ABSTRACT
In genome-wide association studies, agnostic searches for gene-environment interactions (G × $ \times $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315154084/5e5abef9-a934-4c3a-a7bb-f3e6e5296d03/content/inline-math25_1.tif"/> E) are routinely conducted (Hunter, 2005); Hutter2013; Thomas2010, though with limited success. The statistical interaction in a logistic regression model, defined as deviation from an additive contribution of two predictors on the logit-transformed risk scale, demands a much larger sample size to reach the same power than a genetic association with a similar effect size (Smith and Day, 1984). This inadequate power is exacerbated by the necessity of a multiple-testing correction for millions of genetic variants that are being interrogated one at a time, even though the vast majority of these genetic variants have no G × $ \times $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315154084/5e5abef9-a934-4c3a-a7bb-f3e6e5296d03/content/inline-math25_2.tif"/> E. Progress has been made to improve efficiency of design and estimation for a single variant G × $ \times $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315154084/5e5abef9-a934-4c3a-a7bb-f3e6e5296d03/content/inline-math25_3.tif"/> E test by incorporating the assumptions such as independence of G and E in the population and the Hardy-Weinberg equilibrium (Chatterjee and Carroll, 2005); Chen12; (Mukherjee and Chatterjee, 2008), as covered in Chapter 24. In this chapter, efficient two-stage procedures are presented for genome-wide searches of G × $ \times $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315154084/5e5abef9-a934-4c3a-a7bb-f3e6e5296d03/content/inline-math25_4.tif"/> E focusing on the “more promising” genetic variants for G × $ \times $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315154084/5e5abef9-a934-4c3a-a7bb-f3e6e5296d03/content/inline-math25_5.tif"/> E interrogation.
