CAUSE And Correlated Pleiotropy

Why Compare Causal and Sharing Explanations?

Across genetic variants, associations with an exposure and an outcome may track one another. That pattern can arise because changing the exposure changes the outcome, but it can also arise when some variants affect both traits through a shared biological mechanism. The latter is correlated pleiotropy: direct genetic effects on the two traits are correlated, so the variants’ association estimates align even without a causal effect of the exposure on the outcome.

CAUSE, or Causal Analysis Using Summary Effect estimates, addresses this ambiguity by fitting and comparing two models to genome-wide summary associations. Its sharing model allows correlated pleiotropic effects but sets the causal effect to zero. Its causal model allows the same kind of sharing and also estimates a causal effect. Thus, the question is not whether a nonzero causal estimate can be fitted, but whether allowing it improves the model’s ability to predict the observed pattern of genetic associations.

A Generative View of the Two Models

Let \(\gamma_j\) and \(\Gamma_j\) denote the true association effects of variant \(j\) on the exposure and outcome, respectively. Their estimated summary associations are \(\hat{\gamma}_j\) and \(\hat{\Gamma}_j\), with standard errors \(s_{Xj}\) and \(s_{Yj}\). A useful representation of the core CAUSE idea separates an exposure effect that can contribute to a causal pathway from a shared pleiotropic component:

Here \(b_j\) is the variant’s exposure effect assigned to the causal component, \(\theta\) is the causal effect parameter, and \(z_j\) indicates whether the variant belongs to the shared-effect component. A common hierarchical specification has \(z_j \sim \text{Bernoulli}(q)\); when \(z_j=1\), \(u_j\) and \(v_j\) have a joint distribution that permits correlation. When \(z_j=0\), that shared component is absent. The model estimates the prevalence and scale of these latent components rather than classifying every variant with certainty.

The sharing model fixes \(\theta=0\). The causal model estimates \(\theta\), while retaining the sharing component. The observed associations are treated as noisy measurements of the true effects. For independent exposure and outcome GWAS, a basic sampling model is

If the GWAS samples overlap, the estimation errors may be correlated; the sampling model must then account for their covariance rather than assume independence. CAUSE uses the distribution across many variants, not merely the ratios for a selected set of exposure-associated variants. In practice, variants are generally chosen and processed to limit linkage disequilibrium so that the model’s treatment of variants as approximately independent is reasonable.

This representation is a way to understand the model’s distinction, not a claim that all biological pathways can be separated cleanly into two observable groups. The latent effects are inferred from the joint pattern of estimates and uncertainty. The causal and sharing models can therefore remain difficult to distinguish when their predictions are similar.

How Model Comparison Works

CAUSE fits the hierarchical models to paired summary estimates and their standard errors, accounting for uncertainty in the latent variant effects. It then compares predictive performance, commonly through expected log pointwise predictive density (ELPD), evaluated using cross-validation. Conceptually, variants or held-out observations are predicted from model fits that do not use those observations for fitting. The log predictive densities are summed: a larger ELPD indicates better predictive performance on the evaluation data.

Because the causal model adds a parameter, it can fit the observed data at least as flexibly as the sharing model in-sample. Predictive comparison helps distinguish an improvement that generalizes from an improvement that merely uses added flexibility. The difference in ELPD should be considered alongside its uncertainty; a small difference relative to its standard error provides weak evidence for preferring either model.

Justifying the Comparison

The logic of predictive comparison follows from the definition of a predictive score. For a held-out observation \(D_{\mathrm{test}}\), a model assigns predictive density \(p(D_{\mathrm{test}}\mid D_{\mathrm{train}},M)\), where \(M\) denotes the model and \(D_{\mathrm{train}}\) is the data used to fit it. The log score is the logarithm of that density. For multiple held-out observations, the difference between models is the sum of their log-score differences:

A positive difference means the causal model assigned higher predictive density overall to the held-out data; a negative difference means the sharing model did. This comparison is meaningful only if the evaluation procedure is applied consistently to both models and the held-out data are suitable for assessing prediction. It is a measure of relative predictive performance, not a direct test of the truth of a biological mechanism.

Assumptions, Diagnostics, and Alternatives

CAUSE’s conclusions depend on the adequacy of its summary-association and latent-effect models. Important conditions include sufficiently well-estimated association effects, appropriate standard errors, and accounting for correlated estimation errors when samples overlap. The variants used should be harmonized so that effect alleles and effect directions correspond across traits. Residual linkage disequilibrium can make variant contributions dependent; substantial dependence violates the simplifying assumption of approximately independent variant-level observations unless explicitly modeled.

The model also assumes that its latent distribution is a useful description of the relevant genetic effects. A poorly represented mixture, unusual tail behavior, or a small number of influential variants can affect parameter estimates and model comparison. The genome-wide set must provide enough information to estimate the shared-effect distribution; using only a few selected variants may leave the key components weakly identified.

Useful checks include reviewing allele harmonization and standard errors, confirming how sample overlap was handled, examining sensitivity to variant inclusion and LD pruning, and checking whether conclusions persist under reasonable model or prior choices. Inspecting the estimated amount of sharing and uncertainty in \(\theta\) can clarify whether a model preference rests on a broad pattern or a narrow set of effects. A strong score preference should still be interpreted cautiously if it disappears under small, defensible changes to the analysis.

CAUSE differs from approaches that estimate a slope using selected instruments or identify variants as outliers. MR-Egger relies on its InSIDE condition for interpreting the slope; weighted median and mode methods depend on assumptions about the proportion or clustering of valid instruments; outlier-oriented methods target particular departures from the main pattern. CAUSE instead compares genome-wide predictions under explicit causal and correlated-sharing models. This can be useful when correlated pleiotropy is a concern, but does not make it universally preferable: its hierarchical assumptions and predictive comparison may be less informative when data are sparse or model fit is poor.

The central limitation is that observed summary associations do not, by themselves, reveal the biological pathway that generated them. CAUSE makes the causal-versus-sharing contrast explicit and uses many variants to evaluate it, but the result is conditional on the model and the quality of the inputs. If neither model predicts adequately, choosing the better of the two does not establish that either is a good description.