A fast algorithm for detecting gene-gene interactions in genome-wide association studies

With the recent advent of high-throughput genotyping techniques, genetic data for genome-wide association studies (GWAS) have become increasingly available, which entails the development of efficient and effective statistical approaches. Although many such approaches have been developed and used to identify single-nucleotide polymorphisms (SNPs) that are associated with complex traits or diseases, few are able to detect gene-gene interactions among different SNPs. Genetic interactions, also known as epistasis, have been recognized to play a pivotal role in contributing to the genetic variation of phenotypic traits. However, because of an extremely large number of SNP-SNP combinations in GWAS, the model dimensionality can quickly become so overwhelming that no prevailing variable selection methods are capable of handling this problem. In this paper, we present a statistical framework for characterizing main genetic effects and epistatic interactions in a GWAS study. Specifically, we first propose a two-stage sure independence screening (TS-SIS) procedure and generate a pool of candidate SNPs and interactions, which serve as predictors to explain and predict the phenotypes of a complex trait. We also propose a rates adjusted thresholding estimation (RATE) approach to determine the size of the reduced model selected by an independence screening. Regularization regression methods, such as LASSO or SCAD, are then applied to further identify important genetic effects. Simulation studies show that the TS-SIS procedure is computationally efficient and has an outstanding finite sample performance in selecting potential SNPs as well as gene-gene interactions. We apply the proposed framework to analyze an ultrahigh-dimensional GWAS data set from the Framingham Heart Study, and select 23 active SNPs and 24 active epistatic interactions for the body mass index variation. It shows the capability of our procedure to resolve the complexity of genetic control.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS771 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bayesian group Lasso for nonparametric varying-coefficient models with application to functional genome-wide association studies

Although genome-wide association studies (GWAS) have proven powerful for comprehending the genetic architecture of complex traits, they are challenged by a high dimension of single-nucleotide polymorphisms (SNPs) as predictors, the presence of complex environmental factors, and longitudinal or functional natures of many complex traits or diseases. To address these challenges, we propose a high-dimensional varying-coefficient model for incorporating functional aspects of phenotypic traits into GWAS to formulate a so-called functional GWAS or fGWAS. The Bayesian group lasso and the associated MCMC algorithms are developed to identify significant SNPs and estimate how they affect longitudinal traits through time-varying genetic actions. The model is generalized to analyze the genetic control of complex traits using subject-specific sparse longitudinal data. The statistical properties of the new model are investigated through simulation studies. We use the new model to analyze a real GWAS data set from the Framingham Heart Study, leading to the identification of several significant SNPs associated with age-specific changes of body mass index. The fGWAS model, equipped with the Bayesian group lasso, will provide a useful tool for genetic and developmental analysis of complex traits or diseases.Comment: Published at http://dx.doi.org/10.1214/15-AOAS808 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Growth and characterization of high-quality bulk hexagonal boron nitride crystals

Doctor of PhilosophyDepartment of Chemical EngineeringJames H. EdgarWhile hexagonal boron nitride (hBN) in polycrystalline form has met demand for its mechanical, chemical, and thermal applications, its new electronic, optoelectronic, and nanophotonic applications required single crystals with low residual impurity concentrations. Grain boundaries and impurities need to be minimized, as they degrade the properties of hBN that are important for these new applications. The present study was undertaken to develop large area, high quality hBN single crystals at low cost, and with control over its boron isotope concentrations. Furthermore, a preliminary study was undertaken to determine if the properties of hBN could be advantageously altered by irradiation. In this study, four processes to grow and manipulate the properties of hBN single crystals were developed. First, high-quality hBN crystals were grown from an iron metal flux. The quality of crystals produced by this novel, low cost and high purity solvent was equivalent to the best reported in the literature, as verified by Raman spectroscopy, photoluminescence, defect density assessment, and current-voltage measurements. Second, hBN crystals were grown via temperature gradient method with iron-chromium flux. This method has the potential to produce larger, higher quality crystals than the slow cooling method. The maximum crystal domain size was up to 4 mm. Both in- and out-plane thermal conductivity was significantly higher than the hBN grown by slow cooling, indicating improved crystallinity. Third, monoisotopic boron hBN (h¹⁰BN and h¹¹BN) was grown from both Fe and Fe-Cr fluxes. Raman and photoluminescence spectra show the quality of crystal grown from Fe and Fe-Cr fluxes was comparable. Fourth, neutron transmutation doping was studied as a possible method of altering the electrical and optical properties of hBN single crystals. Raman spectroscopy, photoluminescence, and electron paramagnetic resonance spectroscopies established that the effects of neutron irradiation were more pronounced on h¹⁰BN than h¹¹BN. Together, these studies demonstrate the versatility of methods available to produce high quality hBN single crystal with specific properties

Functional mapping of reaction norms to multiple environmental signals through nonparametric covariance estimation

<p>Abstract</p> <p>Background</p> <p>The identification of genes or quantitative trait loci that are expressed in response to different environmental factors such as temperature and light, through functional mapping, critically relies on precise modeling of the covariance structure. Previous work used separable parametric covariance structures, such as a Kronecker product of autoregressive one [AR(1)] matrices, that do not account for interaction effects of different environmental factors.</p> <p>Results</p> <p>We implement a more robust nonparametric covariance estimator to model these interactions within the framework of functional mapping of reaction norms to two signals. Our results from Monte Carlo simulations show that this estimator can be useful in modeling interactions that exist between two environmental signals. The interactions are simulated using nonseparable covariance models with spatio-temporal structural forms that mimic interaction effects.</p> <p>Conclusions</p> <p>The nonparametric covariance estimator has an advantage over separable parametric covariance estimators in the detection of QTL location, thus extending the breadth of use of functional mapping in practical settings.</p

A statistical model for mapping morphological shape

<p>Abstract</p> <p>Background</p> <p>Living things come in all shapes and sizes, from bacteria, plants, and animals to humans. Knowledge about the genetic mechanisms for biological shape has far-reaching implications for a range spectrum of scientific disciplines including anthropology, agriculture, developmental biology, evolution and biomedicine.</p> <p>Results</p> <p>We derived a statistical model for mapping specific genes or quantitative trait loci (QTLs) that control morphological shape. The model was formulated within the mixture framework, in which different types of shape are thought to result from genotypic discrepancies at a QTL. The EM algorithm was implemented to estimate QTL genotype-specific shapes based on a shape correspondence analysis. Computer simulation was used to investigate the statistical property of the model.</p> <p>Conclusion</p> <p>By identifying specific QTLs for morphological shape, the model developed will help to ask, disseminate and address many major integrative biological and genetic questions and challenges in the genetic control of biological shape and function.</p

EM Algorithm for Mapping Quantitative Trait Loci in Multivalent Tetraploids

Multivalent tetraploids that include many plant species, such as potato, sugarcane, and rose, are of paramount importance to agricultural production and biological research. Quantitative trait locus (QTL) mapping in multivalent tetraploids is challenged by their unique cytogenetic properties, such as double reduction. We develop a statistical method for mapping multivalent tetraploid QTLs by considering these cytogenetic properties. This method is built in the mixture model-based framework and implemented with the EM algorithm. The method allows the simultaneous estimation of QTL positions, QTL effects, the chromosomal pairing factor, and the degree of double reduction as well as the assessment of the estimation precision of these parameters. We used simulated data to examine the statistical properties of the method and validate its utilization. The new method and its software will provide a useful tool for QTL mapping in multivalent tetraploids that undergo double reduction