On the other hand, when trying to identify G*E interactions for a phenotype with known genetic architecture, the balance between power gained by adding more samples versus power degradation produced by phenotype heterogeneity may favor the latter. The tradeoff between sample size and phenotypic heterogeneity of exposure data is modeled in Figure 2 [Lindstrom et al., 2009]. This hypothetical example considers a rare disease (prevalence 1 in 1,000), no main effect for the binary genetic factor (with 20% prevalence), an odds ratio of 1.5 for the exposure, an interaction odds ratio of 1.35, and a Type I error rate of 5E-8. This illustrates the power of a case-control study to detect a G*E interaction (departure from a multiplicative odds model) when the binary exposure is measured perfectly or via a good proxy with 77% specificity and 99% sensitivity (roughly analogous to self-reported versus measured overweight status). Figure 2 illustrates that even modest misclassification can greatly decrease the power of tests for G*E interaction (and the relative decrease is greater for rare exposures). On the other hand Figure 2 also illustrates
