Reaction-Flux Genetic Interaction
Summary¶
A reaction-flux genetic interaction measures whether the disease association of a risk allele changes with a predicted biochemical reaction flux. Positive interaction is termed amplification and negative interaction buffering, but statistical interaction remains scale- and model-dependent and should not be equated automatically with a molecular mechanism [1].
Interaction-Effect Model¶
For age $t$, risk-allele dosage $G$ and standardized reaction flux $F$, the study fit a Cox proportional-hazards model:
$$h(t) = h_0(t)\exp(\beta_GG + \beta_FF + \beta_{G^2}G^2 + \beta_{F^2}F^2 + \beta_{G:F}GF + \boldsymbol{\gamma}^{T}\mathbf{C})$$
where $\mathbf{C}$ contains covariates and stratification variables. Before fitting the interaction, the candidate SNP's linear effect was regressed out of the genetically predicted flux to reduce correlation caused by risk variants or linked eQTLs contributing to the flux predictor.[1]
| Interaction coefficient | Interpretation for an adverse risk allele |
|---|---|
| $\beta_{G:F} > 0$ | Higher flux amplifies the allele-associated hazard |
| $\beta_{G:F} < 0$ | Higher flux buffers the allele-associated hazard |
| $\beta_{G:F} = 0$ | No multiplicative interaction on the fitted hazard scale |
The Wald test of $\beta_{G:F}$ assumes that the interaction can be represented by the specified polynomial and multiplicative-hazard model.
Dosage-Specific Test¶
As a complementary check, participants are divided by risk-allele dosage $g \in {0,1,2}$. Within each group:
$$h_g(t) = h_{0g}(t)\exp(\beta_{F,g}F + \boldsymbol{\gamma}^{T}\mathbf{C})$$
Welch's ANOVA tests whether $\beta_{F,0}$, $\beta_{F,1}$ and $\beta_{F,2}$ differ without assuming equal variance. A weighted linear regression of the three estimates against dosage, with weights $1/SE_g^2$, produces an effect-size change per additional risk allele.[1]
The paper required both the interaction coefficient test and the dosage-specific test to pass FDR below 0.05. Agreement helps reject model-specific artifacts: the first imposes an interaction form across all participants, while the second estimates flux effects separately by genotype group.[1]
Visualization¶
For descriptive plots, participants can be divided into flux quartiles and the risk-allele hazard estimated within each quartile:
$$h_q(t) = h_{0q}(t)\exp(\beta_{G,q}G + \boldsymbol{\gamma}^{T}\mathbf{C})$$
A monotonic increase in $\beta_{G,q}$ suggests amplification; a decrease suggests buffering. Quartile plots visualize the fitted relationship but are not the primary significance test.
Interpretation Caveats¶
- Interaction is conditional on the hazard-ratio scale and included covariates.
- A significant multiplicative interaction may be weak on an absolute-risk scale, or vice versa.
- Predicted flux measurement error generally reduces power and may distort effect estimates.
- Genotype can enter both the risk term and flux predictor; residualization and LD checks are therefore essential.
- Sparse homozygous-risk groups can destabilize dosage-specific estimates.
- Statistical interaction does not identify the biochemical direction of causation.
- The sign applies to the chosen risk allele and orientation of the flux value; reversing either reverses the coefficient.
Citations¶
[1] Foguet et al. (2025), metabolic reaction flux interaction models