Minimum Sample Size Estimation to Detect Gene-Environment Interaction in Case-Control Designs

As genetic markers become more available, case-control studies will be increasingly important in defining the role of genetic factors in disease causality. The authors estimate the minimum sample size needed to assure adequate statistical power to detect gene-environment interaction. One assumption is made: the prevalence of exposure is independent of marker genotypes among controls. Given the assumption, six parameters (three odds ratios, the prevalence of exposure, the proportion of those with the susceptible genotype, and the ratio of controls to cases) dictate the expected cell sizes in a 2 x 2 x 2 table contrasting genetic susceptibility, exposure, and disease. The three odds ratios reflect the association between disease and 1) exposure among non-susceptibles; 2) susceptible genotypes among nonexposed individuals; and 3) the gene-environment interaction itself, respectively. Given these parameters, the number of cases and controls needed to assure any particular Type I and Type II error rates can be estimated. Results presented here demonstrate that case-control designs can be used to detect gene-environment interaction when there is both a common exposure and a highly polymorphic marker of susceptibility.