A method for indirectly estimating gene-environment effect modification and power given only genotype frequency and odds ratio of environmental exposure

Both genes and environment are important determinants of disease. In this paper we model gene-environment effect modification on the odds ratio scale OR(GEID) and show how to indirectly estimate the effect and 95% confidence intervals (CI) for the simple case of no main genetic and environmental effects [i.e., OR(GE/D) = OR(GE/D) = 1]. A statistic is presented to test the null hypothesis OR(GE/D) = 1 and to calculate corresponding power, given the odds ratio for environmental exposure OR(E/D) and population genotype frequency (g). Direct extension of the above model provides a mathematical framework for estimating confidence bounds in more complex cases involving partial genetic and/or environmental effects.