Table 1.
Parameter configuration for simulation scenarios
| Parameterb | Gene-environment interaction effect modeleda | |||||
|---|---|---|---|---|---|---|
| No Effect | Effect on Average | Effect on Change | ||||
| No Effect on Averagec | No Effect on Changec | Linear Interaction | Non-linear Interactiond | Linear Interaction | Non-linear Interactiond | |
| β0 | 11 | 11 | 11 | 11 | 11 | 11 |
| βS | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
| βT | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 |
| βT’ | −0.8 | −0.8 | − 0.8 | −0.8 | − 0.8 | −0.8 |
| βG | 0 to 1 | 0 | 0.25 | 0 | 0 | 0 |
| βGT | 0 | 0 to 0.03 | 0 | 0 | 0.01 | 0 |
| βE | 0 to 2 | 0 to 1.2 | 0.5 | 0 | 0.5 | 0 |
| σ2A | 3 | 3 | 3 | 3 | 3 | 3 |
| σ2C | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 |
| τ2A | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
| τ2C | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
| σ2E | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 |
| βGE | 0 | 0 | 0.1 to 1 | 0.1 to 1 | 0 | 0 |
| βGTE | 0 | 0 | 0 | 0 | 0.001 to 0.03 | 0.001 to 0.03 |
aA range of values was simulated for some parameters, effect sizes varied at 0.1 increments for βGE when the interaction effect was on the average. For interaction effect on the rate of change scenarios, βGTE varied at an increment of 0.003 before reaching 0.01 and then by 0.005 afterwards. Under no interaction effect scenarios, βG varied at the same increments as βGE (no effect on average), and βGT varied at the same increments as βGTE (no effect on change). βE varied at 0.2 increments (no effect on average) or was inflated by 40 times relative to its corresponding βGT value (no effect on change)
bβ0: average BMI at baseline predictor level; βS: sex effect; βT, βT’: time effect; βG: genetic effect; βGT: gene-time (GT) interaction effect; βE: environmental effect; σ2A: additive genetic effect on random intercept correlation; σ2C: common environmental effect on random intercept correlation; τ2A: additive genetic effect on random slope correlation; τ2C: common environmental effect on random slope correlation; σ2E: common effect on BMI variance; βGE: gene-environment (GE) interaction effect; βGTE: gene-time-environment (GTE) interaction effect
cFor no interaction effect models, the scenarios refer to the trends where there are no GE interaction effect on genetic main effect (no effect on average) or gene-time interaction effect (no effect on change)
dNon-linear interaction scenarios included exclusive OR (XOR) interaction, conditional dominant interaction and small marginal effect interaction