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

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

The challenge for genetic epidemiologists: how to analyze large numbers of SNPs in relation to complex diseases

Genetic epidemiologists have taken the challenge to identify genetic polymorphisms involved in the development of diseases. Many have collected data on large numbers of genetic markers but are not familiar with available methods to assess their association with complex diseases. Statistical methods have been developed for analyzing the relation between large numbers of genetic and environmental predictors to disease or disease-related variables in genetic association studies. In this commentary we discuss logistic regression analysis, neural networks, including the parameter decreasing method (PDM) and genetic programming optimized neural networks (GPNN) and several non-parametric methods, which include the set association approach, combinatorial partitioning method (CPM), restricted partitioning method (RPM), multifactor dimensionality reduction (MDR) method and the random forests approach. The relative strengths and weaknesses of these methods are highlighted. Logistic regression and neural networks can handle only a limited number of predictor variables, depending on the number of observations in the dataset. Therefore, they are less useful than the non-parametric methods to approach association studies with large numbers of predictor variables. GPNN on the other hand may be a useful approach to select and model important predictors, but its performance to select the important effects in the presence of large numbers of predictors needs to be examined. Both the set association approach and random forests approach are able to handle a large number of predictors and are useful in reducing these predictors to a subset of predictors with an important contribution to disease. The combinatorial methods give more insight in combination patterns for sets of genetic and/or environmental predictor variables that may be related to the outcome variable. As the non-parametric methods have different strengths and weaknesses we conclude that to approach genetic association studies using the case-control design, the application of a combination of several methods, including the set association approach, MDR and the random forests approach, will likely be a useful strategy to find the important genes and interaction patterns involved in complex diseases

Properties of selected mutations and genotypic landscapes under Fisher's Geometric Model

The fitness landscape - the mapping between genotypes and fitness - determines properties of the process of adaptation. Several small genetic fitness landscapes have recently been built by selecting a handful of beneficial mutations and measuring fitness of all combinations of these mutations. Here we generate several testable predictions for the properties of these landscapes under Fisher's geometric model of adaptation (FGMA). When far from the fitness optimum, we analytically compute the fitness effect of beneficial mutations and their epistatic interactions. We show that epistasis may be negative or positive on average depending on the distance of the ancestral genotype to the optimum and whether mutations were independently selected or co-selected in an adaptive walk. Using simulations, we show that genetic landscapes built from FGMA are very close to an additive landscape when the ancestral strain is far from the optimum. However, when close to the optimum, a large diversity of landscape with substantial ruggedness and sign epistasis emerged. Strikingly, landscapes built from different realizations of stochastic adaptive walks in the same exact conditions were highly variable, suggesting that several realizations of small genetic landscapes are needed to gain information about the underlying architecture of the global adaptive landscape.Comment: 51 pages, 8 figure

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

Post-transcriptional knowledge in pathway analysis increases the accuracy of phenotypes classification

Motivation: Prediction of phenotypes from high-dimensional data is a crucial task in precision biology and medicine. Many technologies employ genomic biomarkers to characterize phenotypes. However, such elements are not sufficient to explain the underlying biology. To improve this, pathway analysis techniques have been proposed. Nevertheless, such methods have shown lack of accuracy in phenotypes classification. Results: Here we propose a novel methodology called MITHrIL (Mirna enrIched paTHway Impact anaLysis) for the analysis of signaling pathways, which has built on top of the work of Tarca et al., 2009. MITHrIL extends pathways by adding missing regulatory elements, such as microRNAs, and their interactions with genes. The method takes as input the expression values of genes and/or microRNAs and returns a list of pathways sorted according to their deregulation degree, together with the corresponding statistical significance (p-values). Our analysis shows that MITHrIL outperforms its competitors even in the worst case. In addition, our method is able to correctly classify sets of tumor samples drawn from TCGA. Availability: MITHrIL is freely available at the following URL: http://alpha.dmi.unict.it/mithril

Information Preserving Component Analysis: Data Projections for Flow Cytometry Analysis

Flow cytometry is often used to characterize the malignant cells in leukemia and lymphoma patients, traced to the level of the individual cell. Typically, flow cytometric data analysis is performed through a series of 2-dimensional projections onto the axes of the data set. Through the years, clinicians have determined combinations of different fluorescent markers which generate relatively known expression patterns for specific subtypes of leukemia and lymphoma -- cancers of the hematopoietic system. By only viewing a series of 2-dimensional projections, the high-dimensional nature of the data is rarely exploited. In this paper we present a means of determining a low-dimensional projection which maintains the high-dimensional relationships (i.e. information) between differing oncological data sets. By using machine learning techniques, we allow clinicians to visualize data in a low dimension defined by a linear combination of all of the available markers, rather than just 2 at a time. This provides an aid in diagnosing similar forms of cancer, as well as a means for variable selection in exploratory flow cytometric research. We refer to our method as Information Preserving Component Analysis (IPCA).Comment: 26 page