From Shared Variant Evidence to Causal Claims

From a Shared Variant to a Carefully Bounded Claim

When a genetic association for a molecular phenotype and an association for a trait occur in the same genomic region, colocalization asks whether the evidence is compatible with a shared causal variant or instead supports different causal variants for the two associations. This is an important distinction: two nearby signals can look similar because variants in linkage disequilibrium tag one another, even when different variants underlie the molecular and trait associations.

A strong result for a shared variant can sharpen the interpretation of a transcriptome association. It supports the claim that one genetic cause is implicated in both the measured expression phenotype and the trait, under the colocalization model and its assumptions. It does not, by itself, show that changing expression causes the trait, establish a particular biological pathway, or prove that the measured transcript is the relevant molecular intermediate.

“Causal variant” here refers to the variant posited to generate the genetic association signal for a phenotype in the statistical model. Even a high posterior probability for \(H_4\) is not a direct observation of a molecular mechanism. Its interpretation depends on such matters as the variant set, allele harmonization, linkage disequilibrium information, prior probabilities, and whether the model represents the number and pattern of causal signals adequately. Earlier material on multiple signals and diagnostic cases explains why these assumptions matter.

What Colocalization Establishes—and What It Does Not

A colocalization result is about the relationship between genetic association signals. When the evidence favors \(H_4\) over \(H_3\), it weighs against an explanation in which the molecular and trait associations are generated by different variants in the region. This can make a transcriptome association more plausibly relevant to the trait than a TWAS association alone: the shared-variant evidence reduces one important form of ambiguity caused by linkage disequilibrium.

The result does not determine the direction of causation between expression and the trait. A shared variant could affect expression, which could in turn affect the trait. It could also affect expression and the trait through separate routes. Or the measured expression phenotype could be a correlated molecular readout rather than the intermediate responsible for the trait association. These possibilities can produce association signals that are compatible with the same shared variant.

The distinction is between shared genetic cause and causal mediation by expression. The first concerns whether the same variant underlies both genetic associations. The second concerns whether the effect of genetic variation on the trait passes through expression. Colocalization addresses the first question; it does not by itself identify the answer to the second.

Why a Shared Variant Does Not Identify Mediation

The distinction can be shown by comparing simple models. Let \(G\) denote the number of copies of an allele, \(X\) a measured expression level, and \(Y\) a quantitative trait. Suppose \(G\) is coded as allele copies, \(X\) is measured in normalized expression units, and \(Y\) is measured in trait units. A model in which expression partly transmits a genetic effect can be written as

For the genetic association slopes in this example, assume \(E[U\mid G]=0\) and \(E[V\mid G,X]=0\). The first condition makes the conditional mean of expression linear in \(G\) with slope \(0.8\). The second makes the conditional mean of \(Y\), given \(G\) and \(X\), follow the stated structural equation without a residual mean that varies with either predictor. Interpreting the coefficient \(0.6\) as a causal effect of \(X\) on \(Y\) requires further structural assumptions; the equations and these mean conditions alone are not evidence that those assumptions hold.

Substitute the expression equation into the trait equation:

Since \(E[U\mid G]=0\) and \(E[V\mid G]=E\{E[V\mid G,X]\mid G\}=0\), it follows that \(E[Y\mid G]=0.78G\). Thus, the genetic association slope for expression is \(0.8\) normalized expression units per allele copy, and the marginal genetic association slope for the trait is \(0.78\) trait units per allele copy. The term \(0.6X\) provides a mediated component in this illustrative structural model, while \(0.3G\) represents an additional direct component.

Now consider a separate-effects model:

Assume \(E[U_X\mid G]=E[W\mid G]=0\), and stipulate that \(Y\) is not caused by \(X\) in this model. The marginal association slopes are again \(0.8\) for expression and \(0.78\) for the trait. Both models therefore have the same genetic association pattern at \(G\), even though only the first includes an expression-to-trait pathway. The zero conditional-mean assumptions are essential to these slope calculations: the equation coefficients alone do not determine marginal genetic associations if residuals are associated with \(G\).

A Short Derivation of the Association-Slope Point

The example above uses a general algebraic fact. Suppose \(X=aG+U\) and \(Y=bX+cG+V\), with \(E[U\mid G]=0\) and \(E[V\mid G,X]=0\). Substitution gives \(Y=(ab+c)G+bU+V\). Taking conditional expectations given \(G\) yields the genetic association slopes below.

Consequently, the observed pair of slopes \(a\) and \(ab+c\) can be consistent with different choices of the expression effect \(b\) and the direct genetic effect \(c\). For example, the same trait slope can arise from a positive mediated component and a positive direct component, or from a model with no causal effect of expression on the trait. The conditional-mean assumptions justify the marginal slopes; without them, residual association with \(G\) can change those slopes. Colocalization compares the genetic signals, not the decomposition of a trait effect into these pathways.

Shared-Variant Evidence Is Not a Complete Mechanism

Even when the shared-variant interpretation is well supported, several questions remain. The causal variant may not be known precisely if multiple variants remain plausible. The measured expression phenotype may be specific to the assayed tissue, cell mixture, condition, or measurement platform; a result for that phenotype does not automatically establish effects in every biological context. Nor does a shared variant alone determine which molecular changes, downstream processes, or cellular functions connect the locus to the trait.

The practical value of colocalization is therefore substantial but bounded. It can help prioritize a molecular association that shares genetic evidence with a trait, and it can make a distinct-variant explanation less plausible under the model. It does not convert association into a complete causal account. A responsible interpretation reports the evidence for a shared variant, the relevant model limitations, and the additional assumptions or analyses needed before making claims about mediation or mechanism.

Common Mistakes and Careful Reporting

• Overclaim: “The high \(H_4\) posterior proves that expression causes the trait.” Correction: It supports a shared genetic cause for the two association signals under the colocalization model; it does not establish a causal effect of expression on the trait.
• Overclaim: “The gene is the mechanism.” Correction: Shared-variant evidence can prioritize a gene or molecular phenotype, but it does not by itself identify the biological pathway or prove that the measured phenotype is the operative intermediate.
• Overclaim: “The causal variant has been identified.” Correction: A high posterior for \(H_4\) can coexist with uncertainty about which variant is shared. Report variant-level uncertainty separately from the regional hypothesis posterior.
• Reasoning error: “The coefficients in the equations are the genetic association slopes.” Correction: That conclusion requires conditions on the residuals, such as zero conditional means given \(G\). State the assumptions and derive the marginal slopes.
• Reporting error: Treating a posterior probability as independent of the model and prior. Correction: Describe it as posterior support conditional on the specified hypotheses, priors, and data, and consider whether the model’s assumptions are credible.