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

Abstract

We develop an information-theoretic method for gene-gene (GGI) and gene-environmental interactions (GEI) analysis of syndromes, defined as a phenotype vector comprising multiple quantitative traits (QTs). The K-way interaction information (KWII), an information-theoretic metric, was derived for multivariate normal distributed phenotype vectors. The utility of the method was challenged with three simulated data sets, the Genetic Association Workshop-15 (GAW15) rheumatoid arthritis data set, a highdensity lipoprotein (HDL) and atherosclerosis data set from a mouse QT locus study, and the 1000 Genomes data. The dependence of the KWII on effect size, minor allele frequency, linkage disequilibrium, population stratification/admixture, as well as the power and computational time requirements of the novel method was systematically assessed in simulation studies. In these studies, phenotype vectors containing two and three constituent multivariate normally distributed QTs were used and the KWII was found to be effective at detecting GEI associated with the phenotype. High KWII values were observed for variables and variable combinations associated with the syndrome phenotype compared with uninformative variables not associated with the phenotype. The KWII values for the phenotype-associated combinations increased monotonically with increasing effect size values. The KWII also exhibited utility in simulations with non-linear dependence between the constituent QTs. Analysis of the HDL and atherosclerosis data set indicated that the simultaneous analysis of both phenotypes identified interactions not detected in the analysis of the individual traits. The information-theoretic approach may be useful for non-parametric analysis of GGI and GEI of complex syndromes.

Transferring entropy to the realm of GxG interactions

“…Although most authors agree on the general structure of 3WII and TCI, but they disagree with respect to the variables to choose in the general definition. In fact, 3WII and TCI as described in [ 25 , 26 , 27 , 28 , 29 , 30 , 31 ], other than in [ 17 ], are given by and where Chanda et al [ 27 ] explain the as ‘the information that cannot be obtained without observing all variables and the phenotype at the same time’. Because the latter group treats and as measures for third-order interactions, we list them in this section.…”

“…A further expansion of the concept of TCI was given by the same groups [ 25 , 26 , 27 , 30 , 31 ] in the form of the phenotype-associated interaction information (PAI). Specifically, PAI is given by the difference between the TCI including the phenotype as a variable and the TCI excluding the phenotype, i.e.…”

“…First, Chanda et al [ 27 ] extended the previously published algorithm AMBIENCE [ 25 ] to a new algorithm called CHORUS, designed specifically for quantitative traits that are normally distributed. Subsequently, CHORUS was extended to the algorithm SYMPHONY in [ 31 ], which is designed for vectors of quantitative traits. The principle of both algorithms is the same: Calculate the first order PAI and retain the θ combinations with the highest PAI.…”

Information Theory in Computational Biology: Where We Stand Today

“…The synergy can be positive, when the joint effect of multiple SNPs is larger than the sum of the individual single SNP effects, or negative, when the joint effect is smaller than the sum, indicating information redundancy among SNPs. Some of the prominent methods addressing higher order interactions through synergy and redundancy use multivariate generalizations of MI such as K -way Interaction Information (KWII) to parsimoniously model both GXG and GxE interactions and help gain deeper insights into the underlying disease causation pathways by combining them in a single analytical framework [ 114 , 115 , 116 , 117 , 118 , 119 , 120 ]. All these methods depend on detection of higher order interactions in terms of synergy/redundancy that relies on robust empirical estimations of metrics such as entropy, MI and KWII.…”

“…Besides analyzing binary traits, often GWAS needs to detect gene-disease associations for quantitative traits involving non-discrete real values. Information theoretic methods dealing with such quantitative phenotypes and environmental variables can be found in [ 116 , 117 , 131 ] that use differential or cross-entropy based generalizations of multivariate test statistics. In a recent review, Galas et al [ 132 ] presented a detailed discussion on the information theoretic formalism for gene association with quantitative phenotypes.…”