Robust tests for gene-environment interaction in case-control and case-only designs

The case-control and case-only designs are commonly used to detect the gene-environment (G-E) interaction. In principle, the tests based on these two designs require a pre-specified genetic model to achieve an expected power of detecting the G-E interaction. Unfortunately, for most complex diseases the underlying genetic models are unknown. It is well known that mis-specification of the genetic model can result in a substantial loss of power in the detection of the main genetic effect. However, limited effort has been dedicated to the study of G-E interaction. This issue has been investigated in this article with a conclusion that the genetic model mis-specification can not only undermine the power of detecting G-E interaction in both case-control and case-only designs but also distort the type I error rate in case-control design. To tackle this problem, a class of robust tests, namely MAX3, have been proposed for both the case-control and case-only designs. The proposed tests can well control the type I error rate and yield satisfactory power even when the genetic model is mis-specified. The asymptotic distribution and the p-value formula for MAX3 have also been derived. Comprehensive simulation studies and a real data application on the genome-wide association study (GWAS) have been conducted using these analytical tools and the results demonstrate desirable operating characteristics of the proposed robust tests.