An ensemble learning approach jointly modeling main and interaction effects in genetic association studies

Abstract

Complex diseases are presumed to be the results of interactions of several genes and environmental factors, with each gene only having a small effect on the disease. Thus, the methods that can account for gene-gene interactions to search for a set of marker loci in different genes or across genome and to analyze these loci jointly are critical. In this article, we propose an ensemble learning approach (ELA) to detect a set of loci whose main and interaction effects jointly have a significant association with the trait. In the ELA, we first search for "base learners" and then combine the effects of the base learners by a linear model. Each base learner represents a main effect or an interaction effect. The result of the ELA is easy to interpret. When the ELA is applied to analyze a data set, we can get a final model, an overall P-value of the association test between the set of loci involved in the final model and the trait, and an importance measure for each base learner and each marker involved in the final model. The final model is a linear combination of some base learners. We know which base learner represents a main effect and which one represents an interaction effect. The importance measure of each base learner or marker can tell us the relative importance of the base learner or marker in the final model. We used intensive simulation studies as well as a real data set to evaluate the performance of the ELA. Our simulation studies demonstrated that the ELA is more powerful than the single-marker test in all the simulation scenarios. The ELA also outperformed the other three existing multi-locus methods in almost all cases. In an application to a large-scale case-control study for Type 2 diabetes, the ELA identified 11 single nucleotide polymorphisms that have a significant multi-locus effect (Pvalue = 0.01), while none of the single nucleotide polymorphisms showed significant marginal effects and none of the two-locus combinations showed significant two-locus interaction effects.

Analysis of North American Rheumatoid Arthritis Consortium data using a penalized logistic regression approach

“…Use of such techniques is just beginning to emerge: ridge regression [11] has been used for distinguishing between causative and non-causative variants for quantitative phenotypes, and penalized logistic and least angle regression have been used for identifying gene-gene interactions in binary traits [7,12]. A closely-related Bayesian penalized regression procedure [13] has also been suggested for genome-wide and/or fine-mapping studies.…”

Ensemble survival tree models to reveal pairwise interactions of variables with time-to-events outcomes in low-dimensional setting

“…There are also a few Bayesian studies for modeling nonlinear, non-additive or interaction covariate effects (Chen et al, 2012; Chipman, George & McCulloch, 1998; Gustafson, 2000). Finally, there is a recent and rich literature for detecting epistasis in GWAS association studies: (Li, Horstman & Chen, 2011; Ueki & Cordell, 2012; Yung et al, 2011; Zhang et al 2008; 2010a; 2010b; 2011). However, all these existing methods, except for the one by Chen et al (2012), are not designed for analyzing time-to-event outcomes, possibly with censoring.…”

“…RSF, being derived from RF, naturally inherits many of its important properties. One of them is that, being fully non-parametric, it is model-assumption free, and, as an (ensemble) tree-based modeling approach, it is suited to adaptively discover non-monotonic, nonlinear, and non-additive or high-order interaction-effects (Ishwaran et al, 2008; Zhang et al, 2008; Li, Horstman & Chen, 2011). Therefore, these approaches provide a natural alternative to build models that bypass the need to impose parametric constraints on the underlying distributions and a way to automatically deal with high-level interactions; both of which should ultimately result in more accurate predictions and more efficient epistasis detections.…”

“…In this study, we took advantage of the aforementioned properties and capabilities of ensemble tree models, such as RF and RSF, as done by others (Zhang et al, 2008; Li, Horstman & Chen, 2011). Specifically, we used RSF to model right-censored time-to-event outcome data and introduce a novel approach that makes use of RF concepts of variable importance (Breiman, 2001) and minimal depth of maximal subtree (Ishwaran, 2007) for selecting and ranking pairwise interaction statistics.…”

Efficient Simulation of Epistatic Interactions in Case-Parent Trios

“…To address this issue, many tools from the statistical and machine learning literature, developed to deal with high-dimensional search spaces, have been applied to multi-marker SNP data, for example neural networks (Ritchie et al, 2003b; North et al, 2003; Tomita et al, 2004), random forests (Breiman, 2001; Lunetta et al, 2004; Bureau et al, 2005; Chen et al, 2007), and various other methods based on partitions, trees, and splines, and ensembles of base learners (e.g. Chen et al, 2003; Cook et al, 2004; Zhang et al, 2008). Some approaches to delineate higher order interactions were specifically developed for SNP data, such as the multifactor dimensionality reduction techniques (Hahn et al, 2003; Ritchie et al, 2003a; Moore, 2004; Ritchie and Motsinger, 2005; Ritchie, 2005), the restricted partition method (Culverhouse et al, 2004, 2007), and logic regression (Kooperberg et al, 2001; Ruczinski et al, 2003, 2004).…”