A General Framework for Formal Tests of Interaction after Exhaustive Search Methods with Applications to MDR and MDR-PDT

The initial presentation of multifactor dimensionality reduction (MDR) featured cross-validation to mitigate over-fitting, computationally efficient searches of the epistatic model space, and variable construction with constructive induction to alleviate the curse of dimensionality. However, the method was unable to differentiate association signals arising from true interactions from those due to independent main effects at individual loci. This issue leads to problems in inference and interpretability for the results from MDR and the family-based compliment the MDR-pedigree disequilibrium test (PDT). A suggestion from previous work was to fit regression models post hoc to specifically evaluate the null hypothesis of no interaction for MDR or MDR-PDT models. We demonstrate with simulation that fitting a regression model on the same data as that analyzed by MDR or MDR-PDT is not a valid test of interaction. This is likely to be true for any other procedure that searches for models, and then performs an uncorrected test for interaction. We also show with simulation that when strong main effects are present and the null hypothesis of no interaction is true, that MDR and MDR-PDT reject at far greater than the nominal rate. We also provide a valid regression-based permutation test procedure that specifically tests the null hypothesis of no interaction, and does not reject the null when only main effects are present. The regression-based permutation test implemented here conducts a valid test of interaction after a search for multilocus models, and can be applied to any method that conducts a search to find a multilocus model representing an interaction

Risk score modeling of multiple gene to gene interactions using aggregated-multifactor dimensionality reduction

BACKGROUND: Multifactor Dimensionality Reduction (MDR) has been widely applied to detect gene-gene (GxG) interactions associated with complex diseases. Existing MDR methods summarize disease risk by a dichotomous predisposing model (high-risk/low-risk) from one optimal GxG interaction, which does not take the accumulated effects from multiple GxG interactions into account. RESULTS: We propose an Aggregated-Multifactor Dimensionality Reduction (A-MDR) method that exhaustively searches for and detects significant GxG interactions to generate an epistasis enriched gene network. An aggregated epistasis enriched risk score, which takes into account multiple GxG interactions simultaneously, replaces the dichotomous predisposing risk variable and provides higher resolution in the quantification of disease susceptibility. We evaluate this new A-MDR approach in a broad range of simulations. Also, we present the results of an application of the A-MDR method to a data set derived from Juvenile Idiopathic Arthritis patients treated with methotrexate (MTX) that revealed several GxG interactions in the folate pathway that were associated with treatment response. The epistasis enriched risk score that pooled information from 82 significant GxG interactions distinguished MTX responders from non-responders with 82% accuracy. CONCLUSIONS: The proposed A-MDR is innovative in the MDR framework to investigate aggregated effects among GxG interactions. New measures (pOR, pRR and pChi) are proposed to detect multiple GxG interactions

Multifactor Dimensionality Reduction as a Filter-Based Approach for Genome Wide Association Studies

Advances in genotyping technology and the multitude of genetic data available now provide a vast amount of data that is proving to be useful in the quest for a better understanding of human genetic diseases through the study of genetic variation. This has led to the development of approaches such as genome wide association studies (GWAS) designed specifically for interrogating variants across the genome for association with disease, typically by testing single locus, univariate associations. More recently it has been accepted that epistatic (interaction) effects may also be great contributors to these genetic effects, and GWAS methods are now being applied to find epistatic effects. The challenge for these methods still remain in prioritization and interpretation of results, as it has also become standard for initial findings to be independently investigated in replication cohorts or functional studies. This is motivating the development and implementation of filter-based approaches to prioritize variants found to be significant in a discovery stage for follow-up for replication. Such filters must be able to detect both univariate and interactive effects. In the current study we present and evaluate the use of multifactor dimensionality reduction (MDR) as such a filter, with simulated data and a wide range of effect sizes. Additionally, we compare the performance of the MDR filter to a similar filter approach using logistic regression (LR), the more traditional approach used in GWAS analysis, as well as evaporative cooling (EC)-another prominent machine learning filtering method. The results of our simulation study show that MDR is an effective method for such prioritization, and that it can detect main effects, and interactions with or without marginal effects. Importantly, it performed as well as EC and LR for main effect models. It also significantly outperforms LR for various two-locus epistatic models, while it has equivalent results as EC for the epistatic models. The results of this study demonstrate the potential of MDR as a filter to detect gene–gene interactions in GWAS studies

Bioinformatics challenges for genome-wide association studies

Motivation: The sequencing of the human genome has made it possible to identify an informative set of >1 million single nucleotide polymorphisms (SNPs) across the genome that can be used to carry out genome-wide association studies (GWASs). The availability of massive amounts of GWAS data has necessitated the development of new biostatistical methods for quality control, imputation and analysis issues including multiple testing. This work has been successful and has enabled the discovery of new associations that have been replicated in multiple studies. However, it is now recognized that most SNPs discovered via GWAS have small effects on disease susceptibility and thus may not be suitable for improving health care through genetic testing. One likely explanation for the mixed results of GWAS is that the current biostatistical analysis paradigm is by design agnostic or unbiased in that it ignores all prior knowledge about disease pathobiology. Further, the linear modeling framework that is employed in GWAS often considers only one SNP at a time thus ignoring their genomic and environmental context. There is now a shift away from the biostatistical approach toward a more holistic approach that recognizes the complexity of the genotype–phenotype relationship that is characterized by significant heterogeneity and gene–gene and gene–environment interaction. We argue here that bioinformatics has an important role to play in addressing the complexity of the underlying genetic basis of common human diseases. The goal of this review is to identify and discuss those GWAS challenges that will require computational methods

An associative classification based approach for detecting SNP-SNP interactions in high dimensional genome

There have been many studies that depict genotype phenotype relationships by identifying genetic variants associated with a specific disease. Researchers focus more attention on interactions between SNPs that are strongly associated with disease in the absence of main effect. In this context, a number of machine learning and data mining tools are applied to identify the combinations of multi-locus SNPs in higher order data.However, none of the current models can identify useful SNPSNP interactions for high dimensional genome data. Detecting these interactions is challenging due to bio-molecular complexities and computational limitations. The goal of this research was to implement associative classification and study its effectiveness for detecting the epistasis in balanced and imbalanced datasets. The proposed approach was evaluated for two locus epistasis interactions using simulated data. The datasets were generated for 5 different penetrance functions by varying heritability, minor allele frequency and sample size. In total, 23,400 datasets were generated and several experiments are conducted to identify the disease causal SNP interactions. The accuracy of classification by the proposed approach wascompared with the previous approaches. Though associative classification showed only relatively small improvement in accuracy for balanced datasets, it outperformed existing approaches in higher order multi-locus interactions in imbalanced datasets

A novel approach to simulate gene-environment interactions in complex diseases

Background: Complex diseases are multifactorial traits caused by both genetic and environmental factors. They represent the major part of human diseases and include those with largest prevalence and mortality (cancer, heart disease, obesity, etc.). Despite a large amount of information that has been collected about both genetic and environmental risk factors, there are few examples of studies on their interactions in epidemiological literature. One reason can be the incomplete knowledge of the power of statistical methods designed to search for risk factors and their interactions in these data sets. An improvement in this direction would lead to a better understanding and description of gene-environment interactions. To this aim, a possible strategy is to challenge the different statistical methods against data sets where the underlying phenomenon is completely known and fully controllable, for example simulated ones. Results: We present a mathematical approach that models gene-environment interactions. By this method it is possible to generate simulated populations having gene-environment interactions of any form, involving any number of genetic and environmental factors and also allowing non-linear interactions as epistasis. In particular, we implemented a simple version of this model in a Gene-Environment iNteraction Simulator (GENS), a tool designed to simulate case-control data sets where a one gene-one environment interaction influences the disease risk. The main aim has been to allow the input of population characteristics by using standard epidemiological measures and to implement constraints to make the simulator behaviour biologically meaningful. Conclusions: By the multi-logistic model implemented in GENS it is possible to simulate case-control samples of complex disease where gene-environment interactions influence the disease risk. The user has full control of the main characteristics of the simulated population and a Monte Carlo process allows random variability. A knowledge-based approach reduces the complexity of the mathematical model by using reasonable biological constraints and makes the simulation more understandable in biological terms. Simulated data sets can be used for the assessment of novel statistical methods or for the evaluation of the statistical power when designing a study

A role for CETP TaqIB polymorphism in determining susceptibility to atrial fibrillation: a nested case control study

BACKGROUND: Studies investigating the genetic and environmental characteristics of atrial fibrillation (AF) may provide new insights in the complex development of AF. We aimed to investigate the association between several environmental factors and loci of candidate genes, which might be related to the presence of AF. METHODS: A nested case-control study within the PREVEND cohort was conducted. Standard 12 lead electrocardiograms were recorded and AF was defined according to Minnesota codes. For every case, an age and gender matched control was selected from the same population (n = 194). In addition to logistic regression analyses, the multifactor-dimensionality reduction (MDR) method and interaction entropy graphs were used for the evaluation of gene-gene and gene-environment interactions. Polymorphisms in genes from the Renin-angiotensin, Bradykinin and CETP systems were included. RESULTS: Subjects with AF had a higher prevalence of electrocardiographic left ventricular hypertrophy, ischemic heart disease, hypertension, renal dysfunction, elevated levels of C-reactive protein (CRP) and increased urinary albumin excretion as compared to controls. The polymorphisms of the Renin-angiotensin system and Bradykinin gene did not show a significant association with AF (p > 0.05). The TaqIB polymorphism of the CETP gene was significantly associated with the presence of AF (p < 0.05). Using the MDR method, the best genotype-phenotype models included the combination of micro- or macroalbuminuria and CETP TaqIB polymorphism, CRP >3 mg/L and CETP TaqIB polymorphism, renal dysfunction and the CETP TaqIB polymorphism, and ischemic heart disease and CETP TaqIB polymorphism (1000 fold permutation testing, P < 0.05). Interaction entropy graph showed that the combination of albuminuria and CETP TaqIB polymorphism removed the most entropy. CONCLUSION: CETP TaqIB polymorphism is significantly associated with the presence of AF in the context of micro- or macroalbuminuria, elevated C-reactive protein, renal dysfunction, and ischemic heart disease