M-regression, false discovery rates and outlier detection with application to genetic association studies

Statistical Approach for Improving Genomic Prediction Accuracy through Efficient Diagnostic Measure of Influential Observation

It is expected the predictive performance of genomic prediction methods may be adversely affected in the presence of outliers. In agriculture science an outlier may arise due to wrong data imputation, outlying response, and in a series of trials over the time or location. Although several statistical procedures are already there in literature for identification of outlier but identification of true outlier is still a challenge especially in case of high dimensional genomic data. Here we have proposed an efficient approach for detecting outlier in high dimensional genomic data, our approach is p-value based combination methods to produce single p-value for detecting the outliers. Robustness of our approach has been tested using simulated data through the evaluation measures like precision, recall etc. It has been observed that significant improvement in the performance of genomic prediction has been obtained by detecting the outliers and handling them accordingly through our proposed approach using real data.

Robust estimation of heritability and predictive accuracy in plant breeding: evaluation using simulation and empirical data

BACKGROUND

Genomic prediction (GP) is used in animal and plant breeding to help identify the best genotypes for selection. One of the most important measures of the effectiveness and reliability of GP in plant breeding is predictive accuracy. An accurate estimate of this measure is thus central to GP. Moreover, regression models are the models of choice for analyzing field trial data in plant breeding. However, models that use the classical likelihood typically perform poorly, often resulting in biased parameter estimates, when their underlying assumptions are violated. This typically happens when data are contaminated with outliers. These biases often translate into inaccurate estimates of heritability and predictive accuracy, compromising the performance of GP. Since phenotypic data are susceptible to contamination, improving the methods for estimating heritability and predictive accuracy can enhance the performance of GP. Robust statistical methods provide an intuitively appealing and a theoretically well justified framework for overcoming some of the drawbacks of classical regression, most notably the departure from the normality assumption. We compare the performance of robust and classical approaches to two recently published methods for estimating heritability and predictive accuracy of GP using simulation of several plausible scenarios of random and block data contamination with outliers and commercial maize and rye breeding datasets.

RESULTS

The robust approach generally performed as good as or better than the classical approach in phenotypic data analysis and in estimating the predictive accuracy of heritability and genomic prediction under both the random and block contamination scenarios. Notably, it consistently outperformed the classical approach under the random contamination scenario. Analyses of the empirical maize and rye datasets further reinforce the stability and reliability of the robust approach in the presence of outliers or missing data.

CONCLUSIONS

The proposed robust approach enhances the predictive accuracy of heritability and genomic prediction by minimizing the deleterious effects of outliers for a broad range of simulation scenarios and empirical breeding datasets. Accordingly, plant breeders should seriously consider regularly using the robust alongside the classical approach and increasing the number of replicates to three or more, to further enhance the accuracy of the robust approach.

A robust Bayesian genome-based median regression model

Current genome-enabled prediction models assumed errors normally distributed, which are sensitive to outliers. We propose a model with errors assumed to follow a Laplace distribution to deal better with outliers. Current genome-enabled prediction models use regressions that fit the expected value (mean) of a response variable with errors assumed normally distributed, which are often sensitive to outliers, either genetic or environmental. For this reason, we propose a robust Bayesian genome median regression (BGMR) model that fits regressions to the medians of a distribution, with errors assumed to follow a Laplace distribution to deal better with outliers. The BGMR model was evaluated under a Bayesian framework with Markov Chain Monte Carlo sampling using a location-scale mixture representation of the Laplace distribution. The BGMR was implemented with two simulated and two real genomic data sets, and we compared its prediction performance with that of a conventional genomic best linear unbiased prediction (GBLUP) model and the Laplace maximum a posteriori (LMAP) method. The prediction accuracies of BGMR were higher than those of the GBLUP and LMAP methods when there were outliers. The BGMR model could be useful to breeders who need to predict and select genotypes based on data with unknown outliers.

A robust DF-REML framework for variance components estimation in genetic studies

Motivation

In genetic association studies, linear mixed models (LMMs) are used to test for associations between phenotypes and candidate single nucleotide polymorphisms (SNPs). These same models are also used to estimate heritability, which is central not only to evolutionary biology but also to the prediction of the response to selection in plant and animal breeding, as well as the prediction of disease risk in humans. However, when one or more of the underlying assumptions are violated, the estimation of variance components may be compromised and therefore so may the estimates of heritability and any other functions of these. Considering that datasets obtained from real life experiments are prone to several sources of contamination, which usually induce the violation of the assumption of the normality of the errors, a robust derivative-free restricted-maximum likelihood framework (DF-REML) together with a robust coefficient of determination are proposed for the LMM in the context of genetic studies of continuous traits.

Results

The proposed approach, in addition to the robust estimation of variance components and robust computation of the coefficient of determination, allows in particular for the robust estimation of SNP-based heritability by reducing the bias and increasing the precision of its estimates. The performance of both classical and robust DF-REML approaches is compared via a Monte Carlo simulation study. Additionally, three examples of application of the methodologies to real datasets are given in order to validate the usefulness of the proposed robust approach. Although the main focus of this article is on plant breeding applications, the proposed methodology is applicable to both human and animal genetic studies.

Availability and implementation

Source code implemented in R is available in the Supplementary Material.

Contact

vmml@fct.unl.pt.

Supplementary information

Supplementary data are available at Bioinformatics online.

Outlier detection methods for generalized lattices: a case study on the transition from ANOVA to REML

We review and propose several methods for identifying possible outliers and evaluate their properties. The methods are applied to a genomic prediction program in hybrid rye. Many plant breeders use ANOVA-based software for routine analysis of field trials. These programs may offer specific in-built options for residual analysis that are lacking in current REML software. With the advance of molecular technologies, there is a need to switch to REML-based approaches, but without losing the good features of outlier detection methods that have proven useful in the past. Our aims were to compare the variance component estimates between ANOVA and REML approaches, to scrutinize the outlier detection method of the ANOVA-based package PlabStat and to propose and evaluate alternative procedures for outlier detection. We compared the outputs produced using ANOVA and REML approaches of four published datasets of generalized lattice designs. Five outlier detection methods are explained step by step. Their performance was evaluated by measuring the true positive rate and the false positive rate in a dataset with artificial outliers simulated in several scenarios. An implementation of genomic prediction using an empirical rye multi-environment trial was used to assess the outlier detection methods with respect to the predictive abilities of a mixed model for each method. We provide a detailed explanation of how the PlabStat outlier detection methodology can be translated to REML-based software together with the evaluation of alternative methods to identify outliers. The method combining the Bonferroni-Holm test to judge each residual and the residual standardization strategy of PlabStat exhibited good ability to detect outliers in small and large datasets and under a genomic prediction application. We recommend the use of outlier detection methods as a decision support in the routine data analyses of plant breeding experiments.

Influence of outliers on accuracy estimation in genomic prediction in plant breeding

Outliers often pose problems in analyses of data in plant breeding, but their influence on the performance of methods for estimating predictive accuracy in genomic prediction studies has not yet been evaluated. Here, we evaluate the influence of outliers on the performance of methods for accuracy estimation in genomic prediction studies using simulation. We simulated 1000 datasets for each of 10 scenarios to evaluate the influence of outliers on the performance of seven methods for estimating accuracy. These scenarios are defined by the number of genotypes, marker effect variance, and magnitude of outliers. To mimic outliers, we added to one observation in each simulated dataset, in turn, 5-, 8-, and 10-times the error SD used to simulate small and large phenotypic datasets. The effect of outliers on accuracy estimation was evaluated by comparing deviations in the estimated and true accuracies for datasets with and without outliers. Outliers adversely influenced accuracy estimation, more so at small values of genetic variance or number of genotypes. A method for estimating heritability and predictive accuracy in plant breeding and another used to estimate accuracy in animal breeding were the most accurate and resistant to outliers across all scenarios and are therefore preferable for accuracy estimation in genomic prediction studies. The performances of the other five methods that use cross-validation were less consistent and varied widely across scenarios. The computing time for the methods increased as the size of outliers and sample size increased and the genetic variance decreased.