Browsing by Author "Iversen, Edwin S"

Tremendous effort has been put into study of the etiology of complex

diseases including the breast cancer, type 2 diabetes,

cardiovascular diseases, and prostate cancers. Despite large numbers of reported disease-associated loci,

few associated loci have been replicated, and some true associations

does not belong to the group of the most significant loci

reported to be associated. We built a Bayesian hierarchical model incorporated

with SNP-level functional data that can help identify associated SNPs in pathway-wide association studies.

We applied the model to an association study for the serous invasive ovarian cancer based on the DNA repair and apoptosis pathways. We found that using our model, blocks of SNPs located in regions enriched for missense SNPs or gene inversions were more likely to be identified as candidates of the association.

As fundamental structural units of the chromatin, nucleosomes are involved in virtually all aspects of genome function. Different methods have been developed to map genome-wide nucleosome positions, including MNase-seq and a recent chemical method requiring genetically engineered cells. However, these methods are either low resolution and prone to enzymatic sequence bias or require genetically modified cells. The DNase I enzyme has been used to probe nucleosome structure since the 1960s, but in the current high throughput sequencing era, DNase-seq has mainly been used to study regulatory sequences known as DNase hypersensitive sites. This thesis shows that DNase-seq data is also very informative about nucleosome positioning. The distinctive oscillatory DNase I cutting patterns on nucleosomal DNA are shown and discussed. Based on these patterns, a Bayes factor is proposed to be used for distinguishing nucleosomal and non-nucleosomal genome positions. The results show that this approach is highly sensitive and specific. A Bayesian method that simulates the data generation process and can provide more interpretable results is further developed based on the Bayes factor investigations. Preliminary results on a test genomic region show that the Bayesian model works well in identifying nucleosome positioning. Estimated posterior distributions also agree with some known biological observations from external data. Taken together, methods developed in this thesis show that DNase-seq can be used to identify nucleosome positioning, adding great value to this widely utilized protocol.

The Bayesian approach to model selection allows for uncertainty in both model specific parameters and in the models themselves. Much of the recent Bayesian model uncertainty literature has focused on defining these prior distributions in an objective manner, providing conditions under which Bayes factors lead to the correct model selection, particularly in the situation where the number of variables, p, increases with the sample size, n. This is certainly the case in our area of motivation; the biological application of genetic association studies involving single nucleotide polymorphisms. While the most common approach to this problem has been to apply a marginal test to all genetic markers, we employ analytical strategies that improve upon these marginal methods by modeling the outcome variable as a function of a multivariate genetic profile using Bayesian variable selection. In doing so, we perform variable selection on a large number of correlated covariates within studies involving modest sample sizes.

In particular, we present an efficient Bayesian model search strategy that searches over the space of genetic markers and their genetic parametrization. The resulting method for Multilevel Inference of SNP Associations MISA, allows computation of multilevel posterior probabilities and Bayes factors at the global, gene and SNP level. We use simulated data sets to characterize MISA's statistical power, and show that MISA has higher power to detect association than standard procedures. Using data from the North Carolina Ovarian Cancer Study (NCOCS), MISA identifies variants that were not identified by standard methods and have been externally 'validated' in independent studies.

In the context of Bayesian model uncertainty for problems involving a large number of correlated covariates we characterize commonly used prior distributions on the model space and investigate their implicit multiplicity correction properties first in the extreme case where the model includes an increasing number of redundant covariates and then under the case of full rank design matrices. We provide conditions on the asymptotic (in n and p) behavior of the model space prior

required to achieve consistent selection of the global hypothesis of at least one associated variable in the analysis using global posterior probabilities (i.e. under 0-1 loss). In particular, under the assumption that the null model is true, we show that the commonly used uniform prior on the model space leads to inconsistent selection of the global hypothesis via global posterior probabilities (the posterior probability of at least one association goes to 1) when the rank of the design matrix is finite. In the full rank case, we also show inconsistency when p goes to infinity faster than the square root of n. Alternatively, we show that any model space prior such that the global prior odds of association increases at a rate slower than the square root of n results in consistent selection of the global hypothesis in terms of posterior probabilities.

Cell division is a biological process fundamental to all life. One aspect of the process that is still under investigation is whether or not cells in a lineage are correlated in their cell-cycle progression. Data on cell-cycle progression is typically acquired either in lineages of single cells or in synchronized cell populations, and each source of data offers complementary information on cell division. To formally assess dependence in cell-cycle progression, I develop a hierarchical statistical model of single-cell measurements and extend a previously proposed model of population cell division in the budding yeast, Saccharomyces cerevisiae. Both models capture correlation and cell-to-cell heterogeneity in cell-cycle progression, and parameter inference is carried out in a fully Bayesian manner. The single-cell model is fit to three published time-lapse microscopy datasets and the population-based model is fit to simulated data for which the true model is known. Based on posterior inferences and formal model comparisons, the single-cell analysis demonstrates that budding yeast mother and daughter cells do not appear to correlate in their cell-cycle progression in two of the three experimental settings. In contrast, mother cells grown in a less preferred sugar source, glycerol/ethanol, did correlate in their rate of cell division in two successive cell cycles. Population model fitting to simulated data suggested that, under typical synchrony experimental conditions, population-based measurements of the cell-cycle were not informative for correlation in cell-cycle progression or heterogeneity in daughter-specific G1 phase progression.