Figure 2.

Power of a case-control study to detect a gene-environment 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)

This figure illustrates several points: a) large samples sizes are needed to detect gene-environment interactions; b) even modest misclassification can greatly decrease the power of tests for gene-environment interaction (and the relative decrease is greater for rare exposures); yet c) a large study using the proxy can have greater power than a smaller study using the perfect measure. This last point is important when the perfect measure is prohibitively expensive or only available on a small fraction of samples, while the good measure is relatively inexpensive or already available on many samples. Power calculations were performed using the methods described in Lindstrom et al. (2009), assuming 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 5×10^-8.