On the use of population attributable fraction to determine sample size for case-control studies of gene-environment interaction

Most methods for calculating the sample size needed to detect gene-environment interactions use odds ratios to measure the effect size. We show that for any combination of susceptible genotype prevalence and exposure prevalence and their associated risks, the odds ratio measuring strength of interaction corresponds to a population attributable fraction (PAF) because of interaction and vice versa. Simultaneous consideration of odds ratio for interaction and the associated PAF attributable to interaction provides additional insight to investigators evaluating the feasibility and public health relevance of a proposed study. We considered gene-environment interactions on a multiplicative scale, and assumed a dichotomous environmental exposure variable and a single two-allele disease-susceptibility locus. Our results show, for example, that for studies of exposures and genotypes that are common in a population (30%-50%), the PAF for interaction is large (>27%) even if the odds ratio for interaction is only moderate (approximately 2). If simultaneous estimates of interaction odds ratio and PAF indicate that the PAF is so large as to be implausible, the investigator may decide to reevaluate the study design based on detecting a more reasonable PAF. In this case, the associated odds ratio for interaction will be weaker and a considerably larger sample size may be needed.