Tests For Interaction Between Unlinked Loci

GWAS (Genome-wide association study) is a sudy to find all base-pair mutations associated with the complex diseases within the range of the human genome.This base pair variation is called a single nucleotide polymorphism (SNP). In 2005, the study of the correlation between macular degeneration and ages started the prelude of GWAS studies. Despite a large number of SNP associated with diseases have been found, the traditional genome-wide association analysis is still insufficient. The traditional genome-wide association analysis of disease associated with the SNP can only explain a small part of the genetic variation. The reasons are as follows.1. The traditional GWAS generally assume common diseases are caused by common mutations.But common diseases can also be caused by multiple rare mutations, each with a low marginal genetic effect.; 2.The traditional GWAS generally ignore the interaction between SNPs; 3, The efficiency of statistics to test gene-gene and gene-environment interaction is relatively low. Therefore there is a need for detecting gene-gene interactions associated with disease based on the traditional GWAS studies.Currently, a number of achievements have been made in detecting gene-gene interactions at home and abroad, a lot of methods have been found to test multi-locus gene-gene interactions. When the number of locus is relatively small, the statistical methods used in common to test the interaction can be divided into three categories:a method based on penetrance, Logistic regression model based method, a method based on linkage disequilibrium. When the number of locus is relatively large, nonparametric statistical methods are often used, such as MDR (the multi-factor dimensionality reduction method), the random forest method, the support vector machine method.This paper mainly studies gene-gene interactions between two unlinked loci associated with the diseases. Firstly, we give a introduction about parts of the existing statistics to test gene-gene interactions, secondly,we use δ method to formulate a new test based on the statistics proposed by Zhao et al.Meanwhile we add the test TWu based linkage disequilibrium to do simulation tests for comparison. Simulation results show that:When both genes had no effect on the disease or either of genes had an effect on disease or both genes had effect on the desease, the three test statistics in the case of three null hypothesis are approximate to the central chi-square distribution with a one degree of freedom.The Type I error can be perfectly controlled. When both risk genes had no effect on the disease with gene-gene interactions changed,the power of the new test statistics is higher than the other two statistics around 0.02 in three common genetic models:Epistasis model, Multiplicative model, Threshold model...