Fast Genomic Predictions via Bayesian G-BLUP and Multilocus Models of Threshold Traits Including Censored Gaussian Data

Abstract

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed.

Simultaneous Discovery, Estimation and Prediction Analysis of Complex Traits Using a Bayesian Mixture Model

“…The predicted phenotypes can then be taken as the probability of being a case and heritability estimates can be transformed to liability of disease scale [ 11 ]. The model can be extended to binary or ordered categorical traits by fitting a liability model [ 31 ], but improvements are expect to be negligible [ 27 , 32 ].…”

Genomic prediction for additive and dominance effects of censored traits in pigs

“…As such, the model with only additive effects was considered, and was fitted by using the coxme function of the R software, since the relationship matrix based on pedigree was replaced by the relationship matrix based on markers. Furthermore, in GS, Kärkkäinen and Sillanpaa (2013) proposed the use of Bayesian threshold models for data in binary and ordinal scale in order to evaluate censored traits.…”

Maximuma posterioriThreshold Genomic Prediction Model for Ordinal Traits

“…Shepherd et al (2010) developed a MAP estimation for the BayesB model, which is a different formulation than the BayesB estimation done by Hayashi and Iwata (2010), who also considered a MAP estimation of the BayesA model. Kärkkäinen and Sillanpää (2013) developed a MAP estimation for the ordinal model with a Laplace prior distribution of the marker effects.…”

“…The ECM algorithm is attractive as a tool for predicting ordinal data in the context of genomic selection since the data sets collected for plant breeding continue growing, and also because there is empirical evidence that the difference in speed between Bayesian models under MCMC and a MAP estimation algorithm is far from trivial. The run time of an MCMC algorithm is typically hours at the lowest, while EM algorithms perform the analyses in significantly less time (Kärkkäinen and Sillanpää, 2013). For this reason, in this paper we propose an expected conditional maximization a posteriori threshold (MAPT) model for parameter estimation in the Threshold Genomic prediction model.…”