Supplementary Material for: An Information Theory Analysis of Gene-Environmental Interactions in Count/Rate Data

<b><i>Objective:</i></b> To develop and critically evaluate an information theory method for identifying gene-gene and gene-environment interactions in count and rate data. <b><i>Methods:</i></b> The entropy-based metric <i>k</i>-way interaction information (KWII) was critically assessed for utility in detecting interactions with count data and over-dispersed count data in three simulation studies of increasing complexity and in datasets from animal models of depression and colitis. The results were compared to Poisson regression. The power and effect size dependence of the KWII for detecting interactions was also assessed. <b><i>Results:</i></b> The KWII was capable of effectively identifying the genetic and environmental predictors and their interactions in all three simulated datasets. The results indicate that the KWII approach may produce more parsimonious results than regression. In a rat model of depression, we successfully identified a prominent gender effect as well as other published associations. Analysis of severity scores from an animal model of colitis identified markers from chromosome 3, as well as unique first- and second-order associations for the individual sections of the colon and cecum. <b><i>Conclusions:</i></b> The results demonstrate the utility and versatility of our entropy-based method for gene-environment interaction analysis of count and rate data with Poisson and over-dispersed distributions.

**研究目标**：开发并严谨评估一种基于信息论的方法，用于识别计数数据与速率数据中的基因-基因、基因-环境交互作用。
**研究方法**：针对复杂度逐步提升的三项模拟研究，以及抑郁症、结肠炎动物模型的数据集，对基于熵的k阶交互信息（k-way interaction information, KWII）这一指标在检测计数数据与过度分散计数数据中交互作用的实用性进行严谨评估，并将其结果与泊松回归（Poisson regression）进行对比；同时评估了KWII检测交互作用时的统计效力与效应量依赖性。
**研究结果**：KWII可在全部三项模拟数据集中有效识别遗传与环境预测因子及其交互作用。结果表明，相较于回归分析方法，KWII方法可得到更为简约的分析结果。在抑郁症大鼠模型中，我们成功识别出显著的性别效应以及其他已发表的关联位点。对结肠炎动物模型的严重程度评分进行分析后，我们从3号染色体中鉴定出相关标记位点，同时明确了结肠与盲肠各分段特有的一阶、二阶关联特征。
**研究结论**：本研究结果证实了我们提出的基于熵的方法在泊松分布与过度分散分布的计数、速率数据的基因-环境交互作用分析中的实用性与通用性。