Instrumental variables and Mendelian randomization
Why this level?
The design family and its defining features have not been specified for this hierarchy. NHMRC 2009 sourceInstrumental-variable and Mendelian-randomisation analyses depend on instrument assumptions that this design table does not certify. The broad design label alone does not establish a published category.
What question does this help answer?
It attempts a causal estimate in observational data without needing to have measured every confounder, which is what makes it attractive and also what makes its assumptions hard to check.
The three assumptions, one of which is untestable
An instrument must be ASSOCIATED with the exposure, must be INDEPENDENT of confounders of the exposure-outcome relationship, and must affect the outcome ONLY through the exposure. The first is testable and should be reported as instrument strength. The second and third are not testable from the data, and the third, the exclusion restriction, is the one that fails most often.
What the three assumptions look like
Why genetic variants
Genotype is fixed at conception and cannot be changed by disease or behaviour, so reverse causation is ruled out and many confounders are implausible. That is the appeal. The exclusion restriction still has to hold, and PLEIOTROPY, where a variant affects the outcome through some other pathway, is its commonest failure.
When not to use it
A weak instrument biases the estimate toward the ordinary confounded association, so a variant explaining a tiny fraction of exposure variance can produce a confident and wrong answer. Do not use an instrument chosen because it gave the expected result.
Why Mallard may recommend it
Mallard may raise an instrumental variable approach when confounding is severe and a plausible instrument is described, but it will not invent an instrument: whether one exists is a subject-matter judgement.
Key assumptions and design requirements
- Instrument strength is reported, typically as an F statistic, and weak instruments are acknowledged as biasing.
- The exclusion restriction is argued from subject knowledge, since it cannot be tested.
- Pleiotropy is examined with sensitivity analyses where genetic instruments are used.
- The estimated quantity is stated: an instrumental variable estimate is a local effect among compliers, not necessarily the population average.
- The estimate is compared with the ordinary observational one, and a large divergence is explained rather than celebrated.
How the estimate is calculated
With a single instrument, the instrumental variable estimate is the ratio of the instrument's association with the outcome to its association with the exposure, called the Wald ratio. Two-stage least squares extends this to several instruments and covariates: the first stage regresses the exposure on the instruments, and the second regresses the outcome on the exposure values predicted by the first stage, so only the part of the exposure driven by the instruments is used. Standard errors must come from the two-stage procedure as a whole; running the second regression by hand on the predicted values gives wrong ones. The first-stage F statistic measures instrument strength, and values below about 10 are the conventional warning of weak-instrument bias. For a binary outcome, two-stage least squares estimates a difference in risk under a linear model, and a logistic second stage does not give a causal odds ratio, so state which quantity is being estimated.
What to watch out for
The whole method rests on the exclusion restriction: the instrument affects the outcome ONLY through the exposure. That assumption is not testable from the data and is the one most often violated, through pleiotropy in genetic instruments or through the instrument being associated with behaviour. A weak instrument also biases the estimate toward the confounded observational one, so instrument strength must be reported.
Clinical example
Question: Does lifelong higher LDL cholesterol cause coronary disease? Design: Use genetic variants known to raise LDL as instruments, report their strength, and test for pleiotropy, acknowledging that the estimate is for lifelong exposure rather than for the effect of lowering LDL at age sixty.
How to report it
STROBE-MR is the guideline for this design. It asks how the genetic variants were measured and selected, how the instrumental variable assumptions were assessed, including the variants' associations with plausible confounders, and which sensitivity analyses tested the results against violations of those assumptions, pleiotropy among them. A reporting guideline is not a design manual: use it to make the study transparent, not as a substitute for careful design. Check the target journal's own requirements as well, which this page cannot know.
- Reading Mendelian randomisation studies: a guide, glossary, and checklist for clinicians (opens in a new tab) · BMJ · doi 10.1136/bmj.k601
- Tutorial on directed acyclic graphs (opens in a new tab) · J Clin Epidemiol · doi 10.1016/j.jclinepi.2021.08.001
- A review of instrumental variable estimators for Mendelian randomization (opens in a new tab) · Stat Methods Med Res · doi 10.1177/0962280215597579
- Strengthening the Reporting of Observational Studies in Epidemiology Using Mendelian Randomization: The STROBE-MR Statement (opens in a new tab) · JAMA · doi 10.1001/jama.2021.18236