Practical and theoretical considerations in study design for detecting gene-gene interactions using MDR and GMDR approaches

Detection of interacting risk factors for complex traits is challenging. The choice of an appropriate method, sample size, and allocation of cases and controls are serious concerns. To provide empirical guidelines for planning such studies and data analyses, we investigated the performance of the multifactor dimensionality reduction (MDR) and generalized MDR (GMDR) methods under various experimental scenarios. We developed the mathematical expectation of accuracy and used it as an indicator parameter to perform a gene-gene interaction study. We then examined the statistical power of GMDR and MDR within the plausible range of accuracy (0.50～0.65) reported in the literature. The GMDR with covariate adjustment had a power of >80% in a case-control design with a sample size of ≥2000, with theoretical accuracy ranging from 0.56 to 0.62. However, when the accuracy was <0.56, a sample size of ≥4000 was required to have sufficient power. In our simulations, the GMDR outperformed the MDR under all models with accuracy ranging from 0.56～0.62 for a sample size of 1000-2000. However, the two methods performed similarly when the accuracy was outside this range or the sample was significantly larger. We conclude that with adjustment of a covariate, GMDR performs better than MDR and a sample size of 1000～2000 is reasonably large for detecting gene-gene interactions in the range of effect size reported by the current literature; whereas larger sample size is required for more subtle interactions with accuracy <0.56.     

Log-linear model-based multifactor dimensionality reduction method to detect gene gene interactions

MOTIVATION: The identification and characterization of susceptibility genes that influence the risk of common and complex diseases remains a statistical and computational challenge in genetic association studies. This is partly because the effect of any single genetic variant for a common and complex disease may be dependent on other genetic variants (gene-gene interaction) and environmental factors (gene-environment interaction). To address this problem, the multifactor dimensionality reduction (MDR) method has been proposed by Ritchie et al. to detect gene-gene interactions or gene-environment interactions. The MDR method identifies polymorphism combinations associated with the common and complex multifactorial diseases by collapsing high-dimensional genetic factors into a single dimension. That is, the MDR method classifies the combination of multilocus genotypes into high-risk and low-risk groups based on a comparison of the ratios of the numbers of cases and controls. When a high-order interaction model is considered with multi-dimensional factors, however, there may be many sparse or empty cells in the contingency tables. The MDR method cannot classify an empty cell as high risk or low risk and leaves it as undetermined. RESULTS: In this article, we propose the log-linear model-based multifactor dimensionality reduction (LM MDR) method to improve the MDR in classifying sparse or empty cells. The LM MDR method estimates frequencies for empty cells from a parsimonious log-linear model so that they can be assigned to high-and low-risk groups. In addition, LM MDR includes MDR as a special case when the saturated log-linear model is fitted. Simulation studies show that the LM MDR method has greater power and smaller error rates than the MDR method. The LM MDR method is also compared with the MDR method using as an example sporadic Alzheimer's disease.     

A Modified Entropy-Based Approach for Identifying Gene-Gene Interactions in Case-Control Study

Gene-gene interactions may play an important role in the genetics of a complex disease. Detection and characterization of gene-gene interactions is a challenging issue that has stimulated the development of various statistical methods to address it. In this study, we introduce a method to measure gene interactions using entropy-based statistics from a contingency table of trait and genotype combinations. We also developed an exploration procedure by using graphs. We propose a standardized relative information gain (RIG) measure to evaluate the interactions between single nucleotide polymorphism (SNP) combinations. To identify the k ^th order interactions, contingency tables of trait and genotype combinations of k SNPs are constructed, with which RIGs are calculated. The RIGs are standardized using the mean and standard deviation from the permuted datasets. SNP combinations yielding high standardized RIG are chosen for gene-gene interactions. Detection of high-order interactions and comparison of interaction strengths between different orders are made possible by using standardized RIG. We have applied the proposed standardized entropy-based method to two types of data sets from a simulation study and a real genetic association study. We have compared our method and the multifactor dimensionality reduction (MDR) method through power analysis of eight different genetic models with varying penetrance rates, number of SNPs, and sample sizes. Our method shows successful identification of genetic associations and gene-gene interactions both in simulation and real genetic data. Simulation results suggest that the proposed entropy-based method is better able to detect high-order interactions and is superior to the MDR method in most cases. The proposed method is well suited for detecting interactions without main effects as well as for models including main effects.     

AMBIENCE: a novel approach and efficient algorithm for identifying informative genetic and environmental associations with complex phenotypes

We developed a computationally efficient algorithm AMBIENCE, for identifying the informative variables involved in gene-gene (GGI) and gene-environment interactions (GEI) that are associated with disease phenotypes. The AMBIENCE algorithm uses a novel information theoretic metric called phenotype-associated information (PAI) to search for combinations of genetic variants and environmental variables associated with the disease phenotype. The PAI-based AMBIENCE algorithm effectively and efficiently detected GEI in simulated data sets of varying size and complexity, including the 10K simulated rheumatoid arthritis data set from Genetic Analysis Workshop 15. The method was also successfully used to detect GGI in a Crohn's disease data set. The performance of the AMBIENCE algorithm was compared to the multifactor dimensionality reduction (MDR), generalized MDR (GMDR), and pedigree disequilibrium test (PDT) methods. Furthermore, we assessed the computational speed of AMBIENCE for detecting GGI and GEI for data sets varying in size from 100 to 10(5) variables. Our results demonstrate that the AMBIENCE information theoretic algorithm is useful for analyzing a diverse range of epidemiologic data sets containing evidence for GGI and GEI.     

Test for interaction between two unlinked loci

Despite the growing consensus on the importance of testing gene-gene interactions in genetic studies of complex diseases, the effect of gene-gene interactions has often been defined as a deviance from genetic additive effects, which is essentially treated as a residual term in genetic analysis and leads to low power in detecting the presence of interacting effects. To what extent the definition of gene-gene interaction at population level reflects the genes' biochemical or physiological interaction remains a mystery. In this article, we introduce a novel definition and a new measure of gene-gene interaction between two unlinked loci (or genes). We developed a general theory for studying linkage disequilibrium (LD) patterns in disease population under two-locus disease models. The properties of using the LD measure in a disease population as a function of the measure of gene-gene interaction between two unlinked loci were also investigated. We examined how interaction between two loci creates LD in a disease population and showed that the mathematical formulation of the new definition for gene-gene interaction between two loci was similar to that of the LD between two loci. This finding motived us to develop an LD-based statistic to detect gene-gene interaction between two unlinked loci. The null distribution and type I error rates of the LD-based statistic for testing gene-gene interaction were validated using extensive simulation studies. We found that the new test statistic was more powerful than the traditional logistic regression under three two-locus disease models and demonstrated that the power of the test statistic depends on the measure of gene-gene interaction. We also investigated the impact of using tagging SNPs for testing interaction on the power to detect interaction between two unlinked loci. Finally, to evaluate the performance of our new method, we applied the LD-based statistic to two published data sets. Our results showed that the P values of the LD-based statistic were smaller than those obtained by other approaches, including logistic regression models.     

A combinatorial approach to detecting gene-gene and gene-environment interactions in family studies

Widespread multifactor interactions present a significant challenge in determining risk factors of complex diseases. Several combinatorial approaches, such as the multifactor dimensionality reduction (MDR) method, have emerged as a promising tool for better detecting gene-gene (G x G) and gene-environment (G x E) interactions. We recently developed a general combinatorial approach, namely the generalized multifactor dimensionality reduction (GMDR) method, which can entertain both qualitative and quantitative phenotypes and allows for both discrete and continuous covariates to detect G x G and G x E interactions in a sample of unrelated individuals. In this article, we report the development of an algorithm that can be used to study G x G and G x E interactions for family-based designs, called pedigree-based GMDR (PGMDR). Compared to the available method, our proposed method has several major improvements, including allowing for covariate adjustments and being applicable to arbitrary phenotypes, arbitrary pedigree structures, and arbitrary patterns of missing marker genotypes. Our Monte Carlo simulations provide evidence that the PGMDR method is superior in performance to identify epistatic loci compared to the MDR-pedigree disequilibrium test (PDT). Finally, we applied our proposed approach to a genetic data set on tobacco dependence and found a significant interaction between two taste receptor genes (i.e., TAS2R16 and TAS2R38) in affecting nicotine dependence.     

机器学习方法在基因交互作用探测中的研究进展

复杂疾病是基因与基因、基因与环境交互作用的结果,高维基因交互作用的探测给计算带来了极大的挑战。在过去20年间,机器学习方法被用于探测基因-基因交互作用,并取得了一定的效果。本文综述了机器学习方法在基因交互作用探测中的研究进展,系统地介绍了神经网络(neural networks, NN)、随机森林(random forest, RF)、支持向量机(support vector machines, SVM)和多因子降维法(multifactor dimensionality reduction, MDR)等机器学习方法在全基因组关联研究(genome wide association study, GWAS)中探测基因交互作用的原理和局限性,并对未来的研究进行了展望。     

UGMDR: a unified conceptual framework for detection of multifactor interactions underlying complex traits

Biological outcomes are governed by multiple genetic and environmental factors that act in concert. Determining multifactor interactions is the primary topic of interest in recent genetics studies but presents enormous statistical and mathematical challenges. The computationally efficient multifactor dimensionality reduction (MDR) approach has emerged as a promising tool for meeting these challenges. On the other hand, complex traits are expressed in various forms and have different data generation mechanisms that cannot be appropriately modeled by a dichotomous model; the subjects in a study may be recruited according to its own analytical goals, research strategies and resources available, not only consisting of homogeneous unrelated individuals. Although several modifications and extensions of MDR have in part addressed the practical problems, they are still limited in statistical analyses of diverse phenotypes, multivariate phenotypes and correlated observations, correcting for potential population stratification and unifying both unrelated and family samples into a more powerful analysis. I propose a comprehensive statistical framework, referred as to unified generalized MDR (UGMDR), for systematic extension of MDR. The proposed approach is quite versatile, not only allowing for covariate adjustment, being suitable for analyzing almost any trait type, for example, binary, count, continuous, polytomous, ordinal, time-to-onset, multivariate and others, as well as combinations of those, but also being applicable to various study designs, including homogeneous and admixed unrelated-subject and family as well as mixtures of them. The proposed UGMDR offers an important addition to the arsenal of analytical tools for identifying nonlinear multifactor interactions and unraveling the genetic architecture of complex traits.     

A flexible computational framework for detecting, characterizing, and interpreting statistical patterns of epistasis in genetic studies of human disease susceptibility

Detecting, characterizing, and interpreting gene-gene interactions or epistasis in studies of human disease susceptibility is both a mathematical and a computational challenge. To address this problem, we have previously developed a multifactor dimensionality reduction (MDR) method for collapsing high-dimensional genetic data into a single dimension (i.e. constructive induction) thus permitting interactions to be detected in relatively small sample sizes. In this paper, we describe a comprehensive and flexible framework for detecting and interpreting gene-gene interactions that utilizes advances in information theory for selecting interesting single-nucleotide polymorphisms (SNPs), MDR for constructive induction, machine learning methods for classification, and finally graphical models for interpretation. We illustrate the usefulness of this strategy using artificial datasets simulated from several different two-locus and three-locus epistasis models. We show that the accuracy, sensitivity, specificity, and precision of a na?ve Bayes classifier are significantly improved when SNPs are selected based on their information gain (i.e. class entropy removed) and reduced to a single attribute using MDR. We then apply this strategy to detecting, characterizing, and interpreting epistatic models in a genetic study (n = 500) of atrial fibrillation and show that both classification and model interpretation are significantly improved.     

From Interaction to Co-Association —A Fisher r-To-z Transformation-Based Simple Statistic for Real World Genome-Wide Association Study

Currently, the genetic variants identified by genome wide association study (GWAS) generally only account for a small proportion of the total heritability for complex disease. One crucial reason is the underutilization of gene-gene joint effects commonly encountered in GWAS, which includes their main effects and co-association. However, gene-gene co-association is often customarily put into the framework of gene-gene interaction vaguely. From the causal graph perspective, we elucidate in detail the concept and rationality of gene-gene co-association as well as its relationship with traditional gene-gene interaction, and propose two Fisher r-to-z transformation-based simple statistics to detect it. Three series of simulations further highlight that gene-gene co-association refers to the extent to which the joint effects of two genes differs from the main effects, not only due to the traditional interaction under the nearly independent condition but the correlation between two genes. The proposed statistics are more powerful than logistic regression under various situations, cannot be affected by linkage disequilibrium and can have acceptable false positive rate as long as strictly following the reasonable GWAS data analysis roadmap. Furthermore, an application to gene pathway analysis associated with leprosy confirms in practice that our proposed gene-gene co-association concepts as well as the correspondingly proposed statistics are strongly in line with reality.     

Using Information Interaction to Discover Epistatic Effects in Complex Diseases

It is widely agreed that complex diseases are typically caused by the joint effects of multiple instead of a single genetic variation. These genetic variations may show stronger effects when considered together than when considered individually, a phenomenon known as epistasis or multilocus interaction. In this work, we explore the applicability of information interaction to discover pairwise epistatic effects related with complex diseases. We start by showing that traditional approaches such as classification methods or greedy feature selection methods (such as the Fleuret method) do not perform well on this problem. We then compare our information interaction method with BEAM and SNPHarvester in artificial datasets simulating epistatic interactions and show that our method is more powerful to detect pairwise epistatic interactions than its competitors. We show results of the application of information interaction method to the WTCCC breast cancer dataset. Our results are validated using permutation tests. We were able to find 89 statistically significant pairwise interactions with a p-value lower than . Even though many recent algorithms have been designed to find epistasis with low marginals, we observed that all (except one) of the SNPs involved in statistically significant interactions have moderate or high marginals. We also report that the interactions found in this work were not present in gene-gene interaction network STRING.     

Alternative contingency table measures improve the power and detection of multifactor dimensionality reduction

Background  

Multifactor Dimensionality Reduction (MDR) has been introduced previously as a non-parametric statistical method for detecting gene-gene interactions. MDR performs a dimensional reduction by assigning multi-locus genotypes to either high- or low-risk groups and measuring the percentage of cases and controls incorrectly labelled by this classification – the classification error. The combination of variables that produces the lowest classification error is selected as the best or most fit model. The correctly and incorrectly labelled cases and controls can be expressed as a two-way contingency table. We sought to improve the ability of MDR to detect gene-gene interactions by replacing classification error with a different measure to score model quality.     

Multifactor-dimensionality reduction versus family-based association tests in detecting susceptibility loci in discordant sib-pair studies

Complex diseases are generally thought to be under the influence of multiple, and possibly interacting, genes. Many association methods have been developed to identify susceptibility genes assuming a single-gene disease model, referred to as single-locus methods. Multilocus methods consider joint effects of multiple genes and environmental factors. One commonly used method for family-based association analysis is implemented in FBAT. The multifactor-dimensionality reduction method (MDR) is a multilocus method, which identifies multiple genetic loci associated with the occurrence of complex disease. Many studies of late onset complex diseases employ a discordant sib pairs design. We compared the FBAT and MDR in their ability to detect susceptibility loci using a discordant sib-pair dataset generated from the simulated data made available to participants in the Genetic Analysis Workshop 14. Using FBAT, we were able to identify the effect of one susceptibility locus. However, the finding was not statistically significant. We were not able to detect any of the interactions using this method. This is probably because the FBAT test is designed to find loci with major effects, not interactions. Using MDR, the best result we obtained identified two interactions. However, neither of these reached a level of statistical significance. This is mainly due to the heterogeneity of the disease trait and noise in the data.     

Explainable deep transfer learning model for disease risk prediction using high-dimensional genomic data

Building an accurate disease risk prediction model is an essential step in the modern quest for precision medicine. While high-dimensional genomic data provides valuable data resources for the investigations of disease risk, their huge amount of noise and complex relationships between predictors and outcomes have brought tremendous analytical challenges. Deep learning model is the state-of-the-art methods for many prediction tasks, and it is a promising framework for the analysis of genomic data. However, deep learning models generally suffer from the curse of dimensionality and the lack of biological interpretability, both of which have greatly limited their applications. In this work, we have developed a deep neural network (DNN) based prediction modeling framework. We first proposed a group-wise feature importance score for feature selection, where genes harboring genetic variants with both linear and non-linear effects are efficiently detected. We then designed an explainable transfer-learning based DNN method, which can directly incorporate information from feature selection and accurately capture complex predictive effects. The proposed DNN-framework is biologically interpretable, as it is built based on the selected predictive genes. It is also computationally efficient and can be applied to genome-wide data. Through extensive simulations and real data analyses, we have demonstrated that our proposed method can not only efficiently detect predictive features, but also accurately predict disease risk, as compared to many existing methods.     

Ideal discrimination of discrete clinical endpoints using multilocus genotypes

Multifactor Dimensionality Reduction (MDR) is a method for the classification and prediction of discrete clinical endpoints using attributes constructed from multilocus genotype data. Empirical studies with both real and simulated data suggest that MDR has good power for detecting gene-gene interactions in the absence of independent main effects. The purpose of this study is to develop an objective, theory-driven approach to evaluate the strengths and limitations of MDR. To accomplish this goal, we borrow concepts from ideal observer analysis used in visual perception to evaluate the theoretical limits of classifying and predicting discrete clinical endpoints using multilocus genotype data. We conclude that MDR ideally discriminates between low risk and high risk subjects using attributes constructed from multilocus genotype data. We also how that the classification approach used once a multilocus attribute is constructed is similar to that of a naive Bayes classifier. This study provides a theoretical foundation for the continued development, evaluation, and application of the MDR as a data mining tool in the domain of statistical genetics and genetic epidemiology.     

Powerful multilocus tests of genetic association in the presence of gene-gene and gene-environment interactions

In modern genetic epidemiology studies, the association between the disease and a genomic region, such as a candidate gene, is often investigated using multiple SNPs. We propose a multilocus test of genetic association that can account for genetic effects that might be modified by variants in other genes or by environmental factors. We consider use of the venerable and parsimonious Tukey's 1-degree-of-freedom model of interaction, which is natural when individual SNPs within a gene are associated with disease through a common biological mechanism; in contrast, many standard regression models are designed as if each SNP has unique functional significance. On the basis of Tukey's model, we propose a novel but computationally simple generalized test of association that can simultaneously capture both the main effects of the variants within a genomic region and their interactions with the variants in another region or with an environmental exposure. We compared performance of our method with that of two standard tests of association, one ignoring gene-gene/gene-environment interactions and the other based on a saturated model of interactions. We demonstrate major power advantages of our method both in analysis of data from a case-control study of the association between colorectal adenoma and DNA variants in the NAT2 genomic region, which are well known to be related to a common biological phenotype, and under different models of gene-gene interactions with use of simulated data.     

A comparison of internal validation techniques for multifactor dimensionality reduction

Background  

It is hypothesized that common, complex diseases may be due to complex interactions between genetic and environmental factors, which are difficult to detect in high-dimensional data using traditional statistical approaches. Multifactor Dimensionality Reduction (MDR) is the most commonly used data-mining method to detect epistatic interactions. In all data-mining methods, it is important to consider internal validation procedures to obtain prediction estimates to prevent model over-fitting and reduce potential false positive findings. Currently, MDR utilizes cross-validation for internal validation. In this study, we incorporate the use of a three-way split (3WS) of the data in combination with a post-hoc pruning procedure as an alternative to cross-validation for internal model validation to reduce computation time without impairing performance. We compare the power to detect true disease causing loci using MDR with both 5- and 10-fold cross-validation to MDR with 3WS for a range of single-locus and epistatic disease models. Additionally, we analyze a dataset in HIV immunogenetics to demonstrate the results of the two strategies on real data.     

Testing gene-gene interactions in the case-parents design

The case-parents design has been widely used to detect genetic associations as it can prevent spurious association that could occur in population-based designs. When examining the effect of an individual genetic locus on a disease, logistic regressions developed by conditioning on parental genotypes provide complete protection from spurious association caused by population stratification. However, when testing gene-gene interactions, it is unknown whether conditional logistic regressions are still robust. Here we evaluate the robustness and efficiency of several gene-gene interaction tests that are derived from conditional logistic regressions. We found that in the presence of SNP genotype correlation due to population stratification or linkage disequilibrium, tests with incorrectly specified main-genetic-effect models can lead to inflated type I error rates. We also found that a test with fully flexible main genetic effects always maintains correct test size and its robustness can be achieved with negligible sacrifice of its power. When testing gene-gene interactions is the focus, the test allowing fully flexible main effects is recommended to be used.     

GxGrare: gene-gene interaction analysis method for rare variants from high-throughput sequencing data

Background

With the rapid advancement of array-based genotyping techniques, genome-wide association studies (GWAS) have successfully identified common genetic variants associated with common complex diseases. However, it has been shown that only a small proportion of the genetic etiology of complex diseases could be explained by the genetic factors identified from GWAS. This missing heritability could possibly be explained by gene-gene interaction (epistasis) and rare variants. There has been an exponential growth of gene-gene interaction analysis for common variants in terms of methodological developments and practical applications. Also, the recent advancement of high-throughput sequencing technologies makes it possible to conduct rare variant analysis. However, little progress has been made in gene-gene interaction analysis for rare variants.

Results

Here, we propose GxGrare which is a new gene-gene interaction method for the rare variants in the framework of the multifactor dimensionality reduction (MDR) analysis. The proposed method consists of three steps; 1) collapsing the rare variants, 2) MDR analysis for the collapsed rare variants, and 3) detect top candidate interaction pairs. GxGrare can be used for the detection of not only gene-gene interactions, but also interactions within a single gene. The proposed method is illustrated with 1080 whole exome sequencing data of the Korean population in order to identify causal gene-gene interaction for rare variants for type 2 diabetes.

Conclusion

The proposed GxGrare performs well for gene-gene interaction detection with collapsing of rare variants. GxGrare is available at http://bibs.snu.ac.kr/software/gxgrare which contains simulation data and documentation. Supported operating systems include Linux and OS X.

     

Multifactor dimensionality reduction software for detecting gene-gene and gene-environment interactions

MOTIVATION: Polymorphisms in human genes are being described in remarkable numbers. Determining which polymorphisms and which environmental factors are associated with common, complex diseases has become a daunting task. This is partly because the effect of any single genetic variation will likely be dependent on other genetic variations (gene-gene interaction or epistasis) and environmental factors (gene-environment interaction). Detecting and characterizing interactions among multiple factors is both a statistical and a computational challenge. To address this problem, we have developed a multifactor dimensionality reduction (MDR) method for collapsing high-dimensional genetic data into a single dimension thus permitting interactions to be detected in relatively small sample sizes. In this paper, we describe the MDR approach and an MDR software package. RESULTS: We developed a program that integrates MDR with a cross-validation strategy for estimating the classification and prediction error of multifactor models. The software can be used to analyze interactions among 2-15 genetic and/or environmental factors. The dataset may contain up to 500 total variables and a maximum of 4000 study subjects. AVAILABILITY: Information on obtaining the executable code, example data, example analysis, and documentation is available upon request. SUPPLEMENTARY INFORMATION: All supplementary information can be found at http://phg.mc.vanderbilt.edu/Software/MDR.