POPH90111 · Genetic Epidemiology
Gene–Environment Interaction
Genes and environment do not always act in separate lanes. Gene–environment interaction (G×E) is the situation where the effect of an environmental exposure on disease differs depending on genotype — equivalently, where the genotype’s effect differs across exposure levels. It is the formal home of “precision prevention”: if a smoker’s extra risk is far larger in one genotype, that genotype is where the smoking-cessation payoff concentrates. But “interaction” is one of the most treacherous words in the course, because whether it is present depends on the scale you measure it on. The centrepiece is exactly this: the course’s four worked risks (0.02 / 0.04 / 0.03 / 0.06) show no multiplicative interaction (equal relative risks) yet positive additive interaction (unequal risk differences) — same data, two answers — and the additive scale is the public-health-relevant one. The chapter then covers the two designs (the standard case-control with a G×E product term, and the efficient but assumption-laden case-only design) and how to critically appraise a G×E claim.
What this chapter covers
- 017.1 What G×E is, and the scale-dependence centrepiece (additive vs multiplicative)
- 02The four course risks: 0.02/0.04 (gene−) and 0.03/0.06 (gene+)
- 037.2 Computing interaction on each scale (no-mult ⇔ equal RRs; no-additive ⇔ equal RDs)
- 047.3 Synergism vs antagonism
- 057.4 Designs for testing G×E (case-control product term vs case-only)
- 067.5 The case-only design — logic, power and its independence-assumption trap
- 077.6 Critically appraising a G×E claim — a scaffold
- 087.7 Why G×E matters — precision prevention
Worked example: deciding interaction on both scales
- +1(a) Multiplicative test (compare the two RRs). RR in gene− = 0.04/0.02 = 2.0; RR in gene+ = 0.06/0.03 = 2.0. Equal ⇒ no multiplicative interaction (joint RR = product of separate RRs).
- +2(b) Additive test (compare the two RDs). RD in gene− = 0.04 − 0.02 = 0.02; RD in gene+ = 0.06 − 0.03 = 0.03. Unequal ⇒ additive interaction present.
- +1State the scale — never just ‘there is/no interaction.’ Report both: “no multiplicative, positive additive.” A bare claim loses marks.
- +1(c) Pick the actionable scale. For public health use the additive scale: the gene+ group has the larger risk difference (0.03 vs 0.02), so it gains more absolute cases prevented per person by removing the exposure — target them. The multiplicative scale (the default logistic/Cox output) misses this.
Key terms
- Gene–environment interaction (G×E)
- When the association between an environmental exposure and disease differs across genotypes (equivalently, the genotype–disease association differs across exposure levels). Statistically it is a departure from a specified no-interaction model — and because ‘no-interaction’ can be defined on a multiplicative or an additive scale, interaction is scale-dependent.
- Multiplicative vs additive scale
- Two no-interaction baselines. Multiplicative no-interaction ⇔ the two relative risks are equal (joint RR = product of the separate RRs); additive no-interaction ⇔ the two risk differences are equal (joint RD = sum of the separate RDs). The two can disagree — equal RRs but unequal RDs gives ‘no multiplicative, yes additive’. The additive scale is the public-health-relevant one; multiplicative is the default logistic/Cox output.
- Case-only design
- An efficient G×E design that uses cases only and tests whether G and E are associated among cases. If G and E are independent in the source population, any G–E association among cases must come from their joint (interaction) effect on disease, so a case-only G–E odds ratio estimates the multiplicative interaction — with no controls and more power than a case-control product term.
- The case-only independence assumption
- The crucial precondition for the case-only design: G and E must be independent in the source population. If the gene influences the exposure (or both track ancestry), cases show a G–E association even with no true interaction, producing a false-positive interaction. The design also estimates the multiplicative scale only and can never speak to the additive (public-health) scale or any main effect.
- Synergism vs antagonism
- Two readings of a positive vs negative departure from a no-interaction model. Synergistic: the joint effect is bigger than predicted — the exposure is more harmful in the susceptible genotype (converging/amplifying pathways). Antagonistic: the joint effect is smaller — one factor blunts the other. Either way the biological interpretation is a hypothesis; statistical interaction does not prove a mechanism.
Gene–Environment Interaction FAQ
How can the same data show interaction on one scale and none on another?
Because ‘no interaction’ has two definitions. On the multiplicative scale, no interaction means equal relative risks (joint RR = product of the separate RRs); on the additive scale, it means equal risk differences (joint RD = sum of the separate RDs). With the course’s risks (0.02/0.04 and 0.03/0.06), the relative risks are both 2.0 (no multiplicative interaction) but the risk differences are 0.02 and 0.03 (additive interaction present). Same numbers, two answers — which is why you must always state the scale.
Which scale should public-health decisions use?
The additive scale. The genotype with the larger risk difference gains the most absolute cases prevented per person by removing the exposure, so that is the group to target for precision prevention. The multiplicative scale — the default output of logistic and Cox regression — answers a different (relative) question and misses who benefits most in absolute terms. Reporting only a logistic product term and then making a public-health claim about who benefits most is the classic two-line failure mode examiners look for.
When is the case-only design valid, and what can’t it give?
It is valid only if G and E are independent in the source population — otherwise cases show a G–E association even with no real interaction, producing a false positive. Even when valid, it estimates the multiplicative interaction only (it is silent on the additive scale that public health needs) and gives no main effects of G or E and no absolute risks. So accept it as efficient evidence of multiplicative interaction if independence is defensible; otherwise treat the ‘interaction’ as potentially spurious and ask for a case-control replication.
What is the two-line failure mode examiners penalise on G×E?
(1) Reporting ‘interaction’ without naming the scale — meaningless, because additive and multiplicative can disagree. (2) Using a multiplicative result (the default model output) to make a public-health claim about who benefits most, which is an additive question. Get the scale right — name it, show the RR or RD comparison, and say the additive scale is the public-health-relevant one — and you have the marks.
Exam move
The whole chapter turns on scale, so over-learn the centrepiece: with the four course risks (0.02/0.04/0.03/0.06), compute both RRs (2.0 = 2.0 → no multiplicative interaction) and both RDs (0.02 ≠ 0.03 → additive interaction present), and recite the rule no-mult ⇔ equal RRs; no-additive ⇔ equal RDs. Never write “there is interaction” without naming the scale, and always flag that the additive scale is the public-health-relevant one while multiplicative is the default logistic/Cox output. For designs, contrast the case-control G+E+G×E product term (under-powered, both scales) with the case-only design (efficient, multiplicative-only, valid only if G⊥E). Then run the appraisal scaffold and tie it back to precision prevention.
