CAUSE for Correlated and Causal Pleiotropy

Why Compare Sharing and Causal Models?

Genetic variants associated with an exposure and an outcome can show a genome-wide pattern consistent with causation even when changing the exposure would not change the outcome. One reason is correlated pleiotropy: some variants affect both traits through a shared biological pathway or heritable factor. Those variants can make genetic associations with the two traits move together, creating an apparent exposure–outcome relationship.

CAUSE, short for Causal Analysis Using Summary Effect estimates, addresses this problem by modeling the joint pattern of genetic associations across many variants. It compares a model that allows shared pleiotropic effects but sets the causal effect to zero with a model that also allows a causal effect. The comparison asks whether allowing causation improves the explanation of the genome-wide data beyond what sharing alone can explain.

The Variant-Level Model

For variant \(j\), let \(\hat\gamma_{Xj}\) and \(\hat\gamma_{Yj}\) be estimated associations with the exposure and outcome, and let \(s_{Xj}\) and \(s_{Yj}\) be their standard errors. Their unknown true associations are \(\gamma_{Xj}\) and \(\gamma_{Yj}\). A basic summary-data likelihood treats the estimates as sampling-noisy measurements of those true effects:

This display assumes independent sampling errors for the two estimates. If the exposure and outcome samples overlap, their estimation errors can be correlated; a suitable joint likelihood must represent that covariance rather than silently treating the errors as independent. The effects and standard errors must also refer to harmonized alleles, so that the direction of each variant’s association has the same meaning for both traits.

CAUSE represents the true effects using a component associated specifically with the exposure, a possible shared component, and an outcome-specific component. In a simplified form:

Here \(\gamma_j\) is the variant’s exposure-specific component, \(\theta\) is the causal effect of the exposure on the outcome, and \(Z_j\) indicates whether variant \(j\) has a shared effect. A common model specification takes \(Z_j\sim\operatorname{Bernoulli}(q)\), where \(q\) is the proportion of variants with such an effect. The random effects \(\gamma_j\), \(\eta_j\), and \(\alpha_j\) represent, respectively, exposure-specific effects, shared effects, and outcome-specific effects. They are commonly modeled as mean-zero distributions with variances estimated from the data. In this formulation, the shared component contributes to both traits, while \(\alpha_j\) contributes only to the outcome.

The sharing model sets \(\theta=0\); the causal model estimates \(\theta\). Both allow shared effects and outcome-specific effects. Consequently, the comparison is not “pleiotropy versus no pleiotropy.” It is whether a causal effect is needed in addition to the modeled pleiotropy to explain the observed pattern.

How Genome-Wide Patterns Separate the Explanations

The distinction becomes clearer when considering both the covariance and the variation of genetic effects. Under the simplified model above, if the effect components are mutually independent and have mean zero, then:

The first term is the covariance associated with the causal pathway: variants with exposure-specific effects also predict outcome effects through \(\theta\gamma_j\). The second term is covariance from sharing. The sharing model can therefore produce a substantial exposure–outcome relationship without a causal effect. The causal model asks whether an additional, approximately proportional contribution from exposure-specific effects improves the fit once sharing is already allowed.

This is a comparison of patterns across many variants, not a test of whether one variant is a valid instrument. Variants with different combinations of exposure-specific and shared effects contribute differently to the joint distribution. If the data contain enough information to distinguish those patterns, the models can make different predictions. If the patterns are too similar, or the estimates are too imprecise, the comparison may not be decisive.

The model’s interpretation depends on its assumptions. The variants should be sufficiently independent for a likelihood that treats them as independent observations, or their linkage disequilibrium must be represented appropriately. The summary associations and their standard errors should be well estimated, variants should be harmonized, and the modeled effect distributions should be a reasonable approximation to the genetic architecture under study. The causal interpretation also relies on the model capturing relevant correlated pleiotropy: an unmodeled source of correlated effects can still make a causal model look useful. CAUSE provides a structured comparison, not a way to guarantee that all possible pleiotropic pathways have been accounted for.

The genome-wide variant set matters. Restricting analysis only to variants selected for strong exposure associations can discard information about the broader pattern and can make selection relevant to interpretation. In practice, variant selection, linkage disequilibrium handling, and any sample overlap should be documented and aligned with the analysis and its likelihood assumptions.

Posterior Estimates and Predictive Model Comparison

Within the causal model, Bayesian inference produces a posterior distribution for \(\theta\), along with posterior distributions for quantities such as \(q\) and the effect variances. A posterior interval describes uncertainty about the parameter conditional on the model, its likelihood, and its priors. It does not settle whether the causal model is preferable to the sharing model: a parameter can have a concentrated posterior within a model that predicts no better than its comparator.

CAUSE compares the models using their predictive performance, commonly summarized by expected log pointwise predictive density (ELPD). For each variant, the model assigns predictive density to the observed association estimates; the log densities are combined across variants. Better predictive performance corresponds to a larger ELPD. A predictive comparison should account for the fact that the same data are used to fit the model, for example through a leave-one-variant-out or other appropriate predictive procedure.

Let \(\widehat{\operatorname{ELPD}}_{\mathrm{causal}}\) and \(\widehat{\operatorname{ELPD}}_{\mathrm{sharing}}\) denote the estimated predictive scores. Their difference is:

A positive difference favors the causal model’s predictive performance; a negative difference favors the sharing model. The size of the difference should be considered alongside its uncertainty. A small positive value with substantial uncertainty is not strong evidence that the causal model predicts better. This score difference is not a posterior probability that one model is true, and it is not automatically a conventional null-hypothesis \(p\)-value.

Common Pitfall and Practical Interpretation

A frequent error is to treat a positive genetic association slope, or a positive posterior estimate of \(\theta\), as proof that the exposure causes the outcome. That reasoning overlooks the shared component: under the sharing model, variants can influence both traits and produce covariance even with \(\theta=0\). The correction is to ask whether allowing \(\theta\) improves prediction relative to a model that already permits sharing, and then interpret that comparison under the model’s assumptions.

CAUSE is especially useful when the concern is that genome-wide correlated pleiotropy may mimic causation. Its central contribution is to place that alternative explanation inside the model comparison rather than assuming that all noncausal genetic effects are uncorrelated. The result remains conditional on the chosen model, the available summary data, and the reliability of its assumptions.