As interactions among genetic variants in different genes can be an important factor for predicting complex diseases, many computational methods have been proposed to detect if a particular set of genes has interaction with a particular complex disease. However, even though many such methods have been shown to be useful, they can be made more effective if the properties of gene–gene interactions can be better understood. Towards this goal, we have attempted to uncover patterns in gene–gene interactions and the patterns reveal an interesting property that can be reflected in an inequality that describes the relationship between two genotype variables and a disease-status variable. We show, in this paper, that this inequality can be generalized to [Formula: see text] genotype variables. Based on this inequality, we establish a conditional independence and redundancy (CIR)-based definition of gene–gene interaction and the concept of an interaction group. From these new definitions, a novel measure of gene–gene interaction is then derived. We discuss the properties of these concepts and explain how they can be used in a novel algorithm to detect high-order gene–gene interactions. Experimental results using both simulated and real datasets show that the proposed method can be very promising.

中文翻译：

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确定与复杂疾病相关的基因-基因相互作用的依赖性和冗余性

由于不同基因中遗传变异之间的相互作用可能是预测复杂疾病的重要因素，因此已经提出了许多计算方法来检测一组特定的基因是否与特定的复杂疾病发生相互作用。然而，尽管许多这样的方法已被证明是有用的，但如果能更好地理解基因-基因相互作用的特性，它们就会变得更有效。朝着这个目标，我们试图揭示基因-基因相互作用的模式，这些模式揭示了一个有趣的特性，可以反映在描述两个基因型变量和疾病状态变量之间关系的不等式中。我们在本文中表明，这种不等式可以推广到 [公式：见文本] 基因型变量。基于这个不等式，我们建立了基于条件独立和冗余（CIR）的基因-基因相互作用定义和相互作用组的概念。从这些新定义中，衍生出一种新的基因-基因相互作用测量方法。我们讨论了这些概念的性质，并解释了如何将它们用于检测高阶基因-基因相互作用的新算法。使用模拟数据集和真实数据集的实验结果表明，所提出的方法非常有前途。