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Summary Cancer is molecularly heterogeneous, with seemingly similar patients having different molecular landscapes and accordingly different clinical behaviors. In recent studies, gene expression networks have been shown as more effective/informative for cancer heterogeneity analysis than some simpler measures. Gene interconnections can be classified as “direct” and “indirect,” where the latter can be caused by shared genomic regulators (such as transcription factors, microRNAs, and other regulatory molecules) and other mechanisms. It has been suggested that incorporating the regulators of gene expressions in network analysis and focusing on the direct interconnections can lead to a deeper understanding of the more essential gene interconnections. Such analysis can be seriously challenged by the large number of parameters (jointly caused by network analysis, incorporation of regulators, and heterogeneity) and often weak signals. To effectively tackle this problem, we propose incorporating prior information contained in the published literature. A key challenge is that such prior information can be partial or even wrong. We develop a two-step procedure that can flexibly accommodate different levels of prior information quality. Simulation demonstrates the effectiveness of the proposed approach and its superiority over relevant competitors. In the analysis of a breast cancer dataset, findings different from the alternatives are made, and the identified sample subgroups have important clinical differences. 

Beyond the main genetic and environmental effects, gene–environment (G–E) interactions have been demonstrated to significantly contribute to the development and progression of complex diseases. Published analyses of G–E interactions have primarily used a supervised framework to model both low-dimensional environmental factors and high-dimensional genetic factors in relation to disease outcomes. In this article, we aim to provide a selective review of methodological developments in G–E interaction analysis from a statistical perspective. The three main families of techniques are hypothesis testing, variable selection, and dimension reduction, which lead to three general frameworks: testing-based, estimation-based, and prediction-based. Linear- and nonlinear-effects analysis, fixed- and random-effects analysis, marginal and joint analysis, and Bayesian and frequentist analysis are reviewed to facilitate the conduct of interaction analysis in a wide range of situations with various assumptions and objectives. Statistical properties, computations, applications, and future directions are also discussed. 

Network estimation has been a critical component of high-dimensional data analysis and can provide an understanding of the underlying complex dependence structures. Among the existing studies, Gaussian graphical models have been highly popular. However, they still have limitations due to the homogeneous distribution assumption and the fact that they are only applicable to small-scale data. For example, cancers have various levels of unknown heterogeneity, and biological networks, which include thousands of molecular components, often differ across subgroups while also sharing some commonalities. In this article, we propose a new joint estimation approach for multiple networks with unknown sample heterogeneity, by decomposing the Gaussian graphical model (GGM) into a collection of sparse regression problems. A reparameterization technique and a composite minimax concave penalty are introduced to effectively accommodate the specific and common information across the networks of multiple subgroups, making the proposed estimator significantly advancing from the existing heterogeneity network analysis based on the regularized likelihood of GGM directly and enjoying scale-invariant, tuning-insensitive, and optimization convexity properties. The proposed analysis can be effectively realized using parallel computing. The estimation and selection consistency properties are rigorously established. The proposed approach allows the theoretical studies to focus on independent network estimation only and has the significant advantage of being both theoretically and computationally applicable to large-scale data. Extensive numerical experiments with simulated data and the TCGA breast cancer data demonstrate the prominent performance of the proposed approach in both subgroup and network identifications. 

Cancer heterogeneity analysis is essential for precision medicine. Most of the existing heterogeneity analyses only consider a single type of data and ignore the possible sparsity of important features. In cancer clinical practice, it has been suggested that two types of data, pathological imaging and omics data, are commonly collected and can produce hierarchical heterogeneous structures, in which the refined sub‐subgroup structure determined by omics features can be nested in the rough subgroup structure determined by the imaging features. Moreover, sparsity pursuit has extraordinary significance and is more challenging for heterogeneity analysis, because the important features may not be the same in different subgroups, which is ignored by the existing heterogeneity analyses. Fortunately, rich information from previous literature (for example, those deposited in PubMed) can be used to assist feature selection in the present study. Advancing from the existing analyses, in this study, we propose a novel sparse hierarchical heterogeneity analysis framework, which can integrate two types of features and incorporate prior knowledge to improve feature selection. The proposed approach has satisfactory statistical properties and competitive numerical performance. A TCGA real data analysis demonstrates the practical value of our approach in analyzing data heterogeneity and sparsity. 

In biomedical research the analysis of disease prevalence is of critical importance. While most of the existing prevalence studies focus on individual diseases, there has been increasing effort that jointly examines the prevalence values and their trends of multiple diseases. Such joint analysis can provide valuable insights not shared by individual-disease analysis. A critical limitation of the existing analysis is that there is a lack of attention to existing information, which has been accumulated through a large number of studies and can be valuable especially when there are a large number of diseases but the number of prevalence values for a specific disease is limited. In this study we conduct the functional clustering analysis of prevalence trends for a large number of diseases. A novel approach based on the penalized fusion technique is developed to incorporate information mined from published articles. It is innovatively designed to take into account that such information may not be fully relevant or correct. Another significant development is that statistical properties are rigorously established. Simulation is conducted and demonstrates its competitive performance. In the analysis of data from Taiwan NHIRD (National Health Insurance Research Database), new and interesting findings that differ from the existing ones are made. 

Online health communities (OHCs) provide free, open, and well-resourced platforms for patients, family members, and others to discuss illnesses, express feelings, and connect with others. Linguistic analysis of OHC posts can assist in better understanding disease conditions as well as monitoring the emotional and mental status of patients and those who are closely related. Many existing OHC linguistic analyses are limited by focusing on individual words. There are a handful of cooccurrence network analyses, which have multiple methodological limitations. In this article we analyze posts that are publicly available at the LUNGevity Foundation’s Lung Cancer Support Community (LCSC). The analyzed data contains 21,028 posts published between April 2018 and February 2022. For word cooccurrence network analysis, we develop a two-part latent space model, which advances from the existing ones by accommodating network weights. Further, we consider the scenario where there are change points in time, networks remain the same between two change points but differ on the two sides of a change point, and the number and locations of change points are unknown. A penalized fusion approach is developed to data-dependently determine change points and estimate networks. In data analysis multiple change points are identified, which reflect significant changes in lung cancer patients’ and their close affiliates’ emotional/mental status and mostly align with the changes in COVID-19. The obtained network structures and other findings are also sensible.