### Introduction

*Helicobacter pylori*infection [3]. However, in addition to the cause, other genetic and genomic factors have been examined for gastritis. Human leukocyte antigen class II allele is an important risk factor for chronic atrophic gastritis and gastric carcinoma in Koreans [4]. Moreover, many studies have reported that single-nucleotide polymorphisms (SNPs), including rs1143627 in interleukin-1 beta (

*IL1B*), rs4073 in interleukin 8 (

*IL8*), rs4986790 in Toll-like receptor 4 (

*TLR4*), and rs16260 in cadherin-1 (

*CDH1*), are associated with susceptibility to gastric diseases, especially gastric cancer [5, 6, 7, 8].

^{2}value [14]. We further transformed this SNP network into a relevant gene-gene epistasis network to validate the biological significance of our findings. A functional analysis was performed on the gene-gene network, and the topological properties of the network were also investigated.

### Methods

### Pre-processing for KARE data

^{2}> 0.8 [16], and SNPs in the X chromosome. PLINK [17] was used for the calculation of these values. The resulting dataset consisted of 185,426 SNPs and 3,770 samples for the case-control study.

### Mutual information

_{x∈X}-

*p*(

*x*)log(

*p*(

*x*)), which shows the uncertainty of the random variable X. Mutual information I(X;Y) between random variables X and Y is defined by the composition of entropy as follows:

*H*(

*X*),

*H*(

*Y*) denote entropies for the random variables X, Y, and

*H*(

*X*,

*Y*) denotes the joint entropy of the two random variables as follows:

*X*

_{1}and

*X*

_{2}are random variables for two SNPs, and

*Y*denotes random variables for the disease. In our recent work [12], we have shown that this measure could identify high-order epistatic interactions both with and without marginal effects by using simulation models, such as in Culverhouse et al.'s [20] and Velez et al.'s studies [21].

*X*can be represented in terms of the partition as follows:

*X*= {

*A*

_{1},

*A*

_{2},…,

*A*

_{n}} is a partition on the set of samples

*S*= {

*A*

_{1}∪

*A*

_{2}∪…∪

*A*

_{n}}, and no intersections exist between elements in the partition. The joint entropy of two random variables for the partition of

*S*,

*X*= {

*A*

_{1},

*A*

_{2},…,

*A*

_{n}} and

*Y*= {B

_{1}, B

_{2},…, B

_{m}} is defined as follows:

### Extraction of statistically significant epistatic interactions

^{2}value and mutual information [14]: where N denotes the number of patients in the study.

### Relevance network construction and assessment of significance

### Results

### Statistically significant epistatic interactions in each chromosome

### Network topologies

*DCC*) locus in gastric cancer.

*PTPRT*), one of the hub genes was reported to be one of 15 genes in CpG islands showing significant differential methylation in gastric carcinoma [28].