Power and sample size calculations for case-control studies of gene-environment interactions with a polytomous exposure variable.

Genetic polymorphisms may appear to the epidemiologist most commonly as different levels of susceptibility to exposure. Epidemiologic studies of heterogeneity in exposure susceptibility aim at estimating the parameter quantifying the gene-environment interaction. In this paper, the authors use a general approach to power and sample size calculations for case-control studies, which is applicable to settings where the exposure variable is polytomous and where the assumption of independence between the distribution of the genotype and the environmental factor may not be met. It was found through exploration of different scenarios that in the cases explored, power calculations were relatively insensitive to assumptions about the odds ratio for the exposure in the referent genotype category and to assumptions about the odds ratio for the genetic factor in the lowest exposure category, yet they were relatively sensitive to assumptions about gene frequency, particularly when gene frequency was low. In general, to detect a small to moderate gene-environment interaction effect, large sample sizes are needed. Because the examples studied represent only a small subset of possible scenarios that could occur in practice, the authors encourage the use of their user-friendly Fortran program for calculating power and sample size for gene-environment interactions with exposures grouped by quantiles that are explicitly tailored to the study at hand.