An EM algorithm for mapping quantitative resistance loci

Xu, Chenwu; Ym, Zhang; Xu, Shutu

doi:10.1038/sj.hdy.6800583

Cited by 13 publications

(16 citation statements)

References 23 publications

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“…So far, for the analyses of ordered categorical traits including binary and polychotomous discrete traits, threshold models have been mainly used (Dempster and Lerner, 1950;Gianola, 1979;Sorensen et al, 1995;Xu and Atchley, 1996;Yi and Xu, 2000;Rao and Li, 2001;Xu et al, 2005). In threshold models, phenotypic values are obtained by discretizing the liabilities with thresholds, where it is assumed that phenotypic values are monotonically related with liabilities.…”

Section: Discussionmentioning

confidence: 99%

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Interval mapping for loci affecting unordered categorical traits

Hayashi

Awata

2006

Heredity

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Many traits including shapes and colors of flowers, fruits and seeds in plants, as well as coat colors and some behavioral properties in animals, are recorded in discrete categories. If categories are ordered, genetic analyses of the categorical traits are often performed using the threshold model, which considers a latent continuous variable, called the liability, underlying a trait and assumes the monotonic relationship between the phenotype and the liability. In some categorical traits, however, descriptions of phenotypes are purely nominal and the phenotypic scores cannot be ordered. The threshold model is unreasonable for the analyses of such unordered categorical traits. In this study, we developed a method for interval mapping of loci affecting unordered categorical traits with more than two categories. The probability of the phenotype of an individual falling in each of the categories was expressed by a polychotomous logistic model, in which the log-odds for each category relative to the reference category were assumed to follow a linear model including genotype at a locus affecting a trait as covariate. Based on the model, the interval mapping using a maximum likelihood method was devised for the analysis of complex categorical traits described with unordered categories. We confined ourselves to the case of F2 populations derived from a cross between two inbred lines, although this approach can easily be extended to the analyses for other populations of general structures. As results of analyses of simulated data show, the method showed high efficiency in detecting the loci affecting unordered categorical traits.

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Section: Discussionmentioning

confidence: 99%

“…Yi and Xu (2000) devised a statistical procedure of Bayesian estimation for mapping binary trait loci using a similar model. The methods of interval mapping based on the threshold model were extended to the ordered categorical traits with more than two categories (Rao and Xu, 1998;Rao and Li, 2001;Xu et al, 2005).…”

Section: Introductionmentioning

confidence: 99%

Interval mapping for loci affecting unordered categorical traits

Hayashi

Awata

2006

Heredity

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“…In quantitative genetics, the latent presentation of the probit model is called the threshold model, which has been widely used to analyze the genetic architecture of binary and ordinal traits (Wright 1934;Lynch and Walsh 1998). Under the threshold model, one can treat the latent variable as an unobservable quantitative trait, and genes controlling ordinal traits can be treated as quantitative trait loci and handled using a QTL mapping approach.A number of statistical methods have been developed to identify QTL for binary or ordinal traits in experimental crosses based on the threshold model of single QTL (Hackett and Weller 1995;Xu and Atchley 1996;Rao and Xu 1998;Xu et al 2003Xu et al , 2005. Recently, several methods have been proposed to simultaneously identify multiple QTL for ordinal traits (Coffman et al 2005;Li et al 2006).…”

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confidence: 99%

“…A number of statistical methods have been developed to identify QTL for binary or ordinal traits in experimental crosses based on the threshold model of single QTL (Hackett and Weller 1995;Xu and Atchley 1996;Rao and Xu 1998;Xu et al 2003Xu et al , 2005. Recently, several methods have been proposed to simultaneously identify multiple QTL for ordinal traits (Coffman et al 2005;Li et al 2006).…”

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Bayesian Mapping of Genomewide Interacting Quantitative Trait Loci for Ordinal Traits

Banerjee

Pomp

et al. 2007

Genetics

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Development of statistical methods and software for mapping interacting QTL has been the focus of much recent research. We previously developed a Bayesian model selection framework, based on the composite model space approach, for mapping multiple epistatic QTL affecting continuous traits. In this study we extend the composite model space approach to complex ordinal traits in experimental crosses. We jointly model main and epistatic effects of QTL and environmental factors on the basis of the ordinal probit model (also called threshold model) that assumes a latent continuous trait underlies the generation of the ordinal phenotypes through a set of unknown thresholds. A data augmentation approach is developed to jointly generate the latent data and the thresholds. The proposed ordinal probit model, combined with the composite model space framework for continuous traits, offers a convenient way for genomewide interacting QTL analysis of ordinal traits. We illustrate the proposed method by detecting new QTL and epistatic effects for an ordinal trait, dead fetuses, in a F 2 intercross of mice. Utility and flexibility of the method are also demonstrated using a simulated data set. Our method has been implemented in the freely available package R/qtlbim, which greatly facilitates the general usage of the Bayesian methodology for genomewide interacting QTL analysis for continuous, binary, and ordinal traits in experimental crosses. MOST complex traits are influenced by interacting networks of multiple genetic (QTL) and environmental factors. Recently several statistical methods and software have been developed to map multiple interacting QTL for continuous traits (Kao et al. 1999;Carlborg et al. 2000;Reifsnyder et al. 2000;Bogdan et al. 2004;Yi et al. 2005;Baierl et al. 2006). However, many complex traits in humans and other organisms are measured in an ordinal manner. For example, many diseases are scored in several ordered categories on the basis of the magnitude of the disease symptom. Although the phenotypes of these characters are discrete, their inheritance is determined by many factors, including multiple genes and environmental components (Lynch and Walsh 1998). Theoretically, the statistical methods for continuous traits are not optimal for ordinal traits because the normality assumption is violated (Johnson and Albert 1999;Gelman et al. 2003). Therefore, mapping QTL for ordinal traits requires new methods.The probit model is commonly used to analyze discrete binary and ordinal data (Albert and Chib 1993;Johnson and Albert 1999). An important way for the statistical inference and interpretation of the probit model is to postulate the existence of a latent (unobserved) continuous variable associated with each response through a series of unknown thresholds (Albert and Chib 1993;Johnson and Albert 1999). In quantitative genetics, the latent presentation of the probit model is called the threshold model, which has been widely used to analyze the genetic architecture of binary and ordinal traits (Wright 1...

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“…As the genotypes of the QTL are unobservable, the distribution of the quantitative trait follows a finite mixture model, say a mixture of two normal distributions as many authors proposed. For some recent developments on the QTL mapping method, see, e.g., Zeng (1994), Hackett and Weller (1995), Kao and Zeng (1997), Lange and Whittaker (2001), Broman (2003), Thomson (2003), Chen and Chen (2005), Sillanpaa and Bhattacharjee (2005), and Xu et al (2005).…”

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A Logistic Regression Mixture Model for Interval Mapping of Genetic Trait Loci Affecting Binary Phenotypes

Deng

Chen

2006

Genetics

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Often in genetic research, presence or absence of a disease is affected by not only the trait locus genotypes but also some covariates. The finite logistic regression mixture models and the methods under the models are developed for detection of a binary trait locus (BTL) through an interval-mapping procedure. The maximum-likelihood estimates (MLEs) of the logistic regression parameters are asymptotically unbiased. The null asymptotic distributions of the likelihood-ratio test (LRT) statistics for detection of a BTL are found to be given by the supremum of a x 2 -process. The limiting null distributions are free of the null model parameters and are determined explicitly through only four (backcross case) or nine (intercross case) independent standard normal random variables. Therefore a threshold for detecting a BTL in a flanking marker interval can be approximated easily by using a Monte Carlo method. It is pointed out that use of a threshold incorrectly determined by reading off a x 2 -probability table can result in an excessive false BTL detection rate much more severely than many researchers might anticipate. Simulation results show that the BTL detection procedures based on the thresholds determined by the limiting distributions perform quite well when the sample sizes are moderately large.A variety of quantitative and/or qualitative traits in plants and animals are attributed mainly to genotypes at certain chromosome locations (so-called trait loci). Extensive studies on quantitative trait locus (QTL) mapping have been conducted since Sax (1923). For experimental organisms, there are several statistical methods developed for mapping QTL systematically. Soller and Brody (1976) proposed the traditional approach of detecting a QTL by using a nearby marker as a surrogate for a QTL. Lander and Botstein (1989) developed the interval-mapping (IM) method to test for a QTL in a flanking marker interval. As the genotypes of the QTL are unobservable, the distribution of the quantitative trait follows a finite mixture model, say a mixture of two normal distributions as many authors proposed. For some recent developments on the QTL mapping method, see, e.g

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An EM algorithm for mapping quantitative resistance loci

Cited by 13 publications

References 23 publications

Interval mapping for loci affecting unordered categorical traits

Interval mapping for loci affecting unordered categorical traits

Bayesian Mapping of Genomewide Interacting Quantitative Trait Loci for Ordinal Traits

A Logistic Regression Mixture Model for Interval Mapping of Genetic Trait Loci Affecting Binary Phenotypes

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