Entropy-based information gain approaches to detect and to characterize gene-gene and gene-environment interactions/correlations of complex diseases

Abstract

For complex diseases, the relationship between genotypes, environment factors and phenotype is usually complex and nonlinear. Our understanding of the genetic architecture of diseases has considerably increased over the last years. However, both conceptually and methodologically, detecting gene-gene and gene-environment interactions remains a challenge, despite the existence of a number of efficient methods. One method that offers great promises but has not yet been widely applied to genomic data is the entropy-based approach of information theory. In this paper we first develop entropy-based test statistics to identify 2-way and higher order gene-gene and gene-environment interactions. We then apply these methods to a bladder cancer data set and thereby test their power and identify strengths and weaknesses. For two-way interactions, we propose an information-gain approach based on mutual information. For three-ways and higher order interactions, an interaction-information-gain approach is used. In both case we develop one-dimensional test statistics to analyze sparse data. Compared to the naive chi-square test, the test statistics we develop have similar or higher power and is robust. Applying it to the bladder cancer data set allowed to investigate the complex interactions between DNA repair gene SNPs, smoking status, and bladder cancer susceptibility. Although not yet widely applied, entropy-based approaches appear as a useful tool for detecting gene-gene and gene-environment interactions. The test statistics we develop add to a growing body methodologies that will gradually shed light on the complex architecture of common diseases.

A New Laboratory-Based Algorithm to Predict Development of Hepatocellular Carcinoma in Patients With Hepatitis C and Cirrhosis

“…Therefore, in addition to the mean-based measures (i.e., c-index or IDI) that would be subject to a ceiling effect, we measured the enhancement to the HCC predictive model by the increase in conditional variance of predicted HCC probabilities within AFP strata 13 and the information gain (Kullback-Leibler divergence) 14 , which quantifies the increase in heterogeneity of the distribution of HCC cases within AFP-strata. This method has been recently applied in biomedical sciences 15-17 . These two concepts are used to define a preferred sequence of attributes; an attribute with high mutual information should be preferred to other attributes.…”

“…However, these conventional measures of discrimination may be insensitive to detecting small improvements in model performance when a new marker is added to a model that already includes important predictors. We therefore also measured changes in conditional variance of predicted HCC probabilities within AFP strata 13 ; this is a component of the total variance (in addition the conditional means variance which is captured by c index); and the information-theoretic information gain (Kullback-Leibler divergence) 14 , which quantifies the increase in heterogeneity of the distribution of HCC cases within AFP-strata 15 . Calibration and model fit were assessed graphically by plotting model-derived probabilities against raw probabilities, and analytically by the Hosmer-Lemeshow chi-square statistic.…”

ClusterMI: Detecting High-Order SNP Interactions Based on Clustering and Mutual Information

“…Given a dataset D with N samples and M SNPs, the clustering process is described as follows:Initialization: k SNPs are randomly selected from M SNPs as initial centroids of k clusters $C_j(j=1,2,\dots ,k)$, and k is the preset number of SNP groups.Clustering: Mutual information can measure the dependency or associativity between two variables [40,41]. Given this, we take mutual information to measure the associativity between two SNPs.…”

“…After dividing all SNPs into k clusters, ClusterMI then applies conditional mutual information to screen two-locus combinations in each cluster as follows:For the m -th cluster, the association between a two-locus combination and the disease can be measured by conditional mutual information [40,41]. The conditional mutual information of a two-locus combination $(S_i,S_j)(S_i,S_j\in G_m)$ under case ( y = 1) can be calculated as: $cMI(S_i,S_j)=\sum _{u=1}^3\sum _{v=1}^{3}P(S_i=u,S_j=v|y=1)log\frac{P(S_i=u,S_j=v|y=1)}{P(S_i=u|y=1)P(S_j=v|y=1)}$ where $P(S_i=u,S_j=v|y=1)$ denotes the joint probability of $S_i$ and $S_j$ under the case; $P(S_i=u|y=1)$ and $P(S_j=v|y=1)$ are the marginal probability of $S_i$ and $S_j$ under the case, respectively.…”

Bayesian reversible-jump for epistasis analysis in genomic studies

“…Learning strategies have been applied for epistasis estimates in the context of big data, such as Machine Learning (ML) decision trees [4, 14], information theory [8, 25] and multifactor dimensionality reduction (MDR) [28]. In the statistical framework, mixed models based on likelihood inference have been used to estimate epistatic effects using animal models and epistatic G-BLUP based on genomic additive and dominant matrices.…”