Derivation of the Shrinkage Estimates of Quantitative Trait Locus Effects

Xu, Shizhong

doi:10.1534/genetics.107.077487

Cited by 14 publications

(7 citation statements)

References 12 publications

(14 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The conditional posterior means of c k and a k are called the shrinkage estimates. Derivation of the shrinkage estimates can be found in Xu (2007).…”

Section: Expectation Stepsmentioning

confidence: 99%

An expectation and maximization algorithm for estimating Q × E interaction effects

Zhao

2012

Theor Appl Genet

Self Cite

View full text Add to dashboard Cite

A Markov chain Monte Carlo (MCMC) implemented Bayesian method has been developed to detect quantitative trait loci (QTL) effects and Q x E interaction effects. However, the MCMC algorithm is time consuming due to repeated samplings of QTL parameters. We developed an expectation and maximization (EM) algorithm as an alternative method for detecting QTL and Q x E interaction. Simulation studies and real data analysis showed that the EM algorithm produced comparable result as the Bayesian method, but with a speed many magnitudes faster than the MCMC algorithm. We used the EM algorithm to analyze a well known barley dataset produced by the North American Barley Genome Mapping Project. The dataset contained eight quantitative traits collected from 150 doubled-haploid (DH) lines evaluated in multiple environments. Each line was genotyped for 495 polymorphic markers. The result showed that all eight traits exhibited QTL main effects and Q x E interaction effects. On average, the main effects and Q x E interaction effects contributed 34.56 and 16.23% of the total phenotypic variance, respectively. Furthermore, we found that whether or not a locus shows Q x E interaction does not depend on the presence of main effect.

show abstract

“…The conditional posterior means of c k and a k are called the shrinkage estimates. Derivation of the shrinkage estimates can be found in Xu (2007).…”

Section: Expectation Stepsmentioning

confidence: 99%

An expectation and maximization algorithm for estimating Q × E interaction effects

Zhao

2012

Theor Appl Genet

Self Cite

View full text Add to dashboard Cite

show abstract

“…In addition, to clearly describe the NLME model, we constructed our model framework in the context of interval mapping. More recently, Xu and group have developed a series of shrinkage models that allow a genome-wide search for all possible QTL (Xu, 2003(Xu, , 2007Wang et al, 2005). These multiple QTL models taking into account epistatic interactions between different QTL can be incorporated into the NLME model.…”

Section: Discussionmentioning

confidence: 99%

A nonlinear mixed-effect mixture model for functional mapping of dynamic traits

Hou

Zhang

et al. 2008

Heredity

View full text Add to dashboard Cite

Functional mapping has emerged as a next-generation statistical tool for mapping quantitative trait loci (QTL) that affect complex dynamic traits. In this article, we incorporated the idea of nonlinear mixed-effect (NLME) models into the mixture-based framework of functional mapping, aimed to generalize the spectrum of applications for functional mapping. NLME-based functional mapping, implemented with the linearization algorithm based on the first-order Taylor expansion, can provide reasonable estimates of QTL genotypic-specific curve parameters (fixed effect) and the between-individual variation of these parameters (random effect). Results from simulation studies suggest that the NLME-based model is more general than traditional functional mapping. The new model can be useful for the identification of the ontogenetic patterns of QTL genetic effects during time course.

show abstract

“…The reason for this is that the method shrinks true small effects and spurious effects in the same way and causes all effects (true and false) to bias downwardly. In theory, shrinkage estimation refers to the biased estimation of a regression coefficient towards zero using a prior variance as a factor to control the degree of shrinkage (Xu, 2007b). To overcome the above shortcomings of the PML method, we should correct the bias in the estimation of QTL effects.…”

Section: Introductionmentioning

confidence: 99%

Bias correction for estimated QTL effects using the penalized maximum likelihood method

Zhang

Yue

2011

Heredity

View full text Add to dashboard Cite

A penalized maximum likelihood method has been proposed as an important approach to the detection of epistatic quantitative trait loci (QTL). However, this approach is not optimal in two special situations: (1) closely linked QTL with effects in opposite directions and (2) small-effect QTL, because the method produces downwardly biased estimates of QTL effects. The present study aims to correct the bias by using correction coefficients and shifting from the use of a uniform prior on the variance parameter of a QTL effect to that of a scaled inverse chi-square prior. The results of Monte Carlo simulation experiments show that the improved method increases the power from 25 to 88% in the detection of two closely linked QTL of equal size in opposite directions and from 60 to 80% in the identification of QTL with small effects (0.5% of the total phenotypic variance). We used the improved method to detect QTL responsible for the barley kernel weight trait using 145 doubled haploid lines developed in the North American Barley Genome Mapping Project. Application of the proposed method to other shrinkage estimation of QTL effects is discussed.

show abstract

Derivation of the Shrinkage Estimates of Quantitative Trait Locus Effects

Cited by 14 publications

References 12 publications

An expectation and maximization algorithm for estimating Q × E interaction effects

An expectation and maximization algorithm for estimating Q × E interaction effects

A nonlinear mixed-effect mixture model for functional mapping of dynamic traits

Bias correction for estimated QTL effects using the penalized maximum likelihood method

Contact Info

Product

Resources

About