevant conditions were held fixed. A haplotype table contains no direct information about that intervention. Even a very high \(r^2\) cannot decide whether the marker, a correlated candidate, another unmeasured variant, or a combination of factors accounts for the association.

Perfect LD makes the limitation especially clear. If two variants have identical genotypes in every analyzed individual, their single-variant association tests contain the same genotype information. An association at both sites cannot distinguish which site, if either, has a causal effect. Less-than-perfect LD may provide some statistical separation, but LD values alone still do not prove a causal mechanism. Functional evidence and other appropriately designed analyses may contribute to causal assessment, but they are distinct from calculating LD.

A Short Justification for the Dosage-Correlation Condition

It is useful to see why random pairing matters in the dosage calculation. Let \(A_{M1}\) and \(A_{M2}\) be the coded-allele indicators on the two chromosomes of an individual, and define \(G_M=A_{M1}+A_{M2}\). Define \(G_C\) analogously. If the two haplotypes are independently paired, each chromosome has the same allelic covariance \(\operatorname{Cov}(A_M,A_C)\), and cross-chromosome covariances are zero. Thus:

The allelic correlation is \(r=\operatorname{Cov}(A_M,A_C)/\sqrt{p_M(1-p_M)p_C(1-p_C)}\). Substituting the dosage covariance and variances into the dosage correlation gives:

Standardizing each dosage does not change its correlation, so \(\operatorname{Corr}(Z_M,Z_C)=r\). The argument depends on independent pairing of haplotypes. Haplotype frequencies describe alleles on chromosomes; without the pairing assumption, they alone do not supply every feature of the individual-level joint dosage distribution needed for this equality.

Common Pitfall and Practical Interpretation

A common mistake is to see a lead marker in strong LD with a candidate variant and conclude that the candidate is causal because the marker is associated. The reasoning confuses a predictor with an explanation: LD can make the candidate track the signal, but it does not show that the candidate generated it. A related mistake is to substitute \(\sqrt{r^2}\) from haplotype frequencies directly into a genotype-dosage effect calculation without stating assumptions. That substitution is justified in the example above only because random pairing and the additive model were explicitly assumed.

When interpreting an associated locus, state which variant is the lead marker, report the relevant LD measure and allele coding, and describe the other variants as correlated candidates or proxies unless there is additional evidence. State the population and data context for the LD estimate. Then distinguish the observed association from any causal claim. In concise terms: LD can explain why variants share a signal; LD alone cannot say which variant causes the trait.