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Trace genetic instruments through pleiotropy, family structure and compatible association data using an original four-marker worksheet.
Understand genetic variation and permitted pathways · Chapters 1–3 · Start this route
Calculate valid and misleading marker patterns · Chapters 4–6 · Start this route
Evaluate family designs, datasets and evidence · Chapters 7–10 · Start this route
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A genetic variant can be associated with both a measurable trait and a later outcome. That pattern may fit a causal chain in which the trait changes the outcome. It may also arise because the variant influences another pathway, because related people share environments, or because the two studies being combined are not comparable.
Mendelian randomisation uses genetic variation as an instrument to investigate such causal questions. The central task is to distinguish a useful genetic source of variation from a misleading shortcut. The word “randomisation” does not turn an association study into a treatment trial.
This lesson develops an original, paper-only example with anonymous traits X and Y. It makes no claim about a particular gene, diagnosis or intervention. For the broader assignment distinction, see How Randomisation Works. Here the focus is on genetic instruments, biological pathways, family structure and the limits of agreement between methods.
Contents
Understand genetic variation and permitted pathways · Chapters 1–3
1. Inheritance supplies a starting point, not a finished experiment
Calculate valid and misleading marker patterns · Chapters 4–6
4. Build a four-variant numerical example
Evaluate family designs, datasets and evidence · Chapters 7–10
7. Use families to investigate a different source of bias
8. Check what happens when two datasets are joined
9. New methods improve particular parts of the evidence chain
CHAPTER 1 OF 10 · Understand genetic variation and permitted pathways
1. Inheritance supplies a starting point, not a finished experiment
At many genetic positions, a person carries two copies of a DNA variant, with one inherited from each parent. Conditional on the relevant parental genetic information, transmission provides a source of within-family variation. This helps explain why genetic instruments can sometimes avoid confounding that troubles a straightforward comparison of an exposure with an outcome.
However, comparing unrelated people is not the same as comparing alternative transmissions within the same family. Allele frequencies and environments can vary across populations. Parents can influence the environment through their own characteristics. Partner selection can create correlations between genetic and social factors across generations.
Researchers also do not normally assign a genetic variant, choose when its effects begin or control everything it changes. A variant may influence a trait throughout development. Changing that trait briefly in adulthood may have a different effect, even if the genetic analysis is internally sound.
A useful opening question is therefore precise: does a particular pattern of genetic variation provide evidence about a specified exposure–outcome relationship in a specified population? That is more defensible than asking whether “genes prove” that an exposure causes an outcome.
Genetic variants are often represented by an allele count of zero, one or two. An allele is a version at a genetic position; counting it is a coding convention. Neither the counted allele nor a higher value of the measured trait is automatically beneficial, harmful or biologically dominant.
CHAPTER 2 OF 10 · Understand genetic variation and permitted pathways
2. Trace the proposed biological route
Draw three boxes: genetic variant G, exposure X and outcome Y. The intended route is G → X → Y. Draw an additional variable U that influences X and Y. The genetic instrument is useful only if its relationship with Y can be attributed to the relevant X pathway under the analysis assumptions.
Relevance requires G to predict X. Researchers assess the variant–exposure association, its precision and the strength of the collection of instruments. A tiny association can be useful with adequate information, but weakly estimated associations make inference difficult and can amplify other problems.
Independence requires the instrument to be suitably independent of exposure–outcome confounding. The argument must address the actual sample and design. Adjusting for broad ancestry components may reduce population structure without establishing that all relevant structure has disappeared.
Exclusion requires that G influence Y through X rather than through an alternative route outside the target exposure pathway. If G also changes another biological trait W that changes Y independently of X, the simple instrument interpretation is threatened.
Even these statements need a clearly defined target. Which exposure measure, age range, outcome scale and population are being discussed? Does the model assume a constant linear effect, or estimate something more local and weighted? Assumptions that identify a slope for one formulation need not identify the effect of every conceivable intervention on X.
CHAPTER 3 OF 10 · Understand genetic variation and permitted pathways
3. Distinguish two meanings of multiple biological effects
A variant can affect more than one measured trait because one effect lies downstream of another. For example, the permitted diagram could be G → X → M → Y, with M a mediator. If the question concerns the total effect through X, that downstream chain is compatible with the instrument argument.
This is often called vertical pleiotropy in Mendelian-randomisation discussions. It should not be removed automatically just because several traits appear in the biological story. Blocking M would change the question from the total effect of X towards a more restricted direct-effect question.
Horizontal pleiotropy describes an outcome pathway outside the target exposure route, such as G → W → Y alongside G → X. It can make the genetic outcome association too large, too small or even opposite in direction compared with the association expected from X alone.
The distinction depends on the causal structure, not merely a database count of how many traits are associated with a variant. A long list of associated traits does not reveal which are upstream, downstream or alternative pathways. Biological knowledge and additional designs are needed to interpret the list.
There is a further complication: nearby variants can be correlated through linkage disequilibrium. A measured marker associated with X may tag a different causal variant associated with Y. A shared genomic region is therefore not automatically evidence of a shared causal variant, much less proof that X causes Y.
CHAPTER 4 OF 10 · Calculate valid and misleading marker patterns
4. Build a four-variant numerical example
Our fictional dataset contains four independent genetic markers, A, B, C and D. Exposure X and outcome Y are abstract continuous traits measured in explicitly chosen units. Assume a linear model, compatible study populations, correctly aligned allele coding and no selection problems. Initially, all four markers are valid instruments.
Let the exposure association per counted allele, called γ, be 0.10, 0.20, 0.30 and 0.40 X units respectively. Set the true causal slope θ to 2 Y units per X unit. The corresponding outcome associations Γ are then 0.20, 0.40, 0.60 and 0.80 Y units per allele.
Each marker gives a ratio Γ / γ. Marker A gives 0.20 / 0.10 = 2; the others also give 2. The allele unit cancels, leaving Y units per X unit. This cancellation is useful only when the two associations refer to the same counted allele and compatible trait definitions.
For a deliberately simplified pooling calculation, treat the exposure associations as known without error and give every outcome association the same standard error of 0.05. A weighted regression through the origin then has slope equal to the sum of γΓ divided by the sum of γ squared. Equal outcome precision makes the common weight cancel.
Here the denominator is 0.01 + 0.04 + 0.09 + 0.16 = 0.30. The numerator is 0.02 + 0.08 + 0.18 + 0.32 = 0.60, giving slope 2. This is an exact teaching construction, not a realistic claim that genetic associations are measured perfectly.
CHAPTER 5 OF 10 · Calculate valid and misleading marker patterns
5. Introduce one extra pathway and watch the result change
Now give marker C an additional direct outcome association of +0.30 Y units per allele through a route outside X. Its exposure association stays 0.30, but its outcome association rises from 0.60 to 0.90. The other three markers remain unchanged.
The individual ratios become 2, 2, 3 and 2. The pooled numerator rises to 0.69, while the denominator stays 0.30. The combined slope becomes 2.3. Adding more markers did not automatically cancel the invalid pathway; marker C has substantial influence because it strongly predicts X.
A scatter diagram makes the conflict visible. Put γ on the horizontal axis and Γ on the vertical axis. A, B and D lie on a line of slope 2 through the origin. C sits above that line. The fitted pooled slope of 2.3 tilts towards C rather than identifying why C differs.
Under the simplified equal-error calculation, residual outcome associations around that fitted line are −0.03, −0.06, +0.21 and −0.12. Squaring them, summing and dividing by 0.05 squared gives a heterogeneity statistic of 25.2. We use this as a transparent discrepancy measure; its inferential interpretation requires the assumed error model.
Removing C restores slope 2 in our invented dataset because we know its hidden pathway. In real research, deleting whichever marker spoils the preferred answer is not a valid discovery procedure. Researchers need prospectively defensible criteria, biological evidence and sensitivity reporting that includes the consequences of exclusion.
CHAPTER 6 OF 10 · Calculate valid and misleading marker patterns
6. Agreement can survive a shared bias
Construct a different world. Return to all four original markers, but let every marker have an alternative outcome effect equal numerically to its exposure association. Thus the extra effects are 0.10, 0.20, 0.30 and 0.40 Y units per allele, while the true X-to-Y slope remains 2.
Now Γ equals 3γ for every marker. Every ratio is 3, the pooled slope is 3 and all residuals around that line are zero. The markers agree perfectly, yet their shared alternative pathway creates a biased causal interpretation. This example shows why low heterogeneity cannot certify instrument validity.
The issue is related to correlated horizontal pleiotropy: the alternative effects can track instrument strength instead of averaging away. The original CAUSE methods study explicitly modelled correlated and uncorrelated pleiotropic effects and investigated false positives in simulations. Its results motivate careful comparison of causal and shared-pathway explanations, rather than an assumption that all pleiotropy looks like a single obvious outlier.
Other methods trade one assumption for another. Bowden, Davey Smith and Burgess’s original MR-Egger paper introduced an approach allowing certain invalid instruments under an instrument-strength/direct-effect independence condition. That condition matters: a perfectly strength-correlated alternative route is not repaired merely by adding an intercept to a regression.
A non-significant intercept test is also not proof of no pleiotropy. Precision may be poor, effects may cancel, or the prohibited pathway may have a form the diagnostic does not expose. Agreement across analyses is useful evidence only after asking what assumptions those analyses share.
CHAPTER 7 OF 10 · Evaluate family designs, datasets and evidence
7. Use families to investigate a different source of bias
Family structure creates a problem distinct from a marker’s alternative biological pathway. Suppose parental characteristics influence both inherited alleles and the household environment. Across unrelated people, the child’s genotype can then be associated with an environmental route to Y, even if the allele’s own effect follows the intended X pathway.
Within-family designs compare genetic differences while accounting for the shared family context. They can reduce biases due to population structure and some parental or partner-selection processes. They do not automatically eliminate horizontal pleiotropy, sibling effects, measurement error or every consequence of study selection.
Consider a separate fictional comparison. In unrelated individuals, a marker’s exposure association is 0.20 and its outcome association 0.60, giving ratio 3. Within families, the corresponding associations are 0.15 and 0.30, giving ratio 2. A change in both associations matters; comparing only the outcome coefficient would miss the denominator change.
The difference does not prove the second answer is correct in every real setting. Within-family estimates may be less precise, and the relevant genetic contrast may change. The exercise illustrates why the design and both component associations must be examined together.
In Brumpton and colleagues’ 2020 original study, height–education estimates from unrelated individuals were strongly attenuated in within-family analyses. This is evidence that family-aware designs can materially change an apparently causal interpretation. It does not imply that genetic studies determine a person’s educational potential or justify decisions about individuals.
CHAPTER 8 OF 10 · Evaluate family designs, datasets and evidence
8. Check what happens when two datasets are joined
Two-sample Mendelian randomisation often combines variant–exposure associations from one dataset with variant–outcome associations from another. This can be efficient, but the two columns do not become compatible merely because they contain the same marker identifier.
First check allele alignment. Suppose the exposure file reports +0.20 X units per A allele, while the outcome file reports −0.40 Y units per the opposite allele. Naïvely dividing gives −2. After putting both associations on the A-allele scale, the outcome coefficient becomes +0.40 and the ratio is +2.
Strand ambiguity and allele-frequency information can complicate this step. Incompatible or unresolved markers may need exclusion according to a documented rule. Guessing a sign to make an estimate look plausible is not harmonisation.
Next examine ancestry, age, exposure measurement and recruitment. An allele–exposure association from one population or life stage need not equal the association in the outcome sample. Participant overlap can correlate estimation errors; selecting variants and estimating their strengths in the same discovery data can introduce winner’s-curse problems.
Finally, account for correlation between markers. Our four-marker worksheet assumes independence. If several markers largely track the same inherited region, treating them as independent can exaggerate information. Using suitable linkage-disequilibrium modelling or justified marker selection is a statistical requirement, not a cosmetic adjustment.
These checks are not individual genetic interpretation. The exercise uses aggregate association estimates and contains no personal genetic records. Uploading someone’s DNA file or deriving a personal prediction would be a separate, much more sensitive task and is unnecessary for understanding the causal argument.
CHAPTER 9 OF 10 · Evaluate family designs, datasets and evidence
9. New methods improve particular parts of the evidence chain
A 2025 Nature Genetics study of family-based GWAS designs introduced estimators aimed at improving power and robustness for direct genetic effects. It distinguished those effects from associations that also reflect relatives’ environments and population structure. Better input associations can strengthen downstream research, but estimating a direct genetic effect is still not identical to identifying an exposure’s effect on an outcome.
The 2025 MR-link-2 original study developed a region-based approach that models pleiotropy and linkage disequilibrium using summary associations and a reference dataset. The authors evaluated it in simulations and independent reference datasets. The relevant lesson is that a local genetic region needs an explicit model; choosing variants near an exposure-related gene does not itself guarantee exclusion.
Such methods should be judged by their assumptions, calibration, data requirements and tested settings. A promising benchmark is not a universal guarantee across all traits, populations, linkage structures or measurement errors. A method’s name cannot substitute for reading the conditions under which it was assessed.
Colocalisation provides another useful but bounded question: do the associations appear to share a causal variant? Even convincing support for a shared variant does not decide whether its outcome effect travels through X or through a parallel pathway. It addresses one part of the causal chain.
Evidence is stronger when different designs challenge different weaknesses. Family comparisons, biological pathway studies, independent datasets and appropriately designed interventions may contribute complementary information. Their estimates need not match exactly if they concern different exposure histories, populations or effect scales.
CHAPTER 10 OF 10 · Evaluate family designs, datasets and evidence
10. Complete a genetic-instrument evidence worksheet
Start with the four valid-marker pairs and reproduce slope 2. Then change only C’s outcome association to 0.90 and reproduce 2.3. Write down the specific extra arrow that generated the discrepancy. Explain why the pooled number alone cannot identify that arrow.
Next use the shared-bias world, with outcome associations 0.30, 0.60, 0.90 and 1.20. Reproduce slope 3 and zero residual discrepancy. This is the essential counterexample: agreement between genetic estimates does not establish that their common pathway is the one being investigated.
For a real paper, identify the exposure, outcome, genetic instruments and target population. Record how the authors checked strength, allele alignment, marker correlation and study compatibility. Then separate family or population confounding from horizontal pleiotropy instead of treating all bias as one interchangeable problem.
Ask what each sensitivity analysis can detect and what it assumes. An outlier analysis, within-family comparison and colocalisation analysis answer different questions. If their conclusions differ, investigate those differences rather than counting how many methods produce the preferred sign or a small p-value.
Finally, state the practical boundary. Evidence about genetically influenced exposure differences is not an individual risk prediction or an automatic recommendation to change a treatment, behaviour or policy. Timing, mechanism, population and intervention size may all differ from the genetic contrast.
Return to Science Mastery and the How Science Works roadmap. The scientific achievement is a causal claim whose assumptions have been exposed to serious tests, with the remaining uncertainty made visible.