Statistical Methods For Detecting Gene-Based Gene-Gene Interaction On Multiple Quantitative Traits

Complex disease known as multi-factor disease is controlled by multiple genes, presenting familial assembling tendency but not coinciding with Mendel’s law. In terms of the genetic mechanisms, theoccurrence of complex disease is the result of complicated interaction network between genes and between gene and environment, while every single gene gives very little effect. Thus, detecting the effect of gene-gene interaction for disease (or traits) is one of the core content of genetic epidemiology. Recently, hundreds of genome-wide association studies (GWAS) for complex human traits were completed over the last decade, which have found over1400SNPs associated with complex disease. These results can not only help human understand the genetic mechanism of complex diseases, but provide new technical methods for the prevention and treatment of complex disease. However, the genetic variants discovered account for only a small proportion of the heritability of complex disease. One important reason is that most methods ignored the gene-gene interaction. Furthermore, most analysis methods only tested the association of the phenotype with each SNP individually, which is not well powerful for detecting multiple variants with small effects. The interaction between multiple minor genes and their interaction with the environment often enlarge the effect for diseases (or traits). Therefore, detecting gene-gene interaction has both important theoretical and realistic significance for complex disease in increasing genetic interpretation, building genetic risk assessment model, developing individualized drug targets, promoting the transformation medicine and public health, and reducing the burden of complex diseases eventually.Three statistical methods existed to detect gene-gene interaction,1) Detecting SNP-SNP interaction to represent gene-gene interaction.2) Based on haplotype study, detecting haplotype-haplotype interaction to represent gene-gene interaction.3) Detecting ’Whole gene’-based gene-gene interaction. However, these methods are only appropriate for case-control study or qualitative traits, not for quantitative traits. In fact, common phenotypes are quantitative instead of qualitative. Plomin et al. demonstrated the dialectical unity of quantitative genetics and moleculargenetics, and proposed that common disorders were quantitative in2009. In the framework of thinkingquantitatively to common disorders, a case-control design which is usually furnished by dividing particular continuous quantitative measurement into case and control groups with a cut off might not relateso well with genetic variation. Assigning a cut off to a continuous variablecan lead to loss of information, decrease the statistical power caused by selection bias, and weaken the application value of GWAS results in complex disease treatment and prevention. Thus, studying the gene-gene interaction effect for quantitative traits has become a hot issue in statistical genetics.Although numerous methods are proposed to detect the gene-based gene-gene interaction, they merely focus on single quantitative trait and fall short of consideration on multiple traits, especially when the traits are genetic related. While for some diseases, the relevant quantitative traits may not be entirely clear, and the diseases may be affected by multiple traits. In this paper, thinking multiple quantitatively to complex diseases, we proposed two effective U-statistics to detect gene-gene interaction, which were based on Partial Least Squares Model (PLSPM).Results Simulation study and real data analysisindicated that①The type Ⅰ errors of the Ustatistic is consistent withthe nominal levels,which indicate it is stable.②The statistical power of the U statistic monotonically increases with sample size and interaction effect.③The power for multiple traits are much higher than that for single trait.④Compared with PCA-based methods, power of U statistic was higher.⑤Real data results show the P-values based on PLSPM method are smaller than those based on PCA-based methods.Conclusions1. We have summarized statistical methods used for detecting gene-gene interaction, and pointed out that the necessity of analyzing the gene-based gene-gene interaction for multiple quantitative phenotypes,2. Based on PLSPM, two analytic strategies were proposed, and the Ustatistic was obtained based on the PLSPM algorithm. The advantages of U statistic are①Compared with traditional PLSPM-based statistic, U statisticis more powerful, and can somewhat reduce the heavy calculation burdens.②Compared with SNP-based methods, PLSPM-based U statistic would greatly reduce the number of possible two-locus interactions and aid in the interpretation of the results. The dimensions of the genotyped data are substantially reduced with the PLSPM-based method, which will somewhat relief the multiple correction problems.③Compared with PCA-based methods, PLSPM-based U statistic was designed to extract information from genetic data and quantitative phenotype data, and to improvepower.Reflective model in PLSPM is more adept to handling the high-dimensional aspect of genomic data, which the multicollinearity exist between manifest variables belonging to the same block.