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A backdoor adjustment set contains no descendant of the exposure and blocks every backdoor path from the exposure to the outcome. Averaging the conditional outcome distribution over such a set identifies the total causal effect.

A backdoor path creates noncausal association by entering the exposure through an arrowhead rather than beginning with a causal arrow leaving it.

A backdoor path from exposure $X$ to outcome $Y$ begins with an arrow entering $X$. An adjustment set identifies the total effect when it blocks every such path without conditioning on descendants of $X$.

Calcium intake is the amount of calcium consumed, including food and supplements. It is an exposure that can be changed by an intervention, and should not be identified automatically with serum calcium in a causal inference analysis.

A case–control study selects subjects according to an outcome: cases have the outcome and controls represent an appropriate comparison population. It compares their prior exposures or genetic variants to study association. Its retrospective sampling must be accounted for when interpreting risks; selection bias and confounding can distort an unadjusted association. In genetics, matched family pseudo-control genotypes can replace unrelated controls for a conditional transmission disequilibrium test.

A study following a defined group to relate earlier characteristics or exposures to later outcomes. Prospective measurement improves temporal ordering but does not automatically remove confounding, selective attrition or exposure misclassification.

Conditional front-door adjustment applies the front-door argument within strata of observed covariates and then averages over those covariates. The covariates must remove exposure-mediator confounding, while the exposure together with the covariates must remove mediator-outcome confounding.

The exclusion restriction requires an instrumental variable to affect the outcome only through the exposure whose causal effect is being studied.

An exposure is a condition, behavior, intervention, or environmental factor whose association or causal effect on an outcome is studied.

Front-door adjustment identifies an exposure effect through an observed mediator when the mediator intercepts every directed exposure-outcome path, the exposure-mediator relation has no unblocked backdoor path, and exposure blocks every backdoor path from mediator to outcome.

A genetic risk score combines allele counts from several genetic variants, usually using specified weights. In Mendelian randomization it can act as a combined instrumental variable for an exposure; interpretation still requires instrument relevance, instrumental-variable independence, and the exclusion restriction.

Horizontal pleiotropy occurs when a genetic instrument affects an outcome through a pathway other than the exposure under study. It violates the exclusion restriction in Mendelian randomization.

InSIDE stands for instrument strength independent of direct effect. It requires the genetic associations with the exposure to be independent of the direct, pleiotropic effects of those genetic variants on the outcome. It is a key identifying assumption for MR-Egger regression.

An instrumental variable changes an exposure or treatment but affects the outcome only through that exposure. Together, instrument relevance, instrumental-variable independence, and the exclusion restriction identify causal effects under suitable structural assumptions.

Instrumental-variable monotonicity requires changing the instrument in its encouraging direction never to move any unit's exposure in the opposite direction.

Instrument relevance requires the instrumental variable to change the conditional distribution of the exposure. A nearly irrelevant instrument is a weak instrument and can produce unstable estimates.

Loss of participants or outcome observations across follow-up. If remaining under observation depends on exposure and determinants of the outcome, analyzing only retained participants can induce selection bias.

Mediator-outcome confounding occurs when a common cause of the mediator and outcome is not adequately controlled. If exposure itself affects such a common cause, ordinary adjustment can fail to identify natural direct and indirect effects.

Mendelian randomization uses inherited genetic variants associated with an exposure as instrumental variables. Its causal interpretation requires instrument relevance, instrumental-variable independence, and the exclusion restriction.

Migraine is a neurological disorder that can be an outcome in a clinical trial or an observational study. Its statistical association with an exposure does not alone establish a causal effect.