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Global tests of P-values for multifactor dimensionality reduction models in selection of optimal number of target genes.

ABSTRACT: BACKGROUND:Multifactor Dimensionality Reduction (MDR) is a popular and successful data mining method developed to characterize and detect nonlinear complex gene-gene interactions (epistasis) that are associated with disease susceptibility. Because MDR uses a combinatorial search strategy to detect interaction, several filtration techniques have been developed to remove genes (SNPs) that have no interactive effects prior to analysis. However, the cutoff values implemented for these filtration methods are arbitrary, therefore different choices of cutoff values will lead to different selections of genes (SNPs). METHODS:We suggest incorporating a global test of p-values to filtration procedures to identify the optimal number of genes/SNPs for further MDR analysis and demonstrate this approach using a ReliefF filter technique. We compare the performance of different global testing procedures in this context, including the Kolmogorov-Smirnov test, the inverse chi-square test, the inverse normal test, the logit test, the Wilcoxon test and Tippett's test. Additionally we demonstrate the approach on a real data application with a candidate gene study of drug response in Juvenile Idiopathic Arthritis. RESULTS:Extensive simulation of correlated p-values show that the inverse chi-square test is the most appropriate approach to be incorporated with the screening approach to determine the optimal number of SNPs for the final MDR analysis. The Kolmogorov-Smirnov test has high inflation of Type I errors when p-values are highly correlated or when p-values peak near the center of histogram. Tippett's test has very low power when the effect size of GxG interactions is small. CONCLUSIONS:The proposed global tests can serve as a screening approach prior to individual tests to prevent false discovery. Strong power in small sample sizes and well controlled Type I error in absence of GxG interactions make global tests highly recommended in epistasis studies.

SUBMITTER: Dai H

PROVIDER: S-EPMC3508622 | biostudies-literature | 2012 May

REPOSITORIES: biostudies-literature

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Global tests of P-values for multifactor dimensionality reduction models in selection of optimal number of target genes.

Dai Hongying H Bhandary Madhusudan M Becker Mara M Leeder J Steven JS Gaedigk Roger R Motsinger-Reif Alison A AA

BioData mining 20120522 1

<h4>Background</h4>Multifactor Dimensionality Reduction (MDR) is a popular and successful data mining method developed to characterize and detect nonlinear complex gene-gene interactions (epistasis) that are associated with disease susceptibility. Because MDR uses a combinatorial search strategy to detect interaction, several filtration techniques have been developed to remove genes (SNPs) that have no interactive effects prior to analysis. However, the cutoff values implemented for these filtra ...[more]

PMID: 22616673

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Project description:BackgroundApplying a statistical method implies identifying underlying (model) assumptions and checking their validity in the particular context. One of these contexts is association modeling for epistasis detection. Here, depending on the technique used, violation of model assumptions may result in increased type I error, power loss, or biased parameter estimates. Remedial measures for violated underlying conditions or assumptions include data transformation or selecting a more relaxed modeling or testing strategy. Model-Based Multifactor Dimensionality Reduction (MB-MDR) for epistasis detection relies on association testing between a trait and a factor consisting of multilocus genotype information. For quantitative traits, the framework is essentially Analysis of Variance (ANOVA) that decomposes the variability in the trait amongst the different factors. In this study, we assess through simulations, the cumulative effect of deviations from normality and homoscedasticity on the overall performance of quantitative Model-Based Multifactor Dimensionality Reduction (MB-MDR) to detect 2-locus epistasis signals in the absence of main effects.MethodologyOur simulation study focuses on pure epistasis models with varying degrees of genetic influence on a quantitative trait. Conditional on a multilocus genotype, we consider quantitative trait distributions that are normal, chi-square or Student's t with constant or non-constant phenotypic variances. All data are analyzed with MB-MDR using the built-in Student's t-test for association, as well as a novel MB-MDR implementation based on Welch's t-test. Traits are either left untransformed or are transformed into new traits via logarithmic, standardization or rank-based transformations, prior to MB-MDR modeling.ResultsOur simulation results show that MB-MDR controls type I error and false positive rates irrespective of the association test considered. Empirically-based MB-MDR power estimates for MB-MDR with Welch's t-tests are generally lower than those for MB-MDR with Student's t-tests. Trait transformations involving ranks tend to lead to increased power compared to the other considered data transformations.ConclusionsWhen performing MB-MDR screening for gene-gene interactions with quantitative traits, we recommend to first rank-transform traits to normality and then to apply MB-MDR modeling with Student's t-tests as internal tests for association.

Project description:BackgroundIt 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.ResultsMDR with 3WS is computationally approximately five times faster than 5-fold cross-validation. The power to find the exact true disease loci without detecting false positive loci is higher with 5-fold cross-validation than with 3WS before pruning. However, the power to find the true disease causing loci in addition to false positive loci is equivalent to the 3WS. With the incorporation of a pruning procedure after the 3WS, the power of the 3WS approach to detect only the exact disease loci is equivalent to that of MDR with cross-validation. In the real data application, the cross-validation and 3WS analyses indicate the same two-locus model.ConclusionsOur results reveal that the performance of the two internal validation methods is equivalent with the use of pruning procedures. The specific pruning procedure should be chosen understanding the trade-off between identifying all relevant genetic effects but including false positives and missing important genetic factors. This implies 3WS may be a powerful and computationally efficient approach to screen for epistatic effects, and could be used to identify candidate interactions in large-scale genetic studies.

Project description:BackgroundRecently, one of the greatest challenges in genome-wide association studies is to detect gene-gene and/or gene-environment interactions for common complex human diseases. Ritchie et al. (2001) proposed multifactor dimensionality reduction (MDR) method for interaction analysis. MDR is a combinatorial approach to reduce multi-locus genotypes into high-risk and low-risk groups. Although MDR has been widely used for case-control studies with binary phenotypes, several extensions have been proposed. One of these methods, a generalized MDR (GMDR) proposed by Lou et al. (2007), allows adjusting for covariates and applying to both dichotomous and continuous phenotypes. GMDR uses the residual score of a generalized linear model of phenotypes to assign either high-risk or low-risk group, while MDR uses the ratio of cases to controls.MethodsIn this study, we propose multivariate GMDR, an extension of GMDR for multivariate phenotypes. Jointly analysing correlated multivariate phenotypes may have more power to detect susceptible genes and gene-gene interactions. We construct generalized estimating equations (GEE) with multivariate phenotypes to extend generalized linear models. Using the score vectors from GEE we discriminate high-risk from low-risk groups. We applied the multivariate GMDR method to the blood pressure data of the 7,546 subjects from the Korean Association Resource study: systolic blood pressure (SBP) and diastolic blood pressure (DBP). We compare the results of multivariate GMDR for SBP and DBP to the results from separate univariate GMDR for SBP and DBP, respectively. We also applied the multivariate GMDR method to the repeatedly measured hypertension status from 5,466 subjects and compared its result with those of univariate GMDR at each time point.ResultsResults from the univariate GMDR and multivariate GMDR in two-locus model with both blood pressures and hypertension phenotypes indicate best combinations of SNPs whose interaction has significant association with risk for high blood pressures or hypertension. Although the test balanced accuracy (BA) of multivariate analysis was not always greater than that of univariate analysis, the multivariate BAs were more stable with smaller standard deviations.ConclusionsIn this study, we have developed multivariate GMDR method using GEE approach. It is useful to use multivariate GMDR with correlated multiple phenotypes of interests.

Project description:Identifying gene-gene interactions or gene-environment interactions in studies of human complex diseases remains a big challenge in genetic epidemiology. An additional challenge, often forgotten, is to account for important lower-order genetic effects. These may hamper the identification of genuine epistasis. If lower-order genetic effects contribute to the genetic variance of a trait, identified statistical interactions may simply be due to a signal boost of these effects. In this study, we restrict attention to quantitative traits and bi-allelic SNPs as genetic markers. Moreover, our interaction study focuses on 2-way SNP-SNP interactions. Via simulations, we assess the performance of different corrective measures for lower-order genetic effects in Model-Based Multifactor Dimensionality Reduction epistasis detection, using additive and co-dominant coding schemes. Performance is evaluated in terms of power and familywise error rate. Our simulations indicate that empirical power estimates are reduced with correction of lower-order effects, likewise familywise error rates. Easy-to-use automatic SNP selection procedures, SNP selection based on "top" findings, or SNP selection based on p-value criterion for interesting main effects result in reduced power but also almost zero false positive rates. Always accounting for main effects in the SNP-SNP pair under investigation during Model-Based Multifactor Dimensionality Reduction analysis adequately controls false positive epistasis findings. This is particularly true when adopting a co-dominant corrective coding scheme. In conclusion, automatic search procedures to identify lower-order effects to correct for during epistasis screening should be avoided. The same is true for procedures that adjust for lower-order effects prior to Model-Based Multifactor Dimensionality Reduction and involve using residuals as the new trait. We advocate using "on-the-fly" lower-order effects adjusting when screening for SNP-SNP interactions using Model-Based Multifactor Dimensionality Reduction analysis.

Project description:BackgroundDetection 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.ResultIn 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.ConclusionWe 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 .

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Global tests of P-values for multifactor dimensionality reduction models in selection of optimal number of target genes.

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Global tests of P-values for multifactor dimensionality reduction models in selection of optimal number of target genes.

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