We discuss the theoretical structure and constructive methodology for large-scale graphical models, motivated by their potential in evaluating and aiding the exploration of patterns of association in gene expression data. The theoretical discussion covers basic ideas and connections between Gaussian graphical models, dependency networks and specific classes of directed acyclic graphs we refer to as compositional networks. We describe a constructive approach to generating interesting graphical models for very high-dimensional distributions that builds on the relationships between these various stylized graphical representations. Issues of consistency of models and priors across dimension are key. The resulting methods are of value in evaluating patterns of association in large-scale gene expression data with a view to generating biological insights about genes related to a known molecular pathway or set of specified genes. Some initial examples relate to the estrogen receptor pathway in breast cancer, and the Rb-E2F cell proliferation control pathway. r 2004 Elsevier Inc. All rights reserved.

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Despite the strikingly grave prognosis for older patients with glioblastomas, significant variability in patient outcome is experienced. To explore the potential for developing improved prognostic capabilities based on the elucidation of potential biological relationships, we did analyses of genes commonly mutated, amplified, or deleted in glioblastomas and DNA microarray gene expression data from tumors of glioblastoma patients of age >50 for whom survival is known. No prognostic significance was associated with genetic changes in epidermal growth factor receptor (amplified in 17 of 41 patients), TP53 (mutated in 11 of 41 patients), p16INK4A (deleted in 15 of 33 patients), or phosphatase and tensin homologue (mutated in 15 of 41 patients). Statistical analysis of the gene expression data in connection with survival involved exploration of regression models on small subsets of genes, based on computational search over multiple regression models with cross-validation to assess predictive validity. The analysis generated a set of regression models that, when weighted and combined according to posterior probabilities implied by the statistical analysis, identify patterns in expression of a small subset of genes that are associated with survival and have value in assessing survival risks. The dominant genes across such multiple regression models involve three key genes-SPARC (Osteonectin), Doublecortex, and Semaphorin3B-which play key roles in cellular migration processes. Additional analysis, based on statistical graphical association models constructed using similar computational analysis methods, reveals other genes which support the view that multiple mediators of tumor invasion may be important prognostic factor in glioblastomas in older patients. (Cancer Res 2005; 65(10): 4051-8)

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We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models (CGGMs) and embed graphical model selection inside a semiparametric Gaussian copula. The domain of applicability of our methods is very broad and encompasses many studies from social science and economics. We illustrate the use of the copula Gaussian graphical models in the analysis of a 16-dimensional functional disability contingency table.

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated with graphs that can be decomposable or non-decomposable. We extend our sampling algorithms to a novel class of conditionally autoregressive models for sparse estimation in multivariate lattice data, with a special emphasis on the analysis of spatial data. These models embed a great deal of flexibility in estimating both the correlation structure across outcomes and the spatial correlation structure, thereby allowing for adaptive smoothing and spatial autocorrelation parameters. Our methods are illustrated using a simulated example and a real-world application which concerns cancer mortality surveillance. Supplementary materials with computer code and the datasets needed to replicate our numerical results together with additional tables of results are available online.

Existing public health systems fail to properly account for migration, and actionable knowledge of the health requirements of migrants is still lacking. A large body of research has shown that migrants are more likely to enter into the healthcare system late and are less likely to be retained at successive stages of the HIV treatment cascade. HIV-infected migrants are especially vulnerable to a wide range of social, economic and political factors that include a lack of direct access to healthcare services; exposure to difficult or oppressive work environments; the separation from family, friends and a familiar sociocultural environment. Realizing the full treatment and preventive benefits of the UNAIDS 90-90-90 strategy will require reaching all marginalized subpopulations of which migrants are a particularly large and important group.

Objective:To quantify the space-time dimensions of human mobility in relationship to the risk of HIV acquisition.Methods:We used data from the population cohort located in a high HIV prevalence, rural population in KwaZulu-Natal, South Africa (2000–2014). We geolocated 8006 migration events (representing 1 028 782 km traveled) for 17 743 individuals (≥15 years of age) who were HIV negative at baseline and followed up these individuals for HIV acquisition (70 395 person-years). Based on the complete geolocated residential history of every individual in this cohort, we constructed two detailed time-varying migration indices. We then used interval-censored Cox proportional hazards models to quantify the relationship between the migration indices and the risk of HIV acquisition.Results:In total, 17.4% of participants migrated at least once outside the rural study community during the period of observation (median migration distance = 107.1 km, interquartile range 18.9–387.5). The two migration indices were highly predictive of hazard of HIV acquisition (P < 0.01) in both men and women. Holding other factors equal, the risk of acquiring HIV infection increased by 50% for migration distances of 40 km (men) and 109 km (women). HIV acquisition risk also increased by 50% when participants spent 44% (men) and 90% (women) of their respective time outside the rural study community.Conclusion:This in-depth analysis of a population cohort in a rural sub-Saharan African population has revealed a clear nonlinear relationship between distance migrated and HIV acquisition. Our findings show that even relatively short-distance migration events confer substantial additional risk of acquisition.