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Predicted Residual Error Sum of Squares of Mixed Models: An Application for Genomic Prediction.

ABSTRACT: Genomic prediction is a statistical method to predict phenotypes of polygenic traits using high-throughput genomic data. Most diseases and behaviors in humans and animals are polygenic traits. The majority of agronomic traits in crops are also polygenic. Accurate prediction of these traits can help medical professionals diagnose acute diseases and breeders to increase food products, and therefore significantly contribute to human health and global food security. The best linear unbiased prediction (BLUP) is an important tool to analyze high-throughput genomic data for prediction. However, to judge the efficacy of the BLUP model with a particular set of predictors for a given trait, one has to provide an unbiased mechanism to evaluate the predictability. Cross-validation (CV) is an essential tool to achieve this goal, where a sample is partitioned into K parts of roughly equal size, one part is predicted using parameters estimated from the remaining K - 1 parts, and eventually every part is predicted using a sample excluding that part. Such a CV is called the K-fold CV. Unfortunately, CV presents a substantial increase in computational burden. We developed an alternative method, the HAT method, to replace CV. The new method corrects the estimated residual errors from the whole sample analysis using the leverage values of a hat matrix of the random effects to achieve the predicted residual errors. Properties of the HAT method were investigated using seven agronomic and 1000 metabolomic traits of an inbred rice population. Results showed that the HAT method is a very good approximation of the CV method. The method was also applied to 10 traits in 1495 hybrid rice with 1.6 million SNPs, and to human height of 6161 subjects with roughly 0.5 million SNPs of the Framingham heart study data. Predictabilities of the HAT and CV methods were all similar. The HAT method allows us to easily evaluate the predictabilities of genomic prediction for large numbers of traits in very large populations.

SUBMITTER: Xu S

PROVIDER: S-EPMC5345720 | biostudies-literature | 2017 Mar

REPOSITORIES: biostudies-literature

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Predicted Residual Error Sum of Squares of Mixed Models: An Application for Genomic Prediction.

Xu Shizhong S

G3 (Bethesda, Md.) 20170310 3

Genomic prediction is a statistical method to predict phenotypes of polygenic traits using high-throughput genomic data. Most diseases and behaviors in humans and animals are polygenic traits. The majority of agronomic traits in crops are also polygenic. Accurate prediction of these traits can help medical professionals diagnose acute diseases and breeders to increase food products, and therefore significantly contribute to human health and global food security. The best linear unbiased predicti ...[more]

PMID: 28108552

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Project description:BACKGROUND:Genomic prediction (GP) allows breeders to select plants and animals based on their breeding potential for desirable traits, without lengthy and expensive field trials or progeny testing. We have proposed to use Dissimilarity-based Partial Least Squares (DPLS) for GP. As a case study, we use the DPLS approach to predict Bacterial wilt (BW) in tomatoes using SNPs as predictors. The DPLS approach was compared with the Genomic Best-Linear Unbiased Prediction (GBLUP) and single-SNP regression with SNP as a fixed effect to assess the performance of DPLS. RESULTS:Eight genomic distance measures were used to quantify relationships between the tomato accessions from the SNPs. Subsequently, each of these distance measures was used to predict the BW using the DPLS prediction model. The DPLS model was found to be robust to the choice of distance measures; similar prediction performances were obtained for each distance measure. DPLS greatly outperformed the single-SNP regression approach, showing that BW is a comprehensive trait dependent on several loci. Next, the performance of the DPLS model was compared to that of GBLUP. Although GBLUP and DPLS are conceptually very different, the prediction quality (PQ) measured by DPLS models were similar to the prediction statistics obtained from GBLUP. A considerable advantage of DPLS is that the genotype-phenotype relationship can easily be visualized in a 2-D scatter plot. This so-called score-plot provides breeders an insight to select candidates for their future breeding program. CONCLUSIONS:DPLS is a highly appropriate method for GP. The model prediction performance was similar to the GBLUP and far better than the single-SNP approach. The proposed method can be used in combination with a wide range of genomic dissimilarity measures and genotype representations such as allele-count, haplotypes or allele-intensity values. Additionally, the data can be insightfully visualized by the DPLS model, allowing for selection of desirable candidates from the breeding experiments. In this study, we have assessed the DPLS performance on a single trait.

Project description:Feature selection (FS, i.e., selection of a subset of predictor variables) is essential in high-dimensional datasets to prevent overfitting of prediction/classification models and reduce computation time and resources. In genomics, FS allows identifying relevant markers and designing low-density SNP chips to evaluate selection candidates. In this research, several univariate and multivariate FS algorithms combined with various parametric and non-parametric learners were applied to the prediction of feed efficiency in growing pigs from high-dimensional genomic data. The objective was to find the best combination of feature selector, SNP subset size, and learner leading to accurate and stable (i.e., less sensitive to changes in the training data) prediction models. Genomic best linear unbiased prediction (GBLUP) without SNP pre-selection was the benchmark. Three types of FS methods were implemented: (i) filter methods: univariate (univ.dtree, spearcor) or multivariate (cforest, mrmr), with random selection as benchmark; (ii) embedded methods: elastic net and least absolute shrinkage and selection operator (LASSO) regression; (iii) combination of filter and embedded methods. Ridge regression, support vector machine (SVM), and gradient boosting (GB) were applied after pre-selection performed with the filter methods. Data represented 5,708 individual records of residual feed intake to be predicted from the animal's own genotype. Accuracy (stability of results) was measured as the median (interquartile range) of the Spearman correlation between observed and predicted data in a 10-fold cross-validation. The best prediction in terms of accuracy and stability was obtained with SVM and GB using 500 or more SNPs [0.28 (0.02) and 0.27 (0.04) for SVM and GB with 1,000 SNPs, respectively]. With larger subset sizes (1,000-1,500 SNPs), the filter method had no influence on prediction quality, which was similar to that attained with a random selection. With 50-250 SNPs, the FS method had a huge impact on prediction quality: it was very poor for tree-based methods combined with any learner, but good and similar to what was obtained with larger SNP subsets when spearcor or mrmr were implemented with or without embedded methods. Those filters also led to very stable results, suggesting their potential use for designing low-density SNP chips for genome-based evaluation of feed efficiency.

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Dataset Information

Predicted Residual Error Sum of Squares of Mixed Models: An Application for Genomic Prediction.

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Predicted Residual Error Sum of Squares of Mixed Models: An Application for Genomic Prediction.

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