On information coded in gene-environment independence in case-control studies.

For analysis of case-control genetic association studies, it has recently been shown that gene-environment independence in the population can be leveraged to increase efficiency for estimating gene-environment interaction effects in comparison with the standard prospective analysis. However, for the special case in which data on the binary phenotype and genetic and environmental risk factors can be summarized in a 2 × 2 × 2 table, the authors show here that there is no efficiency gain for estimating interaction effects, nor is there an efficiency gain for estimating the genetic and environmental main effects. This contrasts with the well-known result assuming that rare phenotype prevalence and gene-environment independence in the control population for the same data can lead to efficiency gain. This discrepancy is counterintuitive, since the 2 likelihoods are also approximately equal when the phenotype is rare. An explanation for the paradox based on a theoretical analysis is provided. Implications of these results for data analyses are also examined, and practical guidance on analyzing such case-control studies is offered.