Supplementary Material for: Inferring Gene Network from Candidate SNP Association Studies Using a Bayesian Graphical Model: Application to a Breast Cancer Case-Control Study from Ontario

<b><i>Background/Aims:</i></b> Gene network analysis can be a very valuable approach for elucidating complex dependence between functional SNPs in a candidate genetic pathway and for assessing their association with a disease of interest. Even when the number of SNPs evaluated is relatively small (&lt;20), the number of potential gene networks induced by the SNPs can be very large and the contingency tables representing their joint distribution very sparse. <b><i>Methods:</i></b> In this paper, we propose a Bayesian model determination for gene network analysis using decomposable discrete graphical models combined with Reversible Jump Markov chain Monte Carlo. We show the application of this approach in a study of 13 SNPs in the DNA repair pathway and their association with breast cancer from a case-control study conducted in Ontario, Canada. <b><i>Results:</i></b> The strength of associations among the SNPs and between the SNPs and the disease status is evaluated by computing the posterior probability of any pair of variables. The corresponding gene network is reconstructed by retaining pair-wise associations with the highest posterior probabilities. In our real data analysis, we found evidence for a particular association between one SNP in the gene POLL and the disease status and also several interesting patterns of association between the SNPs themselves. <b><i>Conclusion:</i></b> This general statistical framework could serve as a basis for prioritizing genes and SNPs that play a major role in breast cancer etiology and to better understand their complex interactions in a specific genetic pathway.

**<i>研究背景与目标</i>**：基因网络分析是解析候选遗传通路中功能性单核苷酸多态性（Single Nucleotide Polymorphism, SNP）之间复杂依赖关系，并评估其与目标疾病相关性的极具价值的研究手段。即便所评估的单核苷酸多态性数量相对较少（<20），由这些多态性所诱导的潜在基因网络数量仍可能极为庞大，且表征其联合分布的列联表也会极为稀疏。

**<i>研究方法</i>**：本文提出一种基于贝叶斯模型确定的基因网络分析方法，将可分解离散图模型与可逆跳跃马尔可夫链蒙特卡洛（Reversible Jump Markov Chain Monte Carlo）相结合。我们将该方法应用于一项在加拿大安大略省开展的病例对照研究，分析了DNA修复通路中的13个单核苷酸多态性及其与乳腺癌的相关性。

**<i>研究结果</i>**：通过计算任意变量对的后验概率，可评估单核苷酸多态性之间以及单核苷酸多态性与疾病状态之间的关联强度。通过保留后验概率最高的两两关联，即可重构得到对应的基因网络。在本次真实数据分析中，我们发现基因POLL中的一个单核苷酸多态性与疾病状态存在特定关联，同时还观测到多个单核苷酸多态性之间存在多种有趣的关联模式。

**<i>研究结论</i>**：这一通用统计框架可作为筛选在乳腺癌病因学中发挥关键作用的基因与单核苷酸多态性的基础，同时有助于更深入地理解特定遗传通路中基因与多态性之间的复杂相互作用。