Causal Sharing Versus Effect Portability

Two Questions, Not One

A trans-ancestry fine-mapping analysis can support the conclusion that the same variant is causal in multiple ancestry groups. That conclusion concerns the identity of the variant. It does not, by itself, show that the variant has the same effect size in each group. Conversely, similar effect estimates at a locus do not establish that the same variant is causal: different causal variants can produce similar association patterns.

These distinctions matter when a result is used to understand biology or to predict outcomes across populations. A causal variant may be shared while its effect differs across ancestries. And even when the underlying causal effect is similar, linkage disequilibrium (LD) can make nearby tag variants appear to have different effects. The question “Is the same variant causal?” must therefore be answered separately from “Is its effect portable?”

Define the Effect Before Comparing It

For a quantitative trait, consider a simple ancestry-specific model at candidate variant \(j\):

Here \(i\) indexes individuals and \(a\) indexes ancestry groups. \(Y_{ia}\) is the trait, \(G_{iaj}\) is the allele dosage for variant \(j\), and \(\mathbf{C}_{ia}\) contains covariates. The coefficient \(\beta_{aj}\) is the conditional change in the expected trait per additional copy of the specified effect allele, holding the modeled covariates fixed. The model assumes that the chosen allele is harmonized across groups, the dosage and outcome are appropriately measured, and the conditional mean is represented adequately by the model.

In this model, causal sharing asks whether the same \(j\) is causal in each group. Exact effect portability asks whether \(\beta_{1j}=\beta_{2j}\). Practical portability is often a more useful target: effects may be considered sufficiently similar when their difference is within a prespecified tolerance, denoted \(\Delta\), on a meaningful scale. The tolerance should be chosen for the scientific or clinical use, not selected after seeing the estimates.

The scale must be comparable. For example, effects measured in trait units per allele can be compared if trait units and outcome definitions are aligned. If each ancestry group’s trait was standardized separately, a coefficient is expressed in that group’s standard deviations; equal coefficients then do not necessarily mean equal effects in the original trait units. For a binary outcome, the effect scale also matters: equality of log odds ratios is not the same claim as equality of risk differences. The comparison must state which scale it concerns.

Shared Causality Does Not Guarantee Equal Effects

A causal variant can be the same across ancestry groups even if its effect differs. Differences may reflect genuine context dependence, such as interaction with environmental or genetic background, or differences in the phenotype and measurement process. An apparent difference can also arise from estimation error, allele misalignment, model misspecification, or unequal adjustment. Evidence for heterogeneity is therefore evidence about the estimated effects under a specified analysis, not by itself an explanation for why they differ.

For independent ancestry-specific samples, a direct comparison uses the estimated difference \(\hat{\beta}_{1j}-\hat{\beta}_{2j}\). If the estimates are approximately normal and their standard errors are \(SE_1\) and \(SE_2\), the standard error of the difference is:

This formula assumes independence between the two estimates. If samples overlap, their covariance must be included: the variance of the difference is \(SE_1^2+SE_2^2-2\operatorname{Cov}(\hat{\beta}_{1j},\hat{\beta}_{2j})\). A confidence interval for the difference describes uncertainty in the effect contrast. A test of equality asks whether the data are inconsistent with a zero contrast; it does not establish that effects are practically equivalent when the test is nonsignificant.

LD Can Change Association Patterns Without Changing the Causal Effect

Association estimates at nearby markers are not interchangeable with the causal variant’s effect. When a tag variant is correlated with a causal variant, its marginal association partly reflects that correlation. Because LD patterns can differ across ancestries, a tag can have different association strength even if the causal variant and its effect are shared.

For a simple illustration, suppose the phenotype and genotypes are standardized within each group, there is one causal variant \(c\), and the tag variant \(t\) has no independent effect. In a linear model with standardized genotypes, the marginal regression coefficient for the tag is \(r_{tc}\beta_c\), where \(r_{tc}\) is the correlation between tag and causal genotypes. This relationship relies on the stated single-causal-variant and standardization assumptions; with additional causal variants or other complications, the marginal association can have a more complex form.

Assessing Portability Requires More Than a Nonsignificant Test

A heterogeneity test evaluates a null hypothesis such as \(H_0:\beta_{1j}-\beta_{2j}=0\). A large p-value means the data did not provide strong evidence against equality under the test and its assumptions. It does not show that the difference is small: a wide confidence interval may include both zero and differences large enough to matter.

To make a claim of practical portability, specify a tolerance \(\Delta>0\) in the effect’s units. For two groups, a common criterion is that the confidence interval for \(\beta_{1j}-\beta_{2j}\) lies entirely within \((-\Delta,\Delta)\). This supports the conclusion that differences larger than the chosen tolerance are inconsistent with the interval at its stated confidence level. It does not prove exact equality, and the conclusion depends on the selected tolerance, the analysis scale, and the validity of the model.

Keep the Evidence for Identity and Effect Separate

Fine-mapping evidence, such as posterior support for a particular variant, addresses uncertainty about causal identity under the specified model and variant set. Effect estimates and their contrasts address the size of the effect conditional on the variant and analysis model. Strong posterior support for a shared causal variant does not automatically imply a precise estimate of effect heterogeneity; nor does an effect comparison remove uncertainty about causal identity. When causal identity remains uncertain, effect comparisons should reflect that uncertainty rather than treating one candidate as definitively causal.

A practical interpretation can state the two conclusions separately: for example, “The analysis supports variant \(j\) as causal in both groups; the estimated effects differ by a stated amount, with a confidence interval on a stated scale.” Or, if precision is limited: “The analysis supports shared causal identity, but the effect contrast is too imprecise to establish practical portability.” This wording avoids turning one kind of evidence into a stronger claim about the other.

Common Mistakes

• Equating a shared causal variant with a shared effect. Variant identity and effect magnitude are different parameters. Compare ancestry-specific causal-effect estimates directly.
• Reading different tag-variant associations as different causal effects. LD can change a tag’s marginal association. Check which variant’s effect is being compared and account for ancestry-specific LD.
• Calling effects portable because a heterogeneity test is nonsignificant. A large p-value can result from low precision. Examine the confidence interval and, for practical portability, compare it with a prespecified tolerance.
• Comparing coefficients on incompatible scales. Verify allele alignment, outcome definition, and effect scale before interpreting a difference.
• Claiming a mechanism from a difference alone. Heterogeneous estimates do not identify why effects differ; measurement, modeling, environment, and other factors can contribute.