Genomic prediction based on data from three layer lines: a comparison between linear methods

Background

The prediction accuracy of several linear genomic prediction models, which have previously been used for within-line genomic prediction, was evaluated for multi-line genomic prediction.

Methods

Compared to a conventional BLUP (best linear unbiased prediction) model using pedigree data, we evaluated the following genomic prediction models: genome-enabled BLUP (GBLUP), ridge regression BLUP (RRBLUP), principal component analysis followed by ridge regression (RRPCA), BayesC and Bayesian stochastic search variable selection. Prediction accuracy was measured as the correlation between predicted breeding values and observed phenotypes divided by the square root of the heritability. The data used concerned laying hens with phenotypes for number of eggs in the first production period and known genotypes. The hens were from two closely-related brown layer lines (B1 and B2), and a third distantly-related white layer line (W1). Lines had 1004 to 1023 training animals and 238 to 240 validation animals. Training datasets consisted of animals of either single lines, or a combination of two or all three lines, and had 30 508 to 45 974 segregating single nucleotide polymorphisms.

Results

Genomic prediction models yielded 0.13 to 0.16 higher accuracies than pedigree-based BLUP. When excluding the line itself from the training dataset, genomic predictions were generally inaccurate. Use of multiple lines marginally improved prediction accuracy for B2 but did not affect or slightly decreased prediction accuracy for B1 and W1. Differences between models were generally small except for RRPCA which gave considerably higher accuracies for B2. Correlations between genomic predictions from different methods were higher than 0.96 for W1 and higher than 0.88 for B1 and B2. The greater differences between methods for B1 and B2 were probably due to the lower accuracy of predictions for B1 (~0.45) and B2 (~0.40) compared to W1 (~0.76).

Conclusions

Multi-line genomic prediction did not affect or slightly improved prediction accuracy for closely-related lines. For distantly-related lines, multi-line genomic prediction yielded similar or slightly lower accuracies than single-line genomic prediction. Bayesian variable selection and GBLUP generally gave similar accuracies. Overall, RRPCA yielded the greatest accuracies for two lines, suggesting that using PCA helps to alleviate the “n ≪ p” problem in genomic prediction.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-014-0057-5) contains supplementary material, which is available to authorized users.     

Assessment of survival prediction models based on microarray data

MOTIVATION: In the process of developing risk prediction models, various steps of model building and model selection are involved. If this process is not adequately controlled, overfitting may result in serious overoptimism leading to potentially erroneous conclusions. METHODS: For right censored time-to-event data, we estimate the prediction error for assessing the performance of a risk prediction model (Gerds and Schumacher, 2006; Graf et al., 1999). Furthermore, resampling methods are used to detect overfitting and resulting overoptimism and to adjust the estimates of prediction error (Gerds and Schumacher, 2007). RESULTS: We show how and to what extent the methodology can be used in situations characterized by a large number of potential predictor variables where overfitting may be expected to be overwhelming. This is illustrated by estimating the prediction error of some recently proposed techniques for fitting a multivariate Cox regression model applied to the data of a prognostic study in patients with diffuse large-B-cell lymphoma (DLBCL). AVAILABILITY: Resampling-based estimation of prediction error curves is implemented in an R package called pec available from the authors.     

Genomic prediction of cotton fibre quality and yield traits using Bayesian regression methods

Genomic selection or genomic prediction (GP) has increasingly become an important molecular breeding technology for crop improvement. GP aims to utilise genome-wide marker data to predict genomic breeding value for traits of economic importance. Though GP studies have been widely conducted in various crop species such as wheat and maize, its application in cotton, an essential renewable textile fibre crop, is still significantly underdeveloped. We aim to develop a new GP-based breeding system that can improve the efficiency of our cotton breeding program. This article presents a GP study on cotton fibre quality and yield traits using 1385 breeding lines from the Commonwealth Scientific and Industrial Research Organisation (CSIRO, Australia) cotton breeding program which were genotyped using a high-density SNP chip that generated 12,296 informative SNPs. The aim of this study was twofold: (1) to identify the models and data sources (i.e. genomic and pedigree) that produce the highest prediction accuracies; and (2) to assess the effectiveness of GP as a selection tool in the CSIRO cotton breeding program. The prediction analyses were conducted under various scenarios using different Bayesian predictive models. Results highlighted that the model combining genomic and pedigree information resulted in the best cross validated prediction accuracies: 0.76 for fibre length, 0.65 for fibre strength, and 0.64 for lint yield. Overall, this work represents the largest scale genomic selection studies based on cotton breeding trial data. Prediction accuracies reported in our study indicate the potential of GP as a breeding tool for cotton. The study highlighted the importance of incorporating pedigree and environmental factors in GP models to optimise the prediction performance.Subject terms: Plant breeding, Genome     

Genomic prediction using imputed whole-genome sequence data in Holstein Friesian cattle

Background

In contrast to currently used single nucleotide polymorphism (SNP) panels, the use of whole-genome sequence data is expected to enable the direct estimation of the effects of causal mutations on a given trait. This could lead to higher reliabilities of genomic predictions compared to those based on SNP genotypes. Also, at each generation of selection, recombination events between a SNP and a mutation can cause decay in reliability of genomic predictions based on markers rather than on the causal variants. Our objective was to investigate the use of imputed whole-genome sequence genotypes versus high-density SNP genotypes on (the persistency of) the reliability of genomic predictions using real cattle data.

Methods

Highly accurate phenotypes based on daughter performance and Illumina BovineHD Beadchip genotypes were available for 5503 Holstein Friesian bulls. The BovineHD genotypes (631,428 SNPs) of each bull were used to impute whole-genome sequence genotypes (12,590,056 SNPs) using the Beagle software. Imputation was done using a multi-breed reference panel of 429 sequenced individuals. Genomic estimated breeding values for three traits were predicted using a Bayesian stochastic search variable selection (BSSVS) model and a genome-enabled best linear unbiased prediction model (GBLUP). Reliabilities of predictions were based on 2087 validation bulls, while the other 3416 bulls were used for training.

Results

Prediction reliabilities ranged from 0.37 to 0.52. BSSVS performed better than GBLUP in all cases. Reliabilities of genomic predictions were slightly lower with imputed sequence data than with BovineHD chip data. Also, the reliabilities tended to be lower for both sequence data and BovineHD chip data when relationships between training animals were low. No increase in persistency of prediction reliability using imputed sequence data was observed.

Conclusions

Compared to BovineHD genotype data, using imputed sequence data for genomic prediction produced no advantage. To investigate the putative advantage of genomic prediction using (imputed) sequence data, a training set with a larger number of individuals that are distantly related to each other and genomic prediction models that incorporate biological information on the SNPs or that apply stricter SNP pre-selection should be considered.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-015-0149-x) contains supplementary material, which is available to authorized users.     

Genomic characterization of multiple clinical phenotypes of cancer using multivariate linear regression models

MOTIVATION: The development of gene expression microarray technology has allowed the identification of differentially expressed genes between different clinical phenotypic classes of cancer from a large pool of candidate genes. Although many class comparisons concerned only a single phenotype, simultaneous assessment of the relationship between gene expression and multiple phenotypes would be warranted to better understand the underlying biological structure. RESULTS: We develop a method to select genes related to multiple clinical phenotypes based on a set of multivariate linear regression models. For each gene, we perform model selection based on the doubly-adjusted R-square statistic and use the maximum of this statistic for gene selection. The method can substantially improve the power in gene selection, compared with a conventional method that uses a single model exclusively for gene selection. Application to a bladder cancer study to correlate pre-treatment gene expressions with pathological stage and grade is given. The methods would be useful for screening for genes related to multiple clinical phenotypes. AVAILABILITY: SAS and MATLAB codes are available from author upon request.     

Tests of significance using regression models for ordered categorical data

Regression models of the type proposed by McCullagh (1980, Journal of the Royal Statistical Society, Series B 42, 109-142) are a general and powerful method of analyzing ordered categorical responses, assuming categorization of an (unknown) continuous response of a specified distribution type. Tests of significance with these models are generally based on likelihood-ratio statistics that have asymptotic chi 2 distributions; therefore, investigators with small data sets may be concerned with the small-sample behavior of these tests. In a Monte Carlo sampling study, significance tests based on the ordinal model are found to be powerful, but a modified test procedure (using an F distribution with a finite number of degrees of freedom for the denominator) is suggested such that the empirical significance level agrees more closely with the nominal significance level in small-sample situations. We also discuss the parallels between an ordinal regression model assuming underlying normality and conventional multiple regression. We illustrate the model with two data sets: one from a study investigating the relationship between phosphorus in soil and plant-available phosphorus in corn grown in that soil, and the other from a clinical trial comparing analgesic drugs.     

Genomic prediction based on runs of homozygosity

Background

Genomic prediction is based on the accurate estimation of the genomic relationships among and between training animals and selection candidates in order to obtain accurate estimates of the genomic estimated breeding values (GEBV). Various methods have been used to predict GEBV based on population-wide linkage disequilibrium relationships (G_IBS) or sometimes on linkage analysis relationships (G_LA). Here, we propose a novel method to predict GEBV based on a genomic relationship matrix using runs of homozygosity (G_ROH). Runs of homozygosity were used to derive probabilities of multi-locus identity by descent chromosome segments. The accuracy and bias of the prediction of GEBV using G_ROH were compared to those using G_IBS and G_LA. Comparisons were performed using simulated datasets derived from a random pedigree and a real pedigree of Italian Brown Swiss bulls. The comparison of accuracies of GEBV was also performed on data from 1086 Italian Brown Swiss dairy cattle.

Results

Simulations with various thresholds of minor allele frequency for markers and quantitative trait loci showed that G_ROH achieved consistently more accurate GEBV (0 to 4% points higher) than G_IBS and G_LA. The bias of GEBV prediction for simulated data was higher based on the real pedigree than based on a random pedigree. In the analyses with real data, G_ROH and G_LA had similar accuracies. However, G_LA achieved a higher accuracy when the prediction was done on the youngest animals. The G_IBS matrices calculated with and without standardized marker genotypes resulted in similar accuracies.

Conclusions

The present study proposes G_ROH as a novel method to estimate genomic relationship matrices and predict GEBV based on runs of homozygosity and shows that it can result in higher or similar accuracies of GEBV prediction than G_LA, except for the real data analysis with validation of young animals. Compared to G_IBS, G_ROH resulted in more accurate GEBV predictions.     

Linking data to models: data regression

Mathematical models are an essential tool in systems biology, linking the behaviour of a system to the interactions between its components. Parameters in empirical mathematical models must be determined using experimental data, a process called regression. Because experimental data are noisy and incomplete, diagnostics that test the structural identifiability and validity of models and the significance and determinability of their parameters are needed to ensure that the proposed models are supported by the available data.     

Using linear and non-linear regression to fit biochemical data

For biochemists or chemists the most common form of data analysis is likely to be regression analysis. This is a technique to find the ‘best’ values for various experimental parameters; defined as those values which, when used in an appropriate equation, result in the minimum deviation of the calculated results from the experimental data. Despite the widespread application of regression analysis, the basis of the technique and the underlying assumptions are often poorly understood or appreciated. This article describes the basics of linear and non-linear regression, the role of ‘weighting’ and the potential pitfalls of such analyses.     

A bayesian mixed regression based prediction of quantitative traits from molecular marker and gene expression data

Both molecular marker and gene expression data were considered alone as well as jointly to serve as additive predictors for two pathogen-activity-phenotypes in real recombinant inbred lines of soybean. For unobserved phenotype prediction, we used a bayesian hierarchical regression modeling, where the number of possible predictors in the model was controlled by different selection strategies tested. Our initial findings were submitted for DREAM5 (the 5th Dialogue on Reverse Engineering Assessment and Methods challenge) and were judged to be the best in sub-challenge B3 wherein both functional genomic and genetic data were used to predict the phenotypes. In this work we further improve upon this previous work by considering various predictor selection strategies and cross-validation was used to measure accuracy of in-data and out-data predictions. The results from various model choices indicate that for this data use of both data types (namely functional genomic and genetic) simultaneously improves out-data prediction accuracy. Adequate goodness-of-fit can be easily achieved with more complex models for both phenotypes, since the number of potential predictors is large and the sample size is not small. We also further studied gene-set enrichment (for continuous phenotype) in the biological process in question and chromosomal enrichment of the gene set. The methodological contribution of this paper is in exploration of variable selection techniques to alleviate the problem of over-fitting. Different strategies based on the nature of covariates were explored and all methods were implemented under the bayesian hierarchical modeling framework with indicator-based covariate selection. All the models based in careful variable selection procedure were found to produce significant results based on permutation test.     

Competing regression models for longitudinal data

The choice of an appropriate family of linear models for the analysis of longitudinal data is often a matter of concern for practitioners. To attenuate such difficulties, we discuss some issues that emerge when analyzing this type of data via a practical example involving pretest–posttest longitudinal data. In particular, we consider log‐normal linear mixed models (LNLMM), generalized linear mixed models (GLMM), and models based on generalized estimating equations (GEE). We show how some special features of the data, like a nonconstant coefficient of variation, may be handled in the three approaches and evaluate their performance with respect to the magnitude of standard errors of interpretable and comparable parameters. We also show how different diagnostic tools may be employed to identify outliers and comment on available software. We conclude by noting that the results are similar, but that GEE‐based models may be preferable when the goal is to compare the marginal expected responses.     

Genomic prediction of dichotomous traits with Bayesian logistic models

Bayesian methods are a popular choice for genomic prediction of genotypic values. The methodology is well established for traits with approximately Gaussian phenotypic distribution. However, numerous important traits are of dichotomous nature and the phenotypic counts observed follow a Binomial distribution. The standard Gaussian generalized linear models (GLM) are not statistically valid for this type of data. Therefore, we implemented Binomial GLM with logit link function for the BayesB and Bayesian GBLUP genomic prediction methods. We compared these models with their standard Gaussian counterparts using two experimental data sets from plant breeding, one on female fertility in wheat and one on haploid induction in maize, as well as a simulated data set. With the aid of the simulated data referring to a bi-parental population of doubled haploid lines, we further investigated the influence of training set size (N), number of independent Bernoulli trials for trait evaluation (n _i ) and genetic architecture of the trait on genomic prediction accuracies and abilities in general and on the relative performance of our models. For BayesB, we in addition implemented finite mixture Binomial GLM to account for overdispersion. We found that prediction accuracies increased with increasing N and n _i . For the simulated and experimental data sets, we found Binomial GLM to be superior to Gaussian models for small n _i , but that for large n _i Gaussian models might be used as ad hoc approximations. We further show with simulated and real data sets that accounting for overdispersion in Binomial data can markedly increase the prediction accuracy.     

应用CGH数据和树模型探索癌症的发病机理

比较基因组杂交技术(comparative genomic hybridization, CGH)主要用于检测肿瘤的染色体缺失和扩嘱, 迄今已积累了大量的实验数据, 为全基因组分析肿瘤的发生机制提供了可能。树模型在生物信息学领域通常被用于研究生物形成和进化的历史, 物种之间的进化关系常以系统发生树来表示。树模型同样可以作为一种有力的生物信息学工具来分析CGH数据, 探索癌症的发病机理。文中介绍了两种常见的树模型—— 分支树和距离树, 详细叙述了重建树模型的基本原理和方法, 分析了创建树模型时要注意的几个技术问题, 并对其在肿瘤研究中的应用进行了回顾和总结。肿瘤的树状模型作为单路径线性模型的泛化, 克服了以往单路径线性模型的缺点, 理论上能更加精确地概括到肿脉的多基因、多路径、多阶段的发生发展模式, 从不同角度探讨肿瘤发生发展的分子机制。该模型除可用于分析肿瘤的CGH数据外, 还可用于分析其他多种类型的数据, 包括微阵列CGH(array-CGH)技术等产生的高分辨率数据。     

Bayesian prediction of spatial count data using generalized linear mixed models

Spatial weed count data are modeled and predicted using a generalized linear mixed model combined with a Bayesian approach and Markov chain Monte Carlo. Informative priors for a data set with sparse sampling are elicited using a previously collected data set with extensive sampling. Furthermore, we demonstrate that so-called Langevin-Hastings updates are useful for efficient simulation of the posterior distributions, and we discuss computational issues concerning prediction.     

Genetic markers applied in regression tree prediction models

Classification and regression tree (CART) modelling was used to determine infectious hypodermal and haematopoietic necrosis virus (IHHNV) resistance and susceptibility in Penaeus stylirostris. In a previous study, eight random amplified polymorphic DNA (RAPD) markers and viral load values using real-time quantitative PCR were obtained and used as the training data set in order to create numerous regression tree models. Specifically, the genetic markers were used as categorical predictor variables and viral load values as the dependent response variable. To determine which model has the highest predictive accuracy for future samples, RAPD fingerprint data was generated from new Penaues stylirostris IHHNV resistant and susceptible individuals and used to test the regression models. The best performing tree was a four terminal node tree with three genetic markers as significant variables. Marker-assisted breeding practices may benefit from the creation of regression tree models that apply genetic markers as predictive factors. To our knowledge this is the first study to use RAPD markers as predictors within a CART prediction model to determine viral susceptibility.