Modeling and testing for joint association using a genetic random field model.

Substantial progress has been made in identifying single genetic variants predisposing to common complex diseases. Nonetheless, the genetic etiology of human diseases remains largely unknown. Human complex diseases are likely influenced by the joint effect of a large number of genetic variants instead of a single variant. The joint analysis of multiple genetic variants considering linkage disequilibrium (LD) and potential interactions can further enhance the discovery process, leading to the identification of new disease-susceptibility genetic variants. Motivated by development in spatial statistics, we propose a new statistical model based on the random field theory, referred to as a genetic random field model (GenRF), for joint association analysis with the consideration of possible gene-gene interactions and LD. Using a pseudo-likelihood approach, a GenRF test for the joint association of multiple genetic variants is developed, which has the following advantages: (1) accommodating complex interactions for improved performance; (2) natural dimension reduction; (3) boosting power in the presence of LD; and (4) computationally efficient. Simulation studies are conducted under various scenarios. The development has been focused on quantitative traits and robustness of the GenRF test to other traits, for example, binary traits, is also discussed. Compared with a commonly adopted kernel machine approach, SKAT, as well as other more standard methods, GenRF shows overall comparable performance and better performance in the presence of complex interactions. The method is further illustrated by an application to the Dallas Heart Study.