Multivariate Extensions of the Mixed Model for Quantitative Traits

The mixed model for complex segregation analysis of quantitative data from three-generational nuclear families is extended to the multivariate case. Likelihood functions for hypothesis testing are derived for two types of conditional analysis of multiple traits: first when entry to the study depends on the index case's values of all the quantitative traits that are of interest, and second when entry depends on only one trait, but other correlated traits are to be studied simultaneously. Using direct products of covariance matrices, these functions are seen to be direct multivariate equivalence of the univariate functions.     

Linear Equality Constraints in the General Linear Mixed Model

Scientists may wish to analyze correlated outcome data with constraints among the responses. For example, piecewise linear regression in a longitudinal data analysis can require use of a general linear mixed model combined with linear parameter constraints. Although well developed for standard univariate models, there are no general results that allow a data analyst to specify a mixed model equation in conjunction with a set of constraints on the parameters. We resolve the difficulty by precisely describing conditions that allow specifying linear parameter constraints that insure the validity of estimates and tests in a general linear mixed model. The recommended approach requires only straightforward and noniterative calculations to implement. We illustrate the convenience and advantages of the methods with a comparison of cognitive developmental patterns in a study of individuals from infancy to early adulthood for children from low-income families.     

Bayesian Inference for Generalized Linear Mixed Model Based on the Multivariate t Distribution in Population Pharmacokinetic Study

This article provides a fully Bayesian approach for modeling of single-dose and complete pharmacokinetic data in a population pharmacokinetic (PK) model. To overcome the impact of outliers and the difficulty of computation, a generalized linear model is chosen with the hypothesis that the errors follow a multivariate Student t distribution which is a heavy-tailed distribution. The aim of this study is to investigate and implement the performance of the multivariate t distribution to analyze population pharmacokinetic data. Bayesian predictive inferences and the Metropolis-Hastings algorithm schemes are used to process the intractable posterior integration. The precision and accuracy of the proposed model are illustrated by the simulating data and a real example of theophylline data.     

Efficient Multiple-Trait Association and Estimation of Genetic Correlation Using the Matrix-Variate Linear Mixed Model

Multiple-trait association mapping, in which multiple traits are used simultaneously in the identification of genetic variants affecting those traits, has recently attracted interest. One class of approaches for this problem builds on classical variance component methodology, utilizing a multitrait version of a linear mixed model. These approaches both increase power and provide insights into the genetic architecture of multiple traits. In particular, it is possible to estimate the genetic correlation, which is a measure of the portion of the total correlation between traits that is due to additive genetic effects. Unfortunately, the practical utility of these methods is limited since they are computationally intractable for large sample sizes. In this article, we introduce a reformulation of the multiple-trait association mapping approach by defining the matrix-variate linear mixed model. Our approach reduces the computational time necessary to perform maximum-likelihood inference in a multiple-trait model by utilizing a data transformation. By utilizing a well-studied human cohort, we show that our approach provides more than a 10-fold speedup, making multiple-trait association feasible in a large population cohort on the genome-wide scale. We take advantage of the efficiency of our approach to analyze gene expression data. By decomposing gene coexpression into a genetic and environmental component, we show that our method provides fundamental insights into the nature of coexpressed genes. An implementation of this method is available at http://genetics.cs.ucla.edu/mvLMM.     

Accounting for Population Structure in Gene-by-Environment Interactions in Genome-Wide Association Studies Using Mixed Models

Although genome-wide association studies (GWASs) have discovered numerous novel genetic variants associated with many complex traits and diseases, those genetic variants typically explain only a small fraction of phenotypic variance. Factors that account for phenotypic variance include environmental factors and gene-by-environment interactions (GEIs). Recently, several studies have conducted genome-wide gene-by-environment association analyses and demonstrated important roles of GEIs in complex traits. One of the main challenges in these association studies is to control effects of population structure that may cause spurious associations. Many studies have analyzed how population structure influences statistics of genetic variants and developed several statistical approaches to correct for population structure. However, the impact of population structure on GEI statistics in GWASs has not been extensively studied and nor have there been methods designed to correct for population structure on GEI statistics. In this paper, we show both analytically and empirically that population structure may cause spurious GEIs and use both simulation and two GWAS datasets to support our finding. We propose a statistical approach based on mixed models to account for population structure on GEI statistics. We find that our approach effectively controls population structure on statistics for GEIs as well as for genetic variants.     

A Model for Analysis of Population Structure

Arguments have been presented for the appropriateness of a multinomial Dirichlet distribution for describing single-locus genotypic frequencies in a subdivided population. This distribution is defined as a function of allele frequency, the average (over the entire population) inbreeding coefficient and the correlation between genotypes within a subdivision. Alternative parameterizations and their genetic interpretations are given.-We then show how information from a sample drawn from this subdivided population, in the absence of pedigrees, can be combined with the multinomial Dirichlet model to form a likelihood function. This likelihood function is then used as the basis for estimation and testing hypotheses concerning the genetic parameters of the model. Comparisons of this approach to the alternative procedure of Cockerham (1969) and (1973) are made using human data obtained from Tecumseh, Michigan and Monte Carlo simulations.-Finally, implications of these results to statistical inference and to mutation rates are presented.     

利用DH或RIL群体检测QTL体系并估计其遗传效应

利用ＤＨ和ＲＩＫＬ群体并结合重复内分组随机区组设计对和物产量等遗传率较低的数量性状进行分离分析可提高遗传分析的精度。根据混合分布理论菜了利用ＤＨ或ＲＩＬ群体重复实验数据鉴定数量性状混合遗传模型的分离分析法,特别是２对链锁主基因＋多基因模型。该方法可鉴定数量性状的遗传模型和主基因的作用方式,估计主基因、多基因的遗传疚和遗传方差,在两主基因存在连锁可可估计其重组率。下面通过应用举例说明该方法。     

Analysis of a Generalized Linear Mixed Model: A Case Study and Simulation Results

A class of generalized linear mixed models can be obtained by introducing random effects in the linear predictor of a generalized linear model, e.g. a split plot model for binary data or count data. Maximum likelihood estimation, for normally distributed random effects, involves high-dimensional numerical integration, with severe limitations on the number and structure of the additional random effects. An alternative estimation procedure based on an extension of the iterative re-weighted least squares procedure for generalized linear models will be illustrated on a practical data set involving carcass classification of cattle. The data is analysed as overdispersed binomial proportions with fixed and random effects and associated components of variance on the logit scale. Estimates are obtained with standard software for normal data mixed models. Numerical restrictions pertain to the size of matrices to be inverted. This can be dealt with by absorption techniques familiar from e.g. mixed models in animal breeding. The final model fitted to the classification data includes four components of variance and a multiplicative overdispersion factor. Basically the estimation procedure is a combination of iterated least squares procedures and no full distributional assumptions are needed. A simulation study based on the classification data is presented. This includes a study of procedures for constructing confidence intervals and significance tests for fixed effects and components of variance. The simulation results increase confidence in the usefulness of the estimation procedure.     

Linear Mixed Model Selection for False Discovery Rate Control in Microarray Data Analysis

Summary In a microarray experiment, one experimental design is used to obtain expression measures for all genes. One popular analysis method involves fitting the same linear mixed model for each gene, obtaining gene‐specific p‐values for tests of interest involving fixed effects, and then choosing a threshold for significance that is intended to control false discovery rate (FDR) at a desired level. When one or more random factors have zero variance components for some genes, the standard practice of fitting the same full linear mixed model for all genes can result in failure to control FDR. We propose a new method that combines results from the fit of full and selected linear mixed models to identify differentially expressed genes and provide FDR control at target levels when the true underlying random effects structure varies across genes.     

Comments on Extensions of the Allosteric Model for Haemoglobin

RECENTLY Edelstein¹ has concluded on the basis of a numerical analysis that the sequential model as formulated by Koshland, Nemethy and Filmer (KNF)² describes the oxygen binding curves of a number of species of human haemoglobin less well than does the two-state allosteric model of Monod, Wyman and Changeux (MWC)³. This communication demonstrates that Edelstein's analysis is incomplete and that extension of his analysis reveals that no such conclusion can be drawn from the data considered.     

Estimating and Correcting for Bias in Population Assessments of Sooty Shearwaters

Abstract: We investigated the precision and accuracy of an infrared burrowscope for detecting sooty shearwater (Pufffinus griseus) chicks at 13 plots from 3 islands in southern New Zealand in 2003. We partially excavated burrows systems to reveal the entire burrow contents after 2 teams of observers had prospected all burrow entrances. Accuracy was similar between islands and observer teams at approximately 85%. The majority of the inaccuracy stemmed from failure to detect some chicks. Logistic regression modeling identified 4 burrow characteristics occurring between the entrance and the nest-site that influenced detection of burrow occupants. Detection was lower at nest-sites further from burrow entrances, in burrows with a high rate of burrow division, and in burrows with a high level of curvature. There was a positive relationship between the interaction of rate of division and curvature and detection of chicks. Distance from the burrow entrance was the only parameter that could be reliably used as a predictor of detection rate, so a reduced model containing only this variable was constructed to correct for burrowscope bias. The correction factor performed well on The Snares and Bench Island where predicted bias was very similar to observed levels (within 5%), but bias was overestimated on Putauhinu by up to 19.1%. Consistent bias, lack of damage to burrows from excavation, and the successful application of a correction factor all indicate the value of further testing burrowscope accuracy on other burrow-nesting seabird species.     

A Novel and Fast Approach for Population Structure Inference Using Kernel-PCA and Optimization

Population structure is a confounding factor in genome-wide association studies, increasing the rate of false positive associations. To correct for it, several model-based algorithms such as ADMIXTURE and STRUCTURE have been proposed. These tend to suffer from the fact that they have a considerable computational burden, limiting their applicability when used with large datasets, such as those produced by next generation sequencing techniques. To address this, nonmodel based approaches such as sparse nonnegative matrix factorization (sNMF) and EIGENSTRAT have been proposed, which scale better with larger data. Here we present a novel nonmodel-based approach, population structure inference using kernel-PCA and optimization (PSIKO), which is based on a unique combination of linear kernel-PCA and least-squares optimization and allows for the inference of admixture coefficients, principal components, and number of founder populations of a dataset. PSIKO has been compared against existing leading methods on a variety of simulation scenarios, as well as on real biological data. We found that in addition to producing results of the same quality as other tested methods, PSIKO scales extremely well with dataset size, being considerably (up to 30 times) faster for longer sequences than even state-of-the-art methods such as sNMF. PSIKO and accompanying manual are freely available at https://www.uea.ac.uk/computing/psiko.     

Unbiasedness of the Estimator of the Function of Expected Value in the Mixed Linear Model

The traditional method for estimating the linear function of fixed parameters in mixed linear model is a two-stage procedure. In the first stage of this procedure the variance components estimators are calculated and next in the second stage these estimators are taken as true values of variance components to estimating the linear function of fixed parameters according to generalized least squares method. In this paper the general mixed linear model is considered in which a matrix related to fixed parameters and or/a dispersion matrix of observation vector may be deficient in rank. It is shown that the estimators of a set of functions of fixed parameters obtained in second stage are unbiased if only the observation vector is symmetrically distributed about its expected value and the estimators of variance components from first stage are translation-invariant and are even functions of the observation vector.     

Modeling Longitudinal Microbiome Compositional Data: A Two-Part Linear Mixed Model with Shared Random Effects

Longitudinal microbiome studies have been widely used to unveil the dynamics in the complex host-microbial ecosystems. Modeling the longitudinal microbiome compositional data, which is semi-continuous in nature, is challenging in several aspects: the overabundance of zeros, the heavy skewness of non-zero values that are bounded in (0, 1), and the dependence between the binary and non-zero parts. To deal with these challenges, we first extended the work of Chen and Li [1] and proposed a two-part zero-inflated Beta regression model with shared random effects (ZIBR-SRE), which characterize the dependence between the binary and the continuous parts. Besides, the microbiome compositional data have unit-sum constraint, indicating the existence of negative correlations among taxa. As ZIBR-SRE models each taxon separately, it does not satisfy the sum-to-one constraint. We then proposed a two-part linear mixed model (TPLMM) with shared random effects to formulate the log-transformed standardized relative abundances rather than the original ones. Such transformation is called “additive logistic transformation”, initially developed for cross-sectional compositional data. We extended it to analyze the longitudinal microbiome compositions and showed that the unit-sum constraint can be automatically satisfied under the TPLMM framework. Model performances of TPLMM and ZIBR-SRE were compared with existing methods in simulation studies. Under settings adopted from real data, TPLMM had the best performance and is recommended for practical use. An oral microbiome application further showed that TPLMM and ZIBR-SRE estimated a strong correlation structure in the binary and the continuous parts, suggesting models without accounting for this dependence would lead to biased inferences.