Causal Estimands In Mendelian Randomization

What Is the Causal Effect an MR Analysis Targets?

A causal estimate is meaningful only after its target has been specified. In Mendelian randomization (MR), a genetic variant can serve as an instrument for an exposure, but the effect of interest is not simply “the association between the variant and the outcome.” The causal estimand describes a contrast in outcomes under specified exposure interventions, in a specified target population, and on a specified scale. The assumptions used to identify that estimand from genetic data are separate from its definition.

Let \(Y(x)\) denote the outcome that an individual would have under an intervention setting the exposure to \(x\). Potential outcomes are defined even though, for each person, only the outcome under the exposure actually received is observed. For a binary exposure \(D\), write \(Y(1)\) and \(Y(0)\) for the potential outcomes under exposure and no exposure. The target population must also be named: for example, adults in a particular source population, rather than an unspecified “population.”

For a continuous exposure, a common target is a linear causal slope: the mean change in outcome per one-unit increase in exposure. This interpretation is most direct when the causal response is adequately represented by a linear model with a common slope over the exposure range of interest. If effects vary with exposure level or between people, a single slope may instead summarize a particular average or instrument-weighted contrast. A one-unit change also needs a meaningful definition: a genetically influenced difference accumulated over many years is not automatically equivalent to a short-term clinical intervention.

The MR instrument may identify a population effect only under conditions that connect the genetic variation to the specified exposure intervention and outcome contrast. In broad terms, the instrument must be relevant to the exposure, appropriately independent of causes of the outcome, and have no route to the outcome except through the exposure. For a complier interpretation with a binary instrument and binary exposure, additional structure—especially monotonicity, meaning no individuals respond to the instrument in the opposite direction—is needed. These are identification conditions, not part of the definition of the estimand; the assumptions themselves are treated separately in the material on instrumental-variable assumptions.

Population Effects and Complier Effects

The ATE averages each person’s causal contrast over the target population. An instrumental-variable analysis with a binary instrument and binary exposure can, under the relevant identification conditions, instead target the complier average causal effect (CACE), also called the local average treatment effect. A complier is an individual whose exposure status changes when the instrument changes. “Local” means specific to this instrument-induced subgroup; it does not mean a geographically local effect.

The distinction follows from how the instrument changes exposure. Under monotonicity, individuals are classified as compliers, always-takers, or never-takers. Always-takers receive the exposure for either instrument value; never-takers receive it for neither. Changing the instrument changes treatment only for compliers. Thus an instrument-induced outcome contrast can carry information about the treatment effect for compliers without representing the effects in the other groups.

With genetic instruments, the corresponding target is not always a neatly defined subgroup of people who comply with a binary assignment. Genotype usually shifts a continuous exposure, and people may differ in how much their exposure changes or in their response to exposure. When causal effects are heterogeneous, the effect reflected by an instrument can depend on which individuals and exposure contrasts the genetic variation moves. It is therefore unsafe to label every MR result a population-average effect without stating the model and identification conditions that support that interpretation.

The Outcome Scale Is Part of the Estimand

For a continuous outcome, an effect is often expressed as a mean difference, with units such as mmHg per kg/m² of body mass index. For a binary outcome, several distinct scales are common. The risk difference compares probabilities; the odds ratio compares odds; and a liability-scale effect describes a shift in an assumed continuous latent propensity underlying the binary outcome. These scales answer different questions, so their numerical values are not interchangeable.

In genetic analyses of a binary outcome, a log-odds coefficient is often the scale of the outcome association. Its interpretation depends on how the exposure contrast and outcome model are defined. It does not by itself state an absolute change in disease probability. To obtain an absolute risk contrast, a relevant baseline risk and a compatible model are needed.

A liability model gives another possible scale. It assumes that a binary outcome occurs when an unobserved, continuous liability exceeds a threshold. A liability effect is commonly stated in standard-deviation units of that latent scale. To interpret it, one must specify or assume the liability distribution and threshold; translating it to risk also requires the outcome prevalence or threshold appropriate to the target population.

Interpreting and Checking the Target

A clear MR interpretation names the exposure, outcome, contrast, population, and scale. For example, “a 1 kg/m² increase in BMI is associated with a 2 mmHg higher mean systolic blood pressure under a linear causal model” is more informative than “the causal effect is 2.” If the analysis instead supports a complier effect, the subgroup qualification belongs in the interpretation. For a binary outcome, state whether the effect is a risk difference, odds ratio, log odds, or liability-scale shift.

The effect target also depends on the intervention being represented. A genetic variant may influence exposure across the life course, whereas a clinical intervention may change exposure later in life and over a shorter period. Even if both are expressed in the same exposure units, they need not have the same causal effect when timing, duration, or biological pathway matters. Transporting an estimate to another population likewise requires attention to differences in effect modifiers and baseline risk.

Diagnostics cannot prove that an estimand has been identified, but they can reveal mismatches or fragility. Check that exposure and outcome units, allele orientation, outcome scale, and target population are stated consistently. Examine whether the assumed linear exposure effect is plausible over the genetically induced range, and whether results are sensitive to choices that change the populations or variants contributing information. For a binary outcome, compare the reported scale with the claim: an odds ratio should not be described as a risk ratio, and a liability effect should not be presented as a directly observed probability change.

• Common mistake: calling every IV result a population effect. An instrument that changes treatment only for a subset can identify an effect in that subset. The correction is to state whether the target is an ATE, a CACE, or another explicitly defined contrast.
• Common mistake: treating effect scales as interchangeable. A log-odds coefficient is not a percentage-point change, and a liability standard deviation is not an observed outcome unit. The correction is to name the scale and use a justified conversion if another scale is needed.
• Common mistake: interpreting a genetic perturbation as any clinical intervention. The correction is to state the exposure contrast and consider whether timing, duration, and population make the proposed intervention comparable.

The central limitation is that an estimand is not guaranteed to be identified merely because it has been defined precisely. An MR estimate can have a valid causal interpretation only if the relevant assumptions, measurement choices, and target-population conditions support that interpretation. Distinguishing the estimand from the estimator makes those requirements visible instead of hiding them inside a single reported coefficient.