Unsupervised and Semisupervised Heterogeneity Analysis Based on Gaussian Graphical Models

许多复杂的疾病，如癌症，具有异质性，看似相似的患者，临床行为不同，对治疗的反应也不同。为了更好地理解疾病生物学，更有效地描述和治疗疾病，准确地建立疾病异质性模型至关重要，而组学数据的快速积累使这一目标成为可能。现有的研究仅限于分析简单的数据分布特性。该项目将通过适应组学测量如何连接来推进疾病异质性分析的范式。此外，研究者将全面研究多种数据情景，包括当某些患者的疾病结果（例如，生存）完全未知或已知时，以及当其他数据（例如，人口统计学和临床病史）也可用时。研究者将开发一套前沿的统计方法，并进行严格的理论和数值调查，以与现有方法进行比较。该项目将从根本上推进统计学的多个子领域，包括异质性分析、高维数据分析、模型选择、高维数据优化等。同样重要的是，开发的方法的应用将导致更准确地识别异质患者群体及其多种癌症类型的组学特征。这将有助于识别疾病亚型，选择治疗方法，预测疾病路径，对临床决策产生直接而深远的影响。利用TCGA（癌症基因组图谱）数据，研究者将提供重要的肺癌和皮肤癌异质性模型，对基础科学和临床研究人员有价值。此外，该项目将有利于耶鲁大学本科生和研究生的教育和培训，并促进更多的合作。异质性分析在统计学和生物医学中占有重要地位。高通量分析的发展使得进行更多信息分析成为可能，但也带来了许多统计方面的挑战。许多常用的方法仅限于边际测量，特别是均值和方差。在本项目中，基于最近成功的基于高斯图形模型的异质性分析，研究者将系统地开发基于高斯图形模型的无监督和半监督异质性分析。特别是，研究者将研究具有潜在效应和调节效应的复杂情景，并在层次下进行异质性分析。一系列建立在惩罚融合技术基础上的前沿方法将被开发出来。所开发的方法将在超高维设置下建立一致性。该项目还将开发高效的计算算法，并进行广泛的模拟和比较。研究人员计划分析肺癌和皮肤癌的TCGA（癌症基因组图谱）数据，并提供异质性模型以及变量选择和模型估计结果。这个项目下的统计调查将广泛地揭示高维统计、异质性模型、惩罚和基于网络的分析。数据分析将极大地推动癌症组学领域的发展。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Many complex diseases such as cancer are heterogeneous, with seemingly similar patients having different clinical behaviors and varying responses to treatment. To better understand disease biology and more effectively describe and treat diseases, it is of essential importance to accurately model disease heterogeneity, which has been made possible by the fast accumulation of omics data. The existing studies are limited by analyzing simple data distributional properties. This project will advance the paradigm of disease heterogeneity analysis by accommodating how omics measurements are connected. Additionally, the investigator will comprehensively study multiple data scenarios, including when disease outcome (for example, survival) is completely unknown or known for some patients, and when additional data (for instance, on demographics and clinical history) is also available. The investigator will develop a set of leading-edge statistical methods and conduct rigorous theoretical and numerical investigations to compare with existing approaches. This project will fundamentally advance multiple subfields of statistics, including heterogeneity analysis, analysis of high-dimensional data, model selection, and optimization with high-dimensional data. Equally importantly, applications of the developed methods will lead to more accurate identification of heterogeneous patient groups and their omics characteristics for multiple cancer types. This will facilitate the identification of disease subtypes, treatment selection, and prediction of disease paths, having a direct and profound impact on clinical decision-making. Taking advantage of TCGA (The Cancer Genome Atlas) data, the investigator will deliver important heterogeneity models for lung and skin cancer, valuable to basic science and clinical researchers. Additionally, this project will benefit the education and training of undergraduate and graduate students at Yale University, and foster additional collaborations.Heterogeneity analysis plays an important role in statistics and biomedicine. The development of high-throughput profiling has made it possible to conduct more informative analysis but has also brought numerous statistical challenges. Many commonly used methods are limited to marginal measures especially mean and variance. In this project, building on a recent successful GGM (Gaussian Graphical Model)-based heterogeneity analysis, the investigator will systematically develop GGM-based unsupervised and semisupervised heterogeneity analysis. In particular, the investigator will examine the complicated scenarios with the presence of latent effects and regulating effects as well as heterogeneity analysis under a hierarchy. A series of leading-edge methods built on the penalized fusion technique will be developed. The consistency properties of developed methods will be established under ultrahigh-dimensional settings. The project will also develop efficient computational algorithms and conduct extensive simulations and comparisons. The investigator plans to analyze the TCGA (The Cancer Genome Atlas) data on lung and skin cancer and deliver heterogeneity models along with variable selection and model estimation results. Statistical investigations under this project will broadly shed insight into high-dimensional statistics, heterogeneity modeling, penalization, and network-based analysis. Data analysis will significantly move the field of cancer omics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.