Searching for genetic interactions in complex disease by using distance correlation Fernando Castro-Prado, University and Health Research Institute of Santiago de Compostela, Spain. E-mail:
[email protected] Javier Costas Health Research Institute of Santiago de Compostela, Spain. and Wenceslao González-Manteiga and David R. Penas University of Santiago de Compostela, Spain. Summary. Understanding epistasis (genetic interaction) may shed some light on the ge- nomic basis of common diseases, including disorders of maximum interest due to their high socioeconomic burden, like schizophrenia. Distance correlation is an association measure that characterises general statistical independence between random variables, not only the linear one. Here, we propose distance correlation as a novel tool for the detection of epistasis from case-control data of single nucleotide polymorphisms (SNPs). This approach will be developed both theoretically (mathematical statistics, in a context of high-dimensional statistical inference) and from an applied point of view (simulations and real datasets). Keywords: Association measures; Distance correlation; Epistasis; Genomics; High- dimensional statistical inference; Schizophrenia 1. Introduction The application field that motivates the present article is going to be explained here- inafter. The starting point is a genomic problem, whose importance and interest will be addressed. In addition, the state of the art on this field of knowledge will be sum- marised; underscoring one of the most recent techniques, which has a strong theoretical basis. Upon this, some hypotheses will be made. arXiv:2012.05285v1 [math.ST] 9 Dec 2020 1.1. Epistasis in complex disease The role of heredity in psychiatry has been studied for almost a century, with Pearson (1931) not having “the least hesitation” in asserting its relevance.