Why Causal Wording Requires More Than a Mediation Estimate
A genetic mediation analysis may produce a precise estimate for a pathway from an exposure, through a mediator, to an outcome. Precision alone does not establish that this pathway is causal. The estimate depends on a chain of assumptions about how genetic variants relate to the exposure, how the mediator relates to the outcome, and how the data were selected and measured. A careful report separates the numerical result from the interpretation it can support.
Three claims are often conflated. An association means two measured quantities vary together in the analyzed data. A shared genetic signal means evidence is consistent with the same underlying causal variant influencing two traits. A causal mediated effect means changing the exposure would change the outcome through the mediator, under a defined intervention and a set of identification assumptions. Each is stronger and more specific than the one before it; evidence for one does not automatically establish the next.
On an additive scale, potential-outcome definitions make the causal target explicit. Let \(M(x)\) denote the mediator value that would occur under exposure level \(x\), and let \(Y(x,m)\) denote the outcome under exposure \(x\) and mediator value \(m\). For two exposure levels \(x\) and \(x_0\), the natural indirect effect at exposure level \(x\) is \(E[Y(x,M(x))-Y(x,M(x_0))]\). It compares outcomes under the same exposure level while changing the mediator from the value it would take under \(x_0\) to the value it would take under \(x\). Such a contrast requires assumptions beyond observing that \(M\) and \(Y\) are associated. For binary outcomes, the effect scale also matters; a product or proportion that is meaningful on one scale need not have the same interpretation on another.
What Must Be Stated for a Causal Interpretation
A report should name the target pathway and specify what the effects mean: for example, the change in outcome standard deviations per one-standard-deviation increase in exposure mediated through a named molecular trait. It should also state the genetic and mediation assumptions that support the interpretation. In broad terms, these include:
- Instrument relevance: the genetic instruments predict the exposure or other instrumented quantity being analyzed.
- Instrument independence: conditional on the design and appropriate covariates, the instruments are independent of confounders of the relevant exposure–outcome relations.
- Exclusion: the instruments affect the outcome through the modeled route, rather than through an unmodeled route such as horizontal pleiotropy.
- Mediation identification: the mediator–outcome relation is not confounded in a way that invalidates the mediated-effect estimate. Standard mediation identification also requires attention to exposure-induced mediator–outcome confounding.
- Model and measurement adequacy: the effect scale, functional form, timing, and measured traits correspond to the stated estimand. A linear product interpretation, for example, requires its specified linear-model conditions.
These assumptions are not all verified by a small p-value or a narrow confidence interval. Genetic instruments can reduce some forms of confounding, but they do not make every link in a proposed pathway automatically unconfounded. The interpretation should therefore distinguish assumptions that are supported by diagnostics from assumptions that remain substantive and cannot be established from the observed data alone.
Worked Example: Reporting a Product Estimate With Its Scale
Suppose a hypothetical analysis reports an exposure-to-mediator estimate \(a=0.30\) standard deviations of mediator per one-standard-deviation increase in exposure, with \(SE(a)=0.04\). The estimated mediator-to-outcome effect is \(b=0.20\) standard deviations of outcome per one-standard-deviation increase in mediator, with \(SE(b)=0.05\). For illustration, assume the two estimates are independent and use a first-order delta-method standard error for their product.
The indirect-effect product is:
The units combine to standard deviations of outcome per one-standard-deviation increase in exposure. Under the stated independence approximation, the delta-method variance is \(b^2SE(a)^2+a^2SE(b)^2\). Substitution gives:
A normal-approximation 95% confidence interval is \(0.0600 \pm 1.96(0.0170)\), or approximately \(0.0267\) to \(0.0933\) standard deviations of outcome per one-standard-deviation increase in exposure. If the estimates are not independent, their covariance must also be accounted for; the calculation above is not justified merely because two estimates are reported.
A suitable conclusion is: “The estimated indirect-effect product was 0.060 standard deviations of outcome per one-standard-deviation increase in exposure (95% CI 0.027 to 0.093), under the linear product model and its identifying assumptions.” The interval quantifies sampling uncertainty under that model. It does not show that the pathway is causal if the assumptions fail.
Shared Genetic Signal Is Not the Same as a Mediated Pathway
When an exposure, mediator, and outcome show genetic associations in the same region, shared genetic evidence can strengthen the case that the signals are related rather than being driven by distinct nearby variants. Colocalization is one way to evaluate whether two traits are consistent with sharing a causal variant. However, even strong evidence for a shared variant does not determine how that variant acts. It could influence the outcome through the proposed mediator, through another trait, or through multiple routes. Thus, shared signal is evidence about genetic architecture, not by itself proof of mediation.
The distinction also applies to direction. A shared variant does not alone establish whether changes in the exposure precede changes in the mediator, whether the mediator affects the outcome, or whether an alternative pathway explains the associations. A report should describe the shared-signal result as such, then state what additional assumptions and analyses support the proposed ordering and causal interpretation.
Worked Example: Qualifying a Colocalization Result
In a hypothetical analysis, the estimated posterior probability for a shared causal variant between a molecular mediator and an outcome is 0.92 under the colocalization model and priors used. The analysis also finds that the same allele is associated with higher mediator levels and higher outcome values.
The appropriate direct interpretation is that the data provide strong support, under the model and priors, for a shared causal signal rather than two distinct causal variants. The posterior probability is not a 92% probability that the mediator causes the outcome, nor does allele-direction agreement establish a mediated pathway.
A defensible summary is: “The traits showed strong evidence of a shared genetic signal (posterior probability 0.92 under the specified colocalization model). This result is consistent with, but does not establish, mediation through the molecular trait; alternative pathways and the assumptions required for causal mediation remain relevant.” The wording preserves the evidence while not turning a shared-signal analysis into a causal-pathway test.
Selection and Sensitivity Belong in the Interpretation
Selection can change the associations used in a mediation analysis. Conditioning on study participation, disease status, availability of mediator measurements, or inclusion after selecting strongly associated variants can induce or distort relationships. Sample overlap and index-event selection can also affect estimates. These risks are design-specific: stating that a study is genetic does not make selection bias disappear. A useful report names the selection mechanisms that are plausible, describes how they were assessed, and indicates which results may be affected.
Sensitivity analysis asks how conclusions change under alternative plausible assumptions or modeling choices. It does not prove that the chosen range of assumptions is correct, and it does not mechanically repair bias. The analyst should identify the assumption being varied, show the resulting estimates, and explain whether the substantive conclusion changes.
Worked Example: Sensitivity to Mediator–Outcome Confounding
Suppose a hypothetical linear analysis estimates \(a=0.30\) standard deviations of mediator per standard deviation of exposure and an adjusted mediator–outcome slope of \(0.20\) standard deviations of outcome per standard deviation of mediator. As a simple sensitivity calculation, suppose an omitted, standardized confounder \(U\) is associated with the mediator by \(\delta\) standard deviations of mediator per standard deviation of \(U\), and with the outcome by \(\gamma\) standard deviations of outcome per standard deviation of \(U\). Under this simplified additive model, the omitted-variable contribution to the mediator–outcome slope is approximated by \(\delta\gamma\).
For \(\delta=0.25\) and \(\gamma=0.12\), the approximate bias is:
If this bias is in the positive direction, the sensitivity-adjusted slope is \(0.20-0.03=0.17\), and the corresponding product is \(0.30(0.17)=0.051\) standard deviations of outcome per standard deviation of exposure.
Now consider a stated sensitivity range \(0.10 \leq \delta \leq 0.40\) and \(0.05 \leq \gamma \leq 0.15\), with nonnegative associations in this illustration. The bias range is \(0.10(0.05)=0.005\) to \(0.40(0.15)=0.060\). The adjusted slope therefore ranges from \(0.20-0.060=0.140\) to \(0.20-0.005=0.195\), giving product estimates from \(0.30(0.140)=0.042\) to \(0.30(0.195)=0.0585\). This is a sensitivity range under the stated simplified model, not a confidence interval or a guarantee that the true effect lies inside it. A complete analysis would need to justify whether the model and parameter ranges are plausible for the study.
A Practical Reporting Sequence
A concise but informative interpretation can be built in a sequence that keeps the numerical finding, the genetic evidence, and the causal claim distinct. The wording should be specific enough that another reader can tell what was estimated and what remains uncertain.
State the exposure, mediator, outcome, effect scale, units, and target population or analysis sample.
Report the estimate, standard error or interval, and the model used to obtain it. Describe a confidence interval as a range of values compatible with the data and model at its stated confidence level, not as a probability that the fixed effect lies in that particular interval.
Report association, shared-signal evidence, and pathway evidence as different findings. Do not use one as a substitute for another.
Identify the key instrument, mediation, measurement, and selection assumptions, noting which are assessed and which cannot be verified from the data.
Say which assumptions or analysis choices were varied, give the range of results, and state whether the conclusion changed.
Common Mistake: Turning Compatibility Into Proof
A common error is to write, “The genetic variant colocalized with the mediator and outcome, so the mediator causally transmits the genetic effect.” The reasoning is incomplete: colocalization supports a shared genetic signal, but does not rule out horizontal pleiotropy or another route from the variant to the outcome. Likewise, a nonzero product estimate establishes a product of fitted component effects, not the causal validity of those components.
The correction is to report the evidence at the level it supports: “The analyses are consistent with a mediated pathway under the stated assumptions.” Then identify the assumptions and limitations that matter, including plausible pleiotropic routes and selection into the analyzed sample. If sensitivity analyses show the estimate is stable to specified alternatives, say exactly which alternatives; do not generalize that stability to all possible bias.
Check Your Understanding
Try these questions before moving on.
- What does a nonzero product \(ab\) estimate, and what additional conditions are needed to call it a causal indirect effect?
- Why does evidence for a shared causal variant not, by itself, prove that a mediator transmits the variant’s effect to an outcome?
- A report gives an indirect-effect estimate and a narrow confidence interval. What does the interval quantify, and what does it not establish?
- Name two ways selection into a genetic mediation analysis could affect interpretation.
- In a sensitivity analysis, why should the analyst state the assumptions used to define the sensitivity range?