Yao Tsung-Hung, Ni Yang, Bhadra Anindya, Kang Jian, Baladandayuthapani Veerabhadran
Department of Biostatistics, University of Michigan at Ann Arbor, Ann Arbor, MI 48109, United States.
Department of Statistics, Texas A&M University, College Station, TX 77843, United States.
Biometrics. 2025 Jan 7;81(1). doi: 10.1093/biomtc/ujae160.
Graphical models are powerful tools to investigate complex dependency structures in high-throughput datasets. However, most existing graphical models make one of two canonical assumptions: (i) a homogeneous graph with a common network for all subjects or (ii) an assumption of normality, especially in the context of Gaussian graphical models. Both assumptions are restrictive and can fail to hold in certain applications such as proteomic networks in cancer. To this end, we propose an approach termed robust Bayesian graphical regression (rBGR) to estimate heterogeneous graphs for non-normally distributed data. rBGR is a flexible framework that accommodates non-normality through random marginal transformations and constructs covariate-dependent graphs to accommodate heterogeneity through graphical regression techniques. We formulate a new characterization of edge dependencies in such models called conditional sign independence with covariates, along with an efficient posterior sampling algorithm. In simulation studies, we demonstrate that rBGR outperforms existing graphical regression models for data generated under various levels of non-normality in both edge and covariate selection. We use rBGR to assess proteomic networks in lung and ovarian cancers to systematically investigate the effects of immunogenic heterogeneity within tumors. Our analyses reveal several important protein-protein interactions that are differentially associated with the immune cell abundance; some corroborate existing biological knowledge, whereas others are novel findings.
图形模型是研究高通量数据集中复杂依赖结构的强大工具。然而，大多数现有的图形模型做出以下两种典型假设之一：（i）对所有受试者使用具有共同网络的同质图，或（ii）正态性假设，特别是在高斯图形模型的背景下。这两种假设都具有局限性，在某些应用中可能不成立，例如癌症中的蛋白质组网络。为此，我们提出了一种称为稳健贝叶斯图形回归（rBGR）的方法，用于估计非正态分布数据的异质图。rBGR是一个灵活的框架，通过随机边际变换来适应非正态性，并通过图形回归技术构建依赖协变量的图来适应异质性。我们为此类模型中的边依赖关系制定了一种新的特征描述，称为带协变量的条件符号独立性，以及一种高效的后验采样算法。在模拟研究中，我们证明了在边选择和协变量选择方面，对于在各种非正态水平下生成的数据，rBGR优于现有的图形回归模型。我们使用rBGR评估肺癌和卵巢癌中的蛋白质组网络，以系统地研究肿瘤内免疫原性异质性的影响。我们的分析揭示了几种与免疫细胞丰度差异相关的重要蛋白质 - 蛋白质相互作用；一些证实了现有的生物学知识，而另一些则是新发现。
