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

KNN-MDR: a learning approach for improving interactions mapping performances in genome wide association studies

Background Finding epistatic interactions in large association studies like genome-wide association studies (GWAS) with the nowadays-available large volume of genomic data is a challenging and largely unsolved issue. Few previous studies could handle genome-wide data due to the intractable difficulties met in searching a combinatorial explosive search space and statistically evaluating epistatic interactions given a limited number of samples. Our work is a contribution to this field. We propose a novel approach combining K-Nearest Neighbors (KNN) and Multi Dimensional Reduction (MDR) methods for detecting gene-gene interactions as a possible alternative to existing algorithms, e especially in situations where the number of involved determinants is high. After describing the approach, a comparison of our method (KNN-MDR) to a set of the other most performing methods (i.e., MDR, BOOST, BHIT, MegaSNPHunter and AntEpiSeeker) is carried on to detect interactions using simulated data as well as real genome-wide data. Results Experimental results on both simulated data and real genome-wide data show that KNN-MDR has interesting properties in terms of accuracy and power, and that, in many cases, it significantly outperforms its recent competitors. Conclusions The presented methodology (KNN-MDR) is valuable in the context of loci and interactions mapping and can be seen as an interesting addition to the arsenal used in complex traits analyses

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

MB-MDR: Model-Based Multifactor Dimensionality Reduction for detecting interactions in high-dimensional genomic data

L’anàlisi de l’efecte dels gens i els factors ambientals en el desenvolupament de malalties complexes és un gran repte estadístic i computacional. Entre les diverses metodologies de mineria de dades que s’han proposat per a l’anàlisi d’interaccions una de les més populars és el mètode Multifactor Dimensionality Reduction, MDR, (Ritchie i al. 2001). L’estratègia d’aquest mètode és reduir la dimensió multifactorial a u mitjançant l’agrupació dels diferents genotips en dos grups de risc: alt i baix. Tot i la seva utilitat demostrada, el mètode MDR té alguns inconvenients entre els quals l’agrupació excessiva de genotips pot fer que algunes interaccions importants no siguin detectades i que no permet ajustar per efectes principals ni per variables confusores. En aquest article il•lustrem les limitacions de l’estratègia MDR i d’altres aproximacions no paramètriques i demostrem la conveniència d’utilitzar metodologies parametriques per analitzar interaccions en estudis cas-control on es requereix l’ajust per variables confusores i per efectes principals. Proposem una nova metodologia, una versió paramètrica del mètode MDR, que anomenem Model-Based Multifactor Dimensionality Reduction (MB-MDR). La metodologia proposada té com a objectiu la identificació de genotips específics que estiguin associats a la malaltia i permet ajustar per efectes marginals i variables confusores. La nova metodologia s’il•lustra amb dades de l’Estudi Espanyol de Cancer de Bufeta

FAM-MDR: A Flexible Family-Based Multifactor Dimensionality Reduction Technique to Detect Epistasis Using Related Individuals

We propose a novel multifactor dimensionality reduction method for epistasis detection in small or extended pedigrees, FAM-MDR. It combines features of the Genome-wide Rapid Association using Mixed Model And Regression approach (GRAMMAR) with Model-Based MDR (MB-MDR). We focus on continuous traits, although the method is general and can be used for outcomes of any type, including binary and censored traits. When comparing FAM-MDR with Pedigree-based Generalized MDR (PGMDR), which is a generalization of Multifactor Dimensionality Reduction (MDR) to continuous traits and related individuals, FAM-MDR was found to outperform PGMDR in terms of power, in most of the considered simulated scenarios. Additional simulations revealed that PGMDR does not appropriately deal with multiple testing and consequently gives rise to overly optimistic results. FAM-MDR adequately deals with multiple testing in epistasis screens and is in contrast rather conservative, by construction. Furthermore, simulations show that correcting for lower order (main) effects is of utmost importance when claiming epistasis. As Type 2 Diabetes Mellitus (T2DM) is a complex phenotype likely influenced by gene-gene interactions, we applied FAM-MDR to examine data on glucose area-under-the-curve (GAUC), an endophenotype of T2DM for which multiple independent genetic associations have been observed, in the Amish Family Diabetes Study (AFDS). This application reveals that FAM-MDR makes more efficient use of the available data than PGMDR and can deal with multi-generational pedigrees more easily. In conclusion, we have validated FAM-MDR and compared it to PGMDR, the current state-of-the-art MDR method for family data, using both simulations and a practical dataset. FAM-MDR is found to outperform PGMDR in that it handles the multiple testing issue more correctly, has increased power, and efficiently uses all available information

Aggregated Quantitative Multifactor Dimensionality Reduction

We consider the problem of making predictions for quantitative phenotypes based on gene-to-gene interactions among selected Single Nucleotide Polymorphisms (SNPs). Previously, Quantitative Multifactor Dimensionality Reduction (QMDR) has been applied to detect gene-to-gene interactions associated with elevated quantitative phenotypes, by creating a dichotomous predictor from one interaction which has been deemed optimal. We propose an Aggregated Quantitative Multifactor Dimensionality Reduction (AQMDR), which exhaustively considers all k-way interactions among a set of SNPs and replaces the dichotomous predictor from QMDR with a continuous aggregated score. We evaluate this new AQMDR method in a series of simulations for two-way and three-way interactions, comparing the new method with the original QMDR. In simulation, AQMDR yields consistently smaller prediction error than QMDR when more than one significant interaction is present in the simulation model. Theoretical support is provided for the method, and the method is applied on Alzheimer\u27s Disease (AD) data to identify significant interactions between APOE4 and other AD associated SNPs

Genome-wide environmental interaction analysis using multidimensional data reduction principles to identify asthma pharmacogenetic loci in relation to corticosteroid therapy

Genome-wide gene-environment (GxE) and gene-gene (GxG) interaction studies share a lot of challenges via the common genetic component they involve. GWEI studies may therefore benefit from the abundance of methodologies that are available in the context of genome-wide epistasis detection methods. One of these is Model-Based Multifactor Dimensionality Reduction (MB-MDR), which does not make any assumption about the genetic inheritance model. MB-MDR involves reducing a high-dimensional GxE space to GxE factor levels that either exhibit high or low or no evidence for their association to disease outcome. In contrast to logistic regression and random forests, MB-MDR can be used to detect GxE interactions in the absence of any main effects or when sample sizes are too small to be able to model all main and GxE interaction effects. In this ongoing study, we demonstrate the opportunities and challenges of MB-MDR for genome-wide GxE interaction analysis and analyzed the difference in prebronchodilator FEV1 following 8 weeks of inhaled corticosteroid therapy, for 565 pediatric Caucasian CAMP (ages 5-12) from the SHARE project

An R package implementation of multifactor dimensionality reduction

<p>Abstract</p> <p>Background</p> <p>A breadth of high-dimensional data is now available with unprecedented numbers of genetic markers and data-mining approaches to variable selection are increasingly being utilized to uncover associations, including potential gene-gene and gene-environment interactions. One of the most commonly used data-mining methods for case-control data is Multifactor Dimensionality Reduction (MDR), which has displayed success in both simulations and real data applications. Additional software applications in alternative programming languages can improve the availability and usefulness of the method for a broader range of users.</p> <p>Results</p> <p>We introduce a package for the R statistical language to implement the Multifactor Dimensionality Reduction (MDR) method for nonparametric variable selection of interactions. This package is designed to provide an alternative implementation for R users, with great flexibility and utility for both data analysis and research. The 'MDR' package is freely available online at <url>http://www.r-project.org/</url>. We also provide data examples to illustrate the use and functionality of the package.</p> <p>Conclusions</p> <p>MDR is a frequently-used data-mining method to identify potential gene-gene interactions, and alternative implementations will further increase this usage. We introduce a flexible software package for R users.</p