Heritability Estimation in High-dimensional Mixed Models PDF Download
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Author: Anna Bonnet
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
We study statistical methods toestimate the heritability of a biological trait,which is the proportion of variations of thistrait that can be explained by genetic factors.First, we propose to study the heritability ofquantitative traits using high-dimensionalsparse linear mixed models. We investigate thetheoretical properties of the maximumlikelihood estimator for the heritability and weshow that it is a consistent estimator and that itsatisfies a central limit theorem with a closedformexpression for the asymptotic variance.This result, supported by an extendednumerical study, shows that the variance of ourestimator is strongly affected by the ratiobetween the number of observations and thesize of the random genetic effects. Moreprecisely, when the number of observations issmall compared to the size of the geneticeffects (which is often the case in geneticstudies), the variance of our estimator is verylarge. This motivated the development of avariable selection method in order to capturethe genetic variants which are involved themost in the phenotypic variations and providemore accurate heritability estimations. Wepropose then a variable selection methodadapted to high dimensional settings and weshow that, depending on the number of geneticvariants actually involved in the phenotypicvariations, called causal variants, it was a goodidea to include or not a variable selection stepbefore estimating heritability.The last part of this thesis is dedicated toheritability estimation for binary data, in orderto study the proportion of genetic factorsinvolved in complex diseases. We propose tostudy the theoretical properties of the methoddeveloped by Golan et al. (2014) for casecontroldata, which is very efficient in practice.Our main result is the proof of the consistencyof their heritability estimator.
Author: Anna Bonnet
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
We study statistical methods toestimate the heritability of a biological trait,which is the proportion of variations of thistrait that can be explained by genetic factors.First, we propose to study the heritability ofquantitative traits using high-dimensionalsparse linear mixed models. We investigate thetheoretical properties of the maximumlikelihood estimator for the heritability and weshow that it is a consistent estimator and that itsatisfies a central limit theorem with a closedformexpression for the asymptotic variance.This result, supported by an extendednumerical study, shows that the variance of ourestimator is strongly affected by the ratiobetween the number of observations and thesize of the random genetic effects. Moreprecisely, when the number of observations issmall compared to the size of the geneticeffects (which is often the case in geneticstudies), the variance of our estimator is verylarge. This motivated the development of avariable selection method in order to capturethe genetic variants which are involved themost in the phenotypic variations and providemore accurate heritability estimations. Wepropose then a variable selection methodadapted to high dimensional settings and weshow that, depending on the number of geneticvariants actually involved in the phenotypicvariations, called causal variants, it was a goodidea to include or not a variable selection stepbefore estimating heritability.The last part of this thesis is dedicated toheritability estimation for binary data, in orderto study the proportion of genetic factorsinvolved in complex diseases. We propose tostudy the theoretical properties of the methoddeveloped by Golan et al. (2014) for casecontroldata, which is very efficient in practice.Our main result is the proof of the consistencyof their heritability estimator.
Author: Jiming Jiang
Publisher: Springer Nature
ISBN: 1071612824
Category : Medical
Languages : en
Pages : 343
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Book Description
This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models. It presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it includes recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis.
Author: Momiao Xiong
Publisher: CRC Press
ISBN: 1498725805
Category : Mathematics
Languages : en
Pages : 668
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Book Description
Big Data in Omics and Imaging: Association Analysis addresses the recent development of association analysis and machine learning for both population and family genomic data in sequencing era. It is unique in that it presents both hypothesis testing and a data mining approach to holistically dissecting the genetic structure of complex traits and to designing efficient strategies for precision medicine. The general frameworks for association analysis and machine learning, developed in the text, can be applied to genomic, epigenomic and imaging data. FEATURES Bridges the gap between the traditional statistical methods and computational tools for small genetic and epigenetic data analysis and the modern advanced statistical methods for big data Provides tools for high dimensional data reduction Discusses searching algorithms for model and variable selection including randomization algorithms, Proximal methods and matrix subset selection Provides real-world examples and case studies Will have an accompanying website with R code The book is designed for graduate students and researchers in genomics, bioinformatics, and data science. It represents the paradigm shift of genetic studies of complex diseases– from shallow to deep genomic analysis, from low-dimensional to high dimensional, multivariate to functional data analysis with next-generation sequencing (NGS) data, and from homogeneous populations to heterogeneous population and pedigree data analysis. Topics covered are: advanced matrix theory, convex optimization algorithms, generalized low rank models, functional data analysis techniques, deep learning principle and machine learning methods for modern association, interaction, pathway and network analysis of rare and common variants, biomarker identification, disease risk and drug response prediction.
Author: Jiming Jiang
Publisher: CRC Press
ISBN: 1498700462
Category : Mathematics
Languages : en
Pages : 252
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Book Description
Large sample techniques are fundamental to all fields of statistics. Mixed effects models, including linear mixed models, generalized linear mixed models, non-linear mixed effects models, and non-parametric mixed effects models are complex models, yet, these models are extensively used in practice. This monograph provides a comprehensive account of asymptotic analysis of mixed effects models. The monograph is suitable for researchers and graduate students who wish to learn about asymptotic tools and research problems in mixed effects models. It may also be used as a reference book for a graduate-level course on mixed effects models, or asymptotic analysis.
Author: D.R. Cox
Publisher: CRC Press
ISBN: 1482285940
Category : Mathematics
Languages : en
Pages : 181
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Book Description
The components of variance is a notion essential to statisticians and quantitative research scientists working in a variety of fields, including the biological, genetic, health, industrial, and psychological sciences. Co-authored by Sir David Cox, the pre-eminent statistician in the field, this book provides in-depth discussions that set forth the essential principles of the subject. It focuses on developing the models that form the basis for detailed analyses as well as on the statistical techniques themselves. The authors include a variety of examples from areas such as clinical trial design, plant and animal breeding, industrial design, and psychometrics.
Author: Eugene Demidenko
Publisher: John Wiley & Sons
ISBN: 1118091574
Category : Mathematics
Languages : en
Pages : 768
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Book Description
Praise for the First Edition “This book will serve to greatly complement the growing number of texts dealing with mixed models, and I highly recommend including it in one’s personal library.” —Journal of the American Statistical Association Mixed modeling is a crucial area of statistics, enabling the analysis of clustered and longitudinal data. Mixed Models: Theory and Applications with R, Second Edition fills a gap in existing literature between mathematical and applied statistical books by presenting a powerful examination of mixed model theory and application with special attention given to the implementation in R. The new edition provides in-depth mathematical coverage of mixed models’ statistical properties and numerical algorithms, as well as nontraditional applications, such as regrowth curves, shapes, and images. The book features the latest topics in statistics including modeling of complex clustered or longitudinal data, modeling data with multiple sources of variation, modeling biological variety and heterogeneity, Healthy Akaike Information Criterion (HAIC), parameter multidimensionality, and statistics of image processing. Mixed Models: Theory and Applications with R, Second Edition features unique applications of mixed model methodology, as well as: Comprehensive theoretical discussions illustrated by examples and figures Over 300 exercises, end-of-section problems, updated data sets, and R subroutines Problems and extended projects requiring simulations in R intended to reinforce material Summaries of major results and general points of discussion at the end of each chapter Open problems in mixed modeling methodology, which can be used as the basis for research or PhD dissertations Ideal for graduate-level courses in mixed statistical modeling, the book is also an excellent reference for professionals in a range of fields, including cancer research, computer science, and engineering.
Author: Osval Antonio Montesinos López
Publisher: Springer Nature
ISBN: 3030890104
Category : Technology & Engineering
Languages : en
Pages : 707
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Book Description
This book is open access under a CC BY 4.0 license This open access book brings together the latest genome base prediction models currently being used by statisticians, breeders and data scientists. It provides an accessible way to understand the theory behind each statistical learning tool, the required pre-processing, the basics of model building, how to train statistical learning methods, the basic R scripts needed to implement each statistical learning tool, and the output of each tool. To do so, for each tool the book provides background theory, some elements of the R statistical software for its implementation, the conceptual underpinnings, and at least two illustrative examples with data from real-world genomic selection experiments. Lastly, worked-out examples help readers check their own comprehension.The book will greatly appeal to readers in plant (and animal) breeding, geneticists and statisticians, as it provides in a very accessible way the necessary theory, the appropriate R code, and illustrative examples for a complete understanding of each statistical learning tool. In addition, it weighs the advantages and disadvantages of each tool.
Author: Riyan Cheng
Publisher: Frontiers Media SA
ISBN: 2889712125
Category : Science
Languages : en
Pages : 148
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Book Description
Author: Peter Bühlmann
Publisher: Springer Science & Business Media
ISBN: 364220192X
Category : Mathematics
Languages : en
Pages : 568
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Book Description
Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections. A special characteristic of the book is that it contains comprehensive mathematical theory on high-dimensional statistics combined with methodology, algorithms and illustrations with real data examples. This in-depth approach highlights the methods’ great potential and practical applicability in a variety of settings. As such, it is a valuable resource for researchers, graduate students and experts in statistics, applied mathematics and computer science.
Author: Juhyun Kim
Publisher:
ISBN:
Category :
Languages : en
Pages : 130
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Book Description
Variance component models are a fundamental topic in statistical genetics. These models enable us to estimate the underlying heritability of a phenotype, adjust for confounding in association testing, and assess the strength of effects of a set of genetic markers on a phenotype. Under the overarching theme of variance component models, this dissertation aims to elucidate the genetic architecture of complex diseases and traits by developing and applying variance component model-based methods to analyze high-dimensional genomic data. In the first half of the dissertation, we propose a variance component selection framework that jointly models and prioritizes a set of genetic markers that are associated with quantitative traits. The second half of the dissertation is devoted to quantifying the heritability of diabetes complications. We use various heritability estimation methods, some of which are based on variance component models.
