Adrian Dobra

Gene expression profiling and genetic markers in glioblastoma survival

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.

Experiments in Stochastic Computation for High-Dimensional Graphical Models

We discuss the implementation, development and performance of methods of stochastic computation in Gaussian graphical models. We view these methods from the perspective of high-dimensional model search, with a particular interest in the scalability with dimension of Markov chain Monte Carlo (MCMC) and other stochastic search methods. After reviewing the structure and context of undirected Gaussian graphical models and model uncertainty (covariance selection), we discuss prior specifications, including new priors over models, and then explore a number of examples using various methods of stochastic computation. Traditional MCMC methods are the point of departure for this experimentation; we then develop alternative stochastic search ideas and contrast this new approach with MCMC. Our examples range from low (12–20) to moderate (150) dimension, and combine simple synthetic examples with data analysis from gene expression studies. We conclude with comments about the need and potential for new computational methods in far higher dimensions, including constructive approaches to Gaussian graphical modeling and computation.

Shotgun stochastic search for "large p" regression

Model search in regression with very large numbers of candidate predictors raises challenges for both model specification and computation, for which standard approaches such as Markov chain Monte Carlo (MCMC) methods are often infeasible or ineffective. We describe a novel shotgun stochastic search (SSS) approach that explores “interesting” regions of the resulting high-dimensional model spaces and quickly identifies regions of high posterior probability over models. We describe algorithmic and modeling aspects, priors over the model space that induce sparsity and parsimony over and above the traditional dimension penalization implicit in Bayesian and likelihood analyses, and parallel computation using cluster computers. We discuss an example from gene expression cancer genomics, comparisons with MCMC and other methods, and theoretical and simulation-based aspects of performance characteristics in large-scale regression model searches. We also provide software implementing the methods.

Copula Gaussian graphical models and their application to modeling functional disability data

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.

Bayesian Inference for General Gaussian Graphical Models With Application to Multivariate Lattice Data

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.

A Divide-and-Conquer Algorithm for Generating Markov Bases of Multi-way Tables

SummaryWe describe a divide-and-conquer technique for generating a Markov basis that connects all tables of counts having a fixed set of marginal totals. This procedure is based on decomposing the independence graph induced by these marginals. We discuss the practical imports of using this method in conjunction with other algorithms for determining Markov bases.

Computational Aspects Related to Inference in Gaussian Graphical Models With the G-Wishart Prior

We describe a comprehensive framework for performing Bayesian inference for Gaussian graphical models based on the G-Wishart prior with a special focus on efficiently including nondecomposable graphs in the model space. We develop a new approximation method to the normalizing constant of a G-Wishart distribution based on the Laplace approximation. We review recent developments in stochastic search algorithms and propose a new method, the mode oriented stochastic search (MOSS), that extends these techniques and proves superior at quickly finding graphical models with high posterior probability. We then develop a novel stochastic search technique for multivariate regression models and conclude with a real-world example from the recent covariance estimation literature. Supplemental materials are available online.

Transcriptome profiling of human hippocampus dentate gyrus granule cells in mental illness

This study is, to the best of our knowledge, the first application of whole transcriptome sequencing (RNA-seq) to cells isolated from postmortem human brain by laser capture microdissection. We investigated the transcriptome of dentate gyrus (DG) granule cells in postmortem human hippocampus in 79 subjects with mental illness (schizophrenia, bipolar disorder, major depression) and nonpsychiatric controls. We show that the choice of normalization approach for analysis of RNA-seq data had a strong effect on results; under our experimental conditions a nonstandard normalization method gave superior results. We found evidence of disrupted signaling by miR-182 in mental illness. This was confirmed using a novel method of leveraging microRNA genetic variant information to indicate active targeting. In healthy subjects and those with bipolar disorder, carriers of a high- vs those with a low-expressing genotype of miR-182 had different levels of miR-182 target gene expression, indicating an active role of miR-182 in shaping the DG transcriptome for those subject groups. By contrast, comparing the transcriptome between carriers of different genotypes among subjects with major depression and schizophrenia suggested a loss of DG miR-182 signaling in these conditions.

Preserving confidentiality of high-dimensional tabulated data: Statistical and computational issues

Dissemination of information derived from large contingency tables formed from confidential data is a major responsibility of statistical agencies. In this paper we present solutions to several computational and algorithmic problems that arise in the dissemination of cross-tabulations (marginal sub-tables) from a single underlying table. These include data structures that exploit sparsity to support efficient computation of marginals and algorithms such as iterative proportional fitting, as well as a generalized form of the shuttle algorithm that computes sharp bounds on (small, confidentiality threatening) cells in the full table from arbitrary sets of released marginals. We give examples illustrating the techniques.

Bounding Entries in Multi-way Contingency Tables Given a Set of Marginal Totals

We describe new results for sharp upper and lower bounds on the entries in multi-way tables of counts based on a set of released and possibly overlapping marginal tables. In particular, we present a generalized version of the shuttle algorithm proposed by Buzzigoli and Giusti that computes sharp integer bounds for an arbitrary set of fixed marginals. We also present two examples which illustrate the practical import of the bounds for assessing disclosure risk.