Transferring entropy to the realm of GxG interactions

Abstract

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?

1,000x Faster than PLINK: Genome-Wide Epistasis Detection with Logistic Regression Using Combined FPGA and GPU Accelerators

“…This modification increased the runtime of PLINK by a factor of about 5.7, but the results were almost exactly equal now, showing that the inconsistencies were caused by the different precisions. We believe the remaining small inconsistencies were due to numerical problems in PLINK when accumulating small floating-point values over all samples in steps 2 and 3 of computing the logistic regression test (see (5) and (6) in Sect. 2.1).…”

“…Recently, entropy-based measures for GxG interaction detection gained increasing attention. A well-written overview can be found in [5].…”

Modified entropy-based procedure detects gene-gene-interactions in unconventional genetic models

“…This concept is modelfree and measures the uncertainty or disorder in a system and could therefore lend itself to detect interactions for many genotype constellations. This technique is suggested as particularly powerful and, because of the nonlinearity, as better able to capture nonlinear relationships between genetic variants or other variables [18]. Ferrario et al reviewed different entropy-based measures providing information on suggested test statistics, simulations and implementations [18].…”

“…This technique is suggested as particularly powerful and, because of the nonlinearity, as better able to capture nonlinear relationships between genetic variants or other variables [18]. Ferrario et al reviewed different entropy-based measures providing information on suggested test statistics, simulations and implementations [18]. Focusing on second order interaction, there are three important concepts, namely conditional mutual information, information gain, and relative information gain.…”

“…These are based on the following definitions: First, entropy can be defined as a measure for uncertainty in a random variable [19]. Then, mutual information refers to the reduction of uncertainty of one variable conditional on the knowledge of the other variable [18]. Furthermore, mutual information can also be conditioned on a third variable yielding the conditional mutual information (CMI) [18], which has been used for a test statistic by Zuo et al [20].…”