Abstract
Complex diseases are caused by a combination of genetic and environmental factors, creating a challenge for understanding the disease mechanisms. Understanding the interplay between genes and environmental factors is important, as genes do not operate in isolation but rather in complex networks and pathways influenced by environmental factors. The advent of new technologies has made a massive amount of genetic data available, and various statistical methods have been developed to analyze genetic data and to identify interactions between genes and the environment, i.e., gene-environment (G-E) interactions. In this review article, we introduce various statistical methods for identifying G-E interactions using case-control designs. We review a range of disease risk models for modeling the joint effects of genetic and environmental factors such as multiplicative and additive models. We then introduce various inference methods under these disease risk models, which include a standard prospective likelihood, case-only designs, a retrospective likelihood that exploits a gene-environment independence assumption to boost power, and an empirical Bayes type approach that uses the independence assumption in a data-adaptive way. Several tests for detecting genetic associations in the presence of G-E interactions are also introduced, which include a joint test and a maximum score test that provides a unified approach by integrating a class of disease risk models to maximize over a class of score tests. There are several challenges of G-E interaction analysis that include replication issues. While more powerful statistical methods for detecting interactions are helpful, ultimately studies with larger sample sizes are needed to identify interactions through consortium-based studies to achieve adequate power for G-E analysis.
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