Robust Gene-Gene Interaction Analysis in Genome Wide Association Studies

Haplotype analysis on association between C-reactive protein gene and susceptibility to type 2 diabetes mellitus in Chinese Han population : CRP gene and type 2 diabetes mellitus

AIMS

We aimed to evaluate the impact of C-reactive protein (CRP) gene polymorphism, additional gene-gene interaction, and haplotypes on susceptibility to type 2 diabetes mellitus (T2DM).

METHODS

SNPstats online software ( https://www.snpstats.net/start.htm ) was employed to evaluate the association between CRP gene and T2DM risk. High-order interactions among SNPs was tested using generalized multifactor dimensionality reduction, and the testing balanced accuracy, training balanced accuracy and cross-validation consistency were calculated. The SHEsisPlus ( http://shesisplus.bio-x.cn/SHEsis.html ) online software was used for haplotype analysis.

RESULTS

A total of 730 T2DM patients and 765 controls were enrolled. The T allele of rs1205 is associated with increased susceptibility to T2DM, OR (95% CI) were 1.51 (1.13-2.01), 1.44 (1.10-1.89) and 1.25 (1.01-1.54) for codominant, dominant and over-dominant models, respectively. We also found that minor allele of rs2794521 is associated with decreased susceptibility to T2DM under codominant and recessive models, OR (95%CI) were 0.38 (0.18-0.79) and 0.37 (0.16-0.80) for codominant and recessive models, respectively. No significant gene-gene interaction existed among CRP gene SNPs, all interaction p- values were more than 0.05. Haplotype analyses suggested the CGCA haplotype containing rs1205-C, rs1130864-G, rs2794521- C and rs3093059- A allele was associated with decreased risk of T2DM, OR (95% CI) = 0.83 (0.68-0.98), P = 0.047.

CONCLUSIONS

Minor allele of rs1205 was associated with increased T2DM risk. Minor allele of rs2794521 and the CGCA haplotype were associated with decreased T2DM risk.

Measuring gene-gene interaction using Kullback-Leibler divergence

Genome-wide association studies (GWAS) are used to investigate genetic variants contributing to complex traits. Despite discovering many loci, a large proportion of "missing" heritability remains unexplained. Gene-gene interactions may help explain some of this gap. Traditionally, gene-gene interactions have been evaluated using parametric statistical methods such as linear and logistic regression, with multifactor dimensionality reduction (MDR) used to address sparseness of data in high dimensions. We propose a method for the analysis of gene-gene interactions across independent single-nucleotide polymorphisms (SNPs) in two genes. Typical methods for this problem use statistics based on an asymptotic chi-squared mixture distribution, which is not easy to use. Here, we propose a Kullback-Leibler-type statistic, which follows an asymptotic, positive, normal distribution under the null hypothesis of no relationship between SNPs in the two genes, and normally distributed under the alternative hypothesis. The performance of the proposed method is evaluated by simulation studies, which show promising results. The method is also used to analyze real data and identifies gene-gene interactions among RAB3A, MADD, and PTPRN on type 2 diabetes (T2D) status.

Robust genetic interaction analysis

For the risk, progression, and response to treatment of many complex diseases, it has been increasingly recognized that genetic interactions (including gene-gene and gene-environment interactions) play important roles beyond the main genetic and environmental effects. In practical genetic interaction analyses, model mis-specification and outliers/contaminations in response variables and covariates are not uncommon, and demand robust analysis methods. Compared with their nonrobust counterparts, robust genetic interaction analysis methods are significantly less popular but are gaining attention fast. In this article, we provide a comprehensive review of robust genetic interaction analysis methods, on their methodologies and applications, for both marginal and joint analysis, and for addressing model mis-specification as well as outliers/contaminations in response variables and covariates.

EFMDR-Fast: An Application of Empirical Fuzzy Multifactor Dimensionality Reduction for Fast Execution

Gene-gene interaction is a key factor for explaining missing heritability. Many methods have been proposed to identify gene-gene interactions. Multifactor dimensionality reduction (MDR) is a well-known method for the detection of gene-gene interactions by reduction from genotypes of single-nucleotide polymorphism combinations to a binary variable with a value of high risk or low risk. This method has been widely expanded to own a specific objective. Among those expansions, fuzzy-MDR uses the fuzzy set theory for the membership of high risk or low risk and increases the detection rates of gene-gene interactions. Fuzzy-MDR is expanded by a maximum likelihood estimator as a new membership function in empirical fuzzy MDR (EFMDR). However, EFMDR is relatively slow, because it is implemented by R script language. Therefore, in this study, we implemented EFMDR using RCPP (c++ package) for faster executions. Our implementation for faster EFMDR, called EMMDR-Fast, is about 800 times faster than EFMDR written by R script only.

Fuzzy set-based generalized multifactor dimensionality reduction analysis of gene-gene interactions

BACKGROUND

Gene-gene interactions (GGIs) are a known cause of missing heritability. Multifactor dimensionality reduction (MDR) is one of most commonly used methods for GGI detection. The generalized multifactor dimensionality reduction (GMDR) method is an extension of MDR method that is applicable to various types of traits, and allows covariate adjustments. Our previous Fuzzy MDR (FMDR) is another extension for overcoming simple binary classification. FMDR uses continuous member-ship values instead of binary membership values 0 and 1, improving power for detecting causal SNPs and more intuitive interpretations in real data analysis. Here, we propose the fuzzy generalized multifactor dimensionality reduction (FGMDR) method, as a combined analysis of fuzzy set-based analysis and GMDR method, to detect GGIs associated with diseases using fuzzy set theory.

RESULTS

Through simulation studies for different types of traits, the proposed FGMDR showed a higher detection ratio of causal SNPs, compared to GMDR. We then applied FGMDR to two real data: Crohn's disease (CD) data from the Wellcome Trust Case Control Consortium (WTCCC) with a binary phenotype and the Homeostasis Model Assessment of Insulin Resistance (HOMA-IR) data from Korean population with a continuous phenotype. The interactions derived by our method include the pre-reported interactions associated with phenotypes.

CONCLUSIONS

The proposed FGMDR performs well for GGI detection with covariate adjustments. The program written in R for FGMDR is available at http://statgen.snu.ac.kr/software/FGMDR .

An empirical fuzzy multifactor dimensionality reduction method for detecting gene-gene interactions

BACKGROUND

Detection of gene-gene interaction (GGI) is a key challenge towards solving the problem of missing heritability in genetics. The multifactor dimensionality reduction (MDR) method has been widely studied for detecting GGIs. MDR reduces the dimensionality of multi-factor by means of binary classification into high-risk (H) or low-risk (L) groups. Unfortunately, this simple binary classification does not reflect the uncertainty of H/L classification. Thus, we proposed Fuzzy MDR to overcome limitations of binary classification by introducing the degree of membership of two fuzzy sets H/L. While Fuzzy MDR demonstrated higher power than that of MDR, its performance is highly dependent on the several tuning parameters. In real applications, it is not easy to choose appropriate tuning parameter values.

RESULT

In this work, we propose an empirical fuzzy MDR (EF-MDR) which does not require specifying tuning parameters values. Here, we propose an empirical approach to estimating the membership degree that can be directly estimated from the data. In EF-MDR, the membership degree is estimated by the maximum likelihood estimator of the proportion of cases(controls) in each genotype combination. We also show that the balanced accuracy measure derived from this new membership function is a linear function of the standard chi-square statistics. This relationship allows us to perform the standard significance test using p-values in the MDR framework without permutation. Through two simulation studies, the power of the proposed EF-MDR is shown to be higher than those of MDR and Fuzzy MDR. We illustrate the proposed EF-MDR by analyzing Crohn's disease (CD) and bipolar disorder (BD) in the Wellcome Trust Case Control Consortium (WTCCC) dataset.

CONCLUSION

We propose an empirical Fuzzy MDR for detecting GGI using the maximum likelihood of the proportion of cases(controls) as the membership degree of the genotype combination. The program written in R for EF-MDR is available at http://statgen.snu.ac.kr/software/EF-MDR .