Bayesian Hidden Markov Modeling of Array CGH Data

Genomic alterations have been linked to the development and progression of cancer. The technique of Comparative Genomic Hybridization (CGH) yields data consisting of fluorescence intensity ratios of test and reference DNA samples. The intensity ratios provide information about the number of copies in DNA. Practical issues such as the contamination of tumor cells in tissue specimens and normalization errors necessitate the use of statistics for learning about the genomic alterations from array-CGH data. As increasing amounts of array CGH data become available, there is a growing need for automated algorithms for characterizing genomic profiles. Specifically, there is a need for algorithms that can identify gains and losses in the number of copies based on statistical considerations, rather than merely detect trends in the data. We adopt a Bayesian approach, relying on the hidden Markov model to account for the inherent dependence in the intensity ratios. Posterior inferences are made about gains and losses in copy number. Localized amplifications (associated with oncogene mutations) and deletions (associated with mutations of tumor suppressors) are identified using posterior probabilities. Global trends such as extended regions of altered copy number are detected. Since the posterior distribution is analytically intractable, we implement a Metropolis-within-Gibbs algorithm for efficient simulation-based inference. Publicly available data on pancreatic adenocarcinoma, glioblastoma multiforme and breast cancer are analyzed, and comparisons are made with some widely-used algorithms to illustrate the reliability and success of the technique.

A unified approach to modeling multivariate binary data using copulas over partitions

Many seemingly disparate approaches for marginal modeling have been developed in recent years. We demonstrate that many current approaches for marginal modeling of correlated binary outcomes produce likelihoods that are equivalent to the proposed copula-based models herein. These general copula models of underlying latent threshold random variables yield likelihood based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalized models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate concepts.

Modeling multilevel sleep transitional data via Poisson log-linear multilevel models

This paper proposes Poisson log-linear multilevel models to investigate population variability in sleep state transition rates. We specifically propose a Bayesian Poisson regression model that is more flexible, scalable to larger studies, and easily fit than other attempts in the literature. We further use hierarchical random effects to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of epidemiologic importance. We estimate essentially non-parametric piecewise constant hazards and smooth them, and allow for time varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming piecewise constant hazards. This relationship allows us to synthesize two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed.

Longitudinal data on telomere length in leukocytes from newborn baboons support a marked drop in stem cell turnover around 1 year of age

Stem cells of various tissues are typically defined as multipotent cells with 'self-renewal' properties. Despite the increasing interest in stem cells, surprisingly little is known about the number of times stem cells can or do divide over a lifetime. Based on telomere-length measurements of hematopoietic cells, we previously proposed that the self-renewal capacity of hematopoietic stem cells is limited by progressive telomere attrition and that such cells divide very rapidly during the first year of life. Recent studies of patients with aplastic anemia resulting from inherited mutations in telomerase genes support the notion that the replicative potential of hematopoietic stem cells is directly related to telomere length, which is indirectly related to telomerase levels. To revisit conclusions about stem cell turnover based on cross-sectional studies of telomere length, we performed a longitudinal study of telomere length in leukocytes from newborn baboons. All four individual animals studied showed a rapid decline in telomere length (approximately 2-3 kb) in granulocytes and lymphocytes in the first year after birth. After 50-70 weeks the telomere length appeared to stabilize in all cell types. These observations suggest that hematopoietic stem cells, after an initial phase of rapid expansion, switch at around 1 year of age to a different functional mode characterized by a markedly decreased turnover rate.