Detecting, Characterizing, and Interpreting Nonlinear Gene–Gene Interactions Using Multifactor Dimensionality Reduction

Abstract

Human health is a complex process that is dependent on many genes, many environmental factors and chance events that are perhaps not measurable with current technology or are simply unknowable. Success in the design and execution of population-based association studies to identify those genetic and environmental factors that play an important role in human disease will depend on our ability to embrace, rather that ignore, complexity in the genotype to phenotype mapping relationship for any given human ecology. We review here three general computational challenges that must be addressed. First, data mining and machine learning methods are needed to model nonlinear interactions between multiple genetic and environmental factors. Second, filter and wrapper methods are needed to identify attribute interactions in large and complex solution landscapes. Third, visualization methods are needed to help interpret computational models and results. We provide here an overview of the multifactor dimensionality reduction (MDR) method that was developed for addressing each of these challenges.

Introduction

Human genetics has a long and rich history of research to understand the role of interindividual variation in the human genome and variation in biological traits. We have progress rapidly from unmeasured genetic studies in families to the identification of common variation in the DNA sequence that can be used in population-based association studies. This is an exciting time because we now have access to technology that allows us to efficiently measure many DNA sequence variations from across the human genome. We will within the next 5 years likely have access to cutting-edge technology that will deliver the entire genomic sequence for all subjects in our genetic and epidemiologic studies. Now that we have access to the basic hereditary information it is time to shift our focus toward the analysis of this data. The focus of this chapter is on the important role of computer science, and, more specifically, machine learning for mining patterns of genetic variations that are associated with susceptibility to common human diseases. This approach assumes that the relationship between genotype and phenotype is very complex. Specifically, we will focus on computational methods for identifying gene–gene interactions or epistasis that accounts for part of the complexity of genetic architecture.

Human genetics has been largely successful in identifying the causative mutations in single genes that determine with virtual certainly rare diseases such as sickle-cell anemia. However, the same success has not been had for common human diseases such as sporadic breast cancer, essential hypertension or bipolar depression. This is because diseases that are common in the population have a much more complex etiology that requires different research strategies than were used to identify genes underlying rare diseases that follow a simpler Mendelian inheritance pattern. Complexity can arise from phenomena such as locus heterogeneity (i.e., different DNA sequence variations leading to the same phenotype), phenocopy (i.e., environmentally determined phenotypes), and the dependence of genotypic effects on environmental factors (i.e., gene–environment interactions or plastic reaction norms) and genotypes at other loci (i.e., gene–gene interactions or epistasis). It is this latter source of complexity, epistasis, that is of interest here. Epistasis has been recognized for many years as deviations from the simple inheritance patterns observed by Mendel (Bateson, 1909) or deviations from additivity in a linear statistical model (Fisher, 1918) and is likely due, in part, to canalization or mechanisms of stabilizing selection that evolve robust (i.e., redundant) gene networks (Waddington, 1942).

Epistasis has been defined in multiple different ways (e.g., Phillips, 1998, Phillips, 2008). We have reviewed two types of epistasis, biological and statistical (Moore & Williams, 2005, Moore & Williams, 2009, Tyler et al., 2009). Biological epistasis when the physical interactions between biomolecules (e.g., DNA, RNA, proteins, enzymes, etc.) are influenced by genetic variation at multiple different loci. This type of epistasis occurs at the cellular level in an individual and is what Bateson (1909) had in mind when he coined the term. Statistical epistasis, on the other hand, occurs at the population level and is realized when there is interindividual variation in DNA sequences. The statistical phenomenon of epistasis is what Fisher (1918) had in mind. The relationship between biological and statistical epistasis is often confusing but will be important to understand if we are to make biological inferences from statistical results (Moore & Williams, 2005, Moore & Williams, 2009, Phillips, 1998, Phillips, 2008, Tyler et al., 2009). Moore (2003) has argued that epistasis is likely to be a ubiquitous phenomenon in complex human diseases. The focus of the present study is the detection and characterization of statistical epistasis in human populations using machine learning and data mining methods.

The fields of genetics and epidemiology are undergoing an information explosion and an understanding implosion. That is, our ability to generate data is far outpacing our ability to interpret it. This is especially true today where it is technically and economically feasible to measure a million or more single nucleotide polymorphisms (SNPs) from across the human genome. An important goal in human genetics is to determine which of the millions of SNPs are useful for predicting who is at risk for common diseases. This “genome-wide” approach is expected to revolutionize the genetic analysis of common human diseases and, for better or worse, is quickly replacing the traditional “candidate-gene” approach that focuses on several genes selected by their known or suspected function.

Moore and Ritchie (2004) have outlined three significant challenges that must be overcome if we are to successfully identify genetic predictors of health and disease using a genome-wide approach. First, powerful data mining and machine learning methods will need to be developed to statistically model the relationship between combinations of DNA sequence variations and disease susceptibility. Traditional methods such as logistic regression have limited power for modeling high-order nonlinear interactions (Moore and Williams, 2002). A second challenge is the selection of genetic features or attributes that should be included for analysis. If interactions between genes explain most of the heritability of common diseases, then combinations of DNA sequence variations will need to be evaluated from a list of thousands of candidates. Filter (SNP selection) and wrapper (SNP searching) methods will play an important role because there are more combinations than can be exhaustively evaluated. A third challenge is the interpretation of gene–gene interaction models. Although a statistical model can be used to identify DNA sequence variations that confer risk for disease, this approach cannot be translated into specific prevention and treatment strategies without interpreting the results in the context of human biology. Making etiological inferences from computational models may be the most important and the most difficult challenge of all (Moore and Williams, 2005).

To illustrate the concept of statistical interaction, consider the following simple example of epistasis in the form of a penetrance function. Penetrance is simply the probability (P) of disease (D) given a particular combination of genotypes (G) that was inherited (i.e., P[D|G]). Let us assume for two SNPs labeled A and B that genotypes AA, aa, BB, and bb have population frequencies of 0.25, while genotypes Aa and Bb have frequencies of 0.5. Let us also assume that individuals have a very high risk of disease if they inherit Aa or Bb but not both (i.e., the exclusive OR or XOR logic function). What makes this model interesting is that disease risk is entirely dependent on the particular combination of genotypes inherited at more than one locus. The penetrance for each individual genotype in this model is all the same and is computed by summing the products of the genotype frequencies and penetrance values. Heritability can be calculated as outlined by Culverhouse et al. (2002). Thus, in this model there is no difference in disease risk for each single-locus genotype as specified by penetrance values. This model is labeled M170 by Li and Reich (2000) in their categorization of genetic models involving two SNPs and is an example of a pattern that is not separable by a simple linear function. This model is a special case where all of the heritability is due to epistasis or nonlinear gene–gene interaction.

Combining this type of statistical interaction with the challenge of variable selection yields what computer scientists have called a needle-in-a-haystack problem. That is, there may be a particular combination of SNPs or SNPs and environmental factors that together with the right nonlinear function are a significant predictor of disease susceptibility. However, individually they may not look any different than thousands of other SNPs that are not involved in the disease process and are thus noisy. Under these models, the learning algorithm is truly looking for a genetic needle in a genomic haystack. It is now commonly assumed that at least 1,000,000 carefully selected SNPs may be necessary to capture all of the relevant variation across the Caucasian human genome. Assuming this is true, we would need to scan approximately 500 billion pairwise combinations of SNPs to find a genetic needle. The number of higher order combinations is astronomical. What is the optimal computational approach to this problem?

There are two general approaches to select attributes for predictive models. The filter approach preprocesses the data by algorithmically, statistically, or biologically assessing the quality or relevance of each variable and then using that information to select a subset for analysis. The wrapper approach iteratively selects subsets of attributes for classification using either a deterministic or stochastic algorithm. The key difference between the two approaches is that the learning algorithm plays no role in selecting which attributes to consider in the filter approach. The advantage of the filter is speed while the wrapper approach has the potential to do a better job classifying subjects as sick or healthy. We first discuss a specific machine learning algorithm called multifactor dimensionality reduction (MDR) that has been applied to classifying healthy and disease subjects using their DNA sequence information and then discuss filter and wrapper approaches for the specific problem of detecting epistasis or gene–gene interactions on a genome-wide scale.