SYMPHONY, an information-theoretic method for gene-gene and gene-environment interaction analysis of disease syndromes

Optimized permutation testing for information theoretic measures of multi-gene interactions

Background

Permutation testing is often considered the “gold standard” for multi-test significance analysis, as it is an exact test requiring few assumptions about the distribution being computed. However, it can be computationally very expensive, particularly in its naive form in which the full analysis pipeline is re-run after permuting the phenotype labels. This can become intractable in multi-locus genome-wide association studies (GWAS), in which the number of potential interactions to be tested is combinatorially large.

Results

In this paper, we develop an approach for permutation testing in multi-locus GWAS, specifically focusing on SNP–SNP-phenotype interactions using multivariable measures that can be computed from frequency count tables, such as those based in Information Theory. We find that the computational bottleneck in this process is the construction of the count tables themselves, and that this step can be eliminated at each iteration of the permutation testing by transforming the count tables directly. This leads to a speed-up by a factor of over 10³ for a typical permutation test compared to the naive approach. Additionally, this approach is insensitive to the number of samples making it suitable for datasets with large number of samples.

Conclusions

The proliferation of large-scale datasets with genotype data for hundreds of thousands of individuals enables new and more powerful approaches for the detection of multi-locus genotype-phenotype interactions. Our approach significantly improves the computational tractability of permutation testing for these studies. Moreover, our approach is insensitive to the large number of samples in these modern datasets. The code for performing these computations and replicating the figures in this paper is freely available at https://github.com/kunert/permute-counts.

Information Theory in Computational Biology: Where We Stand Today

"A Mathematical Theory of Communication" was published in 1948 by Claude Shannon to address the problems in the field of data compression and communication over (noisy) communication channels. Since then, the concepts and ideas developed in Shannon's work have formed the basis of information theory, a cornerstone of statistical learning and inference, and has been playing a key role in disciplines such as physics and thermodynamics, probability and statistics, computational sciences and biological sciences. In this article we review the basic information theory based concepts and describe their key applications in multiple major areas of research in computational biology-gene expression and transcriptomics, alignment-free sequence comparison, sequencing and error correction, genome-wide disease-gene association mapping, metabolic networks and metabolomics, and protein sequence, structure and interaction analysis.

Transferring entropy to the realm of GxG interactions

Genome-wide association studies are moving to genome-wide interaction studies, as the genetic background of many diseases appears to be more complex than previously supposed. Thus, many statistical approaches have been proposed to detect gene-gene (GxG) interactions, among them numerous information theory-based methods, inspired by the concept of entropy. These are suggested as particularly powerful and, because of their nonlinearity, as better able to capture nonlinear relationships between genetic variants and/or variables. However, the introduced entropy-based estimators differ to a surprising extent in their construction and even with respect to the basic definition of interactions. Also, not every entropy-based measure for interaction is accompanied by a proper statistical test. To shed light on this, a systematic review of the literature is presented answering the following questions: (1) How are GxG interactions defined within the framework of information theory? (2) Which entropy-based test statistics are available? (3) Which underlying distribution do the test statistics follow? (4) What are the given strengths and limitations of these test statistics?

Functional Regression Models for Epistasis Analysis of Multiple Quantitative Traits

To date, most genetic analyses of phenotypes have focused on analyzing single traits or analyzing each phenotype independently. However, joint epistasis analysis of multiple complementary traits will increase statistical power and improve our understanding of the complicated genetic structure of the complex diseases. Despite their importance in uncovering the genetic structure of complex traits, the statistical methods for identifying epistasis in multiple phenotypes remains fundamentally unexplored. To fill this gap, we formulate a test for interaction between two genes in multiple quantitative trait analysis as a multiple functional regression (MFRG) in which the genotype functions (genetic variant profiles) are defined as a function of the genomic position of the genetic variants. We use large-scale simulations to calculate Type I error rates for testing interaction between two genes with multiple phenotypes and to compare the power with multivariate pairwise interaction analysis and single trait interaction analysis by a single variate functional regression model. To further evaluate performance, the MFRG for epistasis analysis is applied to five phenotypes of exome sequence data from the NHLBI’s Exome Sequencing Project (ESP) to detect pleiotropic epistasis. A total of 267 pairs of genes that formed a genetic interaction network showed significant evidence of epistasis influencing five traits. The results demonstrate that the joint interaction analysis of multiple phenotypes has a much higher power to detect interaction than the interaction analysis of a single trait and may open a new direction to fully uncovering the genetic structure of multiple phenotypes.

The widely used statistical methods test interaction for single phenotype. However, we often observe pleotropic genetic interaction effects. The simultaneous gene-gene (GxG) interaction analysis of multiple complementary traits will increase statistical power to detect GxG interactions. Although GxG interactions play an important role in uncovering the genetic structure of complex traits, the statistical methods for detecting GxG interactions in multiple phenotypes remains less developed owing to its potential complexity. Therefore, we extend functional regression model from single variate to multivariate for simultaneous GxG interaction analysis of multiple correlated phenotypes. Large-scale simulations are conducted to evaluate Type I error rates for testing interaction between two genes with multiple phenotypes and to compare power with traditional multivariate pair-wise interaction analysis and single trait interaction analysis by a single variate functional regression model. To further evaluate performance, the MFRG for interaction analysis is applied to five phenotypes of exome sequence data from the NHLBI’s Exome Sequencing Project (ESP) to detect pleiotropic GxG interactions. 267 pairs of genes that formed a genetic interaction network showed significant evidence of interactions influencing five traits.

Evaluating methods for modeling epistasis networks with application to head and neck cancer

Epistasis helps to explain how multiple single-nucleotide polymorphisms (SNPs) interact to cause disease. A variety of tools have been developed to detect epistasis. In this article, we explore the strengths and weaknesses of an information theory approach for detecting epistasis and compare it to the logistic regression approach through simulations. We consider several scenarios to simulate the involvement of SNPs in an epistasis network with respect to linkage disequilibrium patterns among them and the presence or absence of main and interaction effects. We conclude that the information theory approach more efficiently detects interaction effects when main effects are absent, whereas, in general, the logistic regression approach is appropriate in all scenarios but results in higher false positives. We compute epistasis networks for SNPs in the FSD1L gene using a two-phase head and neck cancer genome-wide association study involving 2,185 cases and 4,507 controls to demonstrate the practical application of the methods.

Detecting epistasis in human complex traits

Genome-wide association studies (GWASs) have become the focus of the statistical analysis of complex traits in humans, successfully shedding light on several aspects of genetic architecture and biological aetiology. Single-nucleotide polymorphisms (SNPs) are usually modelled as having additive, cumulative and independent effects on the phenotype. Although evidently a useful approach, it is often argued that this is not a realistic biological model and that epistasis (that is, the statistical interaction between SNPs) should be included. The purpose of this Review is to summarize recent directions in methodology for detecting epistasis and to discuss evidence of the role of epistasis in human complex trait variation. We also discuss the relevance of epistasis in the context of GWASs and potential hazards in the interpretation of statistical interaction terms.

Genetic factors associated with gemcitabine pharmacokinetics, disposition, and toxicity

AIM

The goal of this work was to investigate the associations of genetic and environmental factors with gemcitabine disposition and toxicity from genomewide data using a novel information theoretic approach.

METHODS

We utilized the information theoretic K-way interaction information (KWII) metric to detect gene-gene and gene-environment interactions associated with gemcitabine disposition and gemcitabine-induced neutropenia in genomic and clinical data from Japanese cancer patients.

RESULTS

The information theoretic KWII analyses identified age and four genes - DMD, HEXDC, CNTN4, and ALOX5AP - to be associated with gemcitabine pharmacokinetics (PK). The rs4769060 single-nucleotide polymorphism in the ALOX5AP gene was associated with all PK parameters studied. For gemcitabine-induced neutropenia, multiple associations with long intergenic noncoding RNA regions were detected. Pathway analysis identified leukotriene and eoxin synthesis, platelet homeostasis, and L1CAM interactions as potential pathways associated with gemcitabine disposition.

CONCLUSION

The KWII analyses detected novel associations with gemcitabine PK and toxicity. These results could be used to inform future investigations involving gemcitabine efficacy in clinical settings.