Fractal Characterizations of MAX Statistical Distribution in Genetic Association Studies

Two non-integer parameters are defined for MAX statistics, which are maxima of $d$ simpler test statistics. The first parameter, $d_{MAX}$, is the fractional number of tests, representing the equivalent numbers of independent tests in MAX. If the $d$ tests are dependent, $d_{MAX} < d$. The second parameter is the fractional degrees of freedom $k$ of the chi-square distribution $\chi^2_k$ that fits the MAX null distribution. These two parameters, $d_{MAX}$ and $k$, can be independently defined, and $k$ can be non-integer even if $d_{MAX}$ is an integer. We illustrate these two parameters using the example of MAX2 and MAX3 statistics in genetic case-control studies. We speculate that $k$ is related to the amount of ambiguity of the model inferred by the test. In the case-control genetic association, tests with low $k$ (e.g. $k=1$) are able to provide definitive information about the disease model, as versus tests with high $k$ (e.g. $k=2$) that are completely uncertain about the disease model. Similar to Heisenberg's uncertain principle, the ability to infer disease model and the ability to detect significant association may not be simultaneously optimized, and $k$ seems to measure the level of their balance

Bayesian model search and multilevel inference for SNP association studies

Technological advances in genotyping have given rise to hypothesis-based association studies of increasing scope. As a result, the scientific hypotheses addressed by these studies have become more complex and more difficult to address using existing analytic methodologies. Obstacles to analysis include inference in the face of multiple comparisons, complications arising from correlations among the SNPs (single nucleotide polymorphisms), choice of their genetic parametrization and missing data. In this paper 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, with the prior distribution on SNP inclusion in the model providing an intrinsic multiplicity correction. 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. We examine sensitivity of the NCOCS results to prior choice and method for imputing missing data. MISA is available in an R package on CRAN.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS322 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Statistical and Computational Methods for Genome-Wide Association Analysis

Technological and scientific advances in recent years have revolutionized genomics. For example, decreases in whole genome sequencing (WGS) costs have enabled larger WGS studies as well as larger imputation reference panels, which in turn provide more comprehensive genomic coverage from lower-cost genotyping methods. In addition, new technologies and large collaborative efforts such as ENCODE and GTEx have shed new light on regulatory genomics and the function of non-coding variation, and produced expansive publicly available data sets. These advances have introduced data of unprecedented size and dimension, unique statistical and computational challenges, and numerous opportunities for innovation. In this dissertation, we develop methods to leverage functional genomics data in post-GWAS analysis, to expedite routine computations with increasingly large genetic data sets, and to address limitations of current imputation reference panels for understudied populations. In Chapter 2, we propose strategies to improve imputation and increase power in GWAS of understudied populations. Genotype imputation is instrumental in GWAS, providing increased genomic coverage from low-cost genotyping arrays. Imputation quality depends crucially on reference panel size and the genetic distance between reference and target haplotypes. Current reference panels provide excellent imputation quality in many European populations, but lower quality in non-European, admixed, and isolate populations. We consider a GWAS strategy in which a subset of participants is sequenced and the rest are imputed using a reference panel that comprises the sequenced participants together with individuals from an external reference panel. Using empirical data from the HRC and TOPMed WGS Project, simulations, and asymptotic analysis, we identify powerful and cost-effective study designs for GWAS of non-European, admixed, and isolated populations. In Chapter 3, we develop efficient methods to estimate linkage disequilibrium (LD) with large data sets. Motivated by practical and logistical constraints, a variety of statistical methods and tools have been developed for analysis of GWAS summary statistics rather than individual-level data. These methods often rely on LD estimates from an external reference panel, which are ideally calculated on-the-fly rather than precomputed and stored. We develop efficient algorithms to estimate LD exploiting sparsity and haplotype structure and implement our methods in an open-source C++ tool, emeraLD. We benchmark performance using genotype data from the 1KGP, HRC, and UK Biobank, and find that emeraLD is up to two orders of magnitude faster than existing tools while using comparable or less memory. In Chapter 4, we develop methods to identify causative genes and biological mechanisms underlying associations in post-GWAS analysis by leveraging regulatory and functional genomics databases. Many gene-based association tests can be viewed as instrumental variable methods in which intermediate phenotypes, e.g. tissue-specific expression or protein alteration, are hypothesized to mediate the association between genotype and GWAS trait. However, LD and pleiotropy can confound these statistics, which complicates their mechanistic interpretation. We develop a hierarchical Bayesian model that accounts for multiple potential mechanisms underlying associations using functional genomic annotations derived from GTEx, Roadmap/ENCODE, and other sources. We apply our method to analyze twenty-five complex traits using GWAS summary statistics from UK Biobank, and provide an open-source implementation of our methods. In Chapter 5, we review our work, discuss its relevance and prospects as new resources emerge, and suggest directions for future research.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147697/1/corbinq_1.pd

The Escherichia coli transcriptome mostly consists of independently regulated modules

Underlying cellular responses is a transcriptional regulatory network (TRN) that modulates gene expression. A useful description of the TRN would decompose the transcriptome into targeted effects of individual transcriptional regulators. Here, we apply unsupervised machine learning to a diverse compendium of over 250 high-quality Escherichia coli RNA-seq datasets to identify 92 statistically independent signals that modulate the expression of specific gene sets. We show that 61 of these transcriptomic signals represent the effects of currently characterized transcriptional regulators. Condition-specific activation of signals is validated by exposure of E. coli to new environmental conditions. The resulting decomposition of the transcriptome provides: a mechanistic, systems-level, network-based explanation of responses to environmental and genetic perturbations; a guide to gene and regulator function discovery; and a basis for characterizing transcriptomic differences in multiple strains. Taken together, our results show that signal summation describes the composition of a model prokaryotic transcriptome

Unconventional machine learning of genome-wide human cancer data

Recent advances in high-throughput genomic technologies coupled with exponential increases in computer processing and memory have allowed us to interrogate the complex aberrant molecular underpinnings of human disease from a genome-wide perspective. While the deluge of genomic information is expected to increase, a bottleneck in conventional high-performance computing is rapidly approaching. Inspired in part by recent advances in physical quantum processors, we evaluated several unconventional machine learning (ML) strategies on actual human tumor data. Here we show for the first time the efficacy of multiple annealing-based ML algorithms for classification of high-dimensional, multi-omics human cancer data from the Cancer Genome Atlas. To assess algorithm performance, we compared these classifiers to a variety of standard ML methods. Our results indicate the feasibility of using annealing-based ML to provide competitive classification of human cancer types and associated molecular subtypes and superior performance with smaller training datasets, thus providing compelling empirical evidence for the potential future application of unconventional computing architectures in the biomedical sciences