Detection of genotype-environment interaction in case-control studies of birth defects: how big a sample size?

Detecting interactions between risk factors in case-control studies of birth defects and other conditions usually requires increasing the sample size beyond that needed to detect marginal effects. A special case of such interaction is genotype-environment interaction in which the effects of an exposure on disease risk are modified by genetic susceptibility. When case-control studies are designed to detect marginal effects of an exposure (i.e., in the whole population), under many plausible interaction schemes, no additional case and control subjects are needed to detect genotype-environment interaction. On the contrary, inclusion of genotypic information generally can improve the statistical power of the original study. Using the example of oral clefts, maternal cigarette smoking, and genetic variation at the transforming growth factor alpha gene, we illustrate sample size and power issues in designing case-control studies when prior information is available on both the marginal effects of the exposure and the genetic factor.