Comparison of approximation methods for genomic estimated breeding values from observed to liability scales in dairy cattle health traits

The GEBV for health traits are typically published as probabilities obtained using threshold models. While these models benefit from theoretical properties, they require substantial computational resources and may face convergence issues. Linear models can be a good alternative, but solutions need to be approximated to the liability scale before converting the GEBV into probabilities. Recently, an approximation from observed to liability scales was presented with limited success for traits with low prevalence (<5%). Our objective was to compare a new approximation with the previous one using health traits with very low (<1%) to moderate prevalences (up to 25%). We used data from Jersey cows for lameness, mastitis, retained placenta, ketosis, metritis, and displaced abomasum (up to 800k phenotypes per trait). Genotypes for 45k SNP were available for 200k animals. The GEBV were predicted using single-trait threshold and linear models implemented in the BLUPF90 software suite. Both approximations involved scaling the GEBV in the observed scale. The scaling factor was (1) the square root of the product of the residual variance and the proportion of unexplained variance in the linear model or (2) the height of the ordinate of a standard normal distribution evaluated at the threshold (new approximation). We used rank correlations, regression parameters, the overlapping of the distributions, mean squared error (MSE), and classification accuracy to compare GEBV from linear and threshold models on the probability scale for both approximations. Correlations between GEBV from threshold and linear models across approximations ranged from 0.87 (very low prevalence) to 0.99 (moderate prevalence). Although no differences were observed in the correlations across approximations, regression parameters, the overlapping of the distributions, MSE, and classification accuracy were improved with the new approximation method. Therefore, the new approximation provides greater consistency for large-scale evaluations using linear models for categorical traits with prevalence ranging from very low to moderate.