FIGURE 3.

Noncentrality parameter (left y-axis) and associated power (right y-axis) as a function of allele prevalence for a 2-degrees-of-freedom chi-square likelihood ratio test for interaction effects. The interaction risk scenario: R₁ = 1.5, R₂ = 3.0, T = 1, U₁ = U₂ = 2.0, with exposure prevalence fixed at 0.15. Calculations assume a nested case-control study with 400 cases and 800 controls within a risk-based cohort (short-dash line) or a randomly sampled cohort (solid line). An example curve corresponding to doubled accrual within the risk-based cohort, based on 800 cases and 1,600 controls, is also shown (long-dash line). Noncentrality is based on A) a multiplicative null model for no interaction, and B) an additive null model for no interaction. Parameters R₁ and R₂ denote the relative risks for offspring with one and with two copies of the variant allele, respectively, relative to those with no copies. The parameter T is the relative risk associated with exposure. U₁ and U₂ are the multiplicative interaction parameters for exposure acting jointly with one and with two inherited copies of the allele, respectively.