Scaling linear-model breeding values to the liability scale: an application to pig binary traits

In commercial pig production, many important traits are recorded as binary phenotypes. For such traits, threshold models offer an appropriate framework but are computationally intensive. Thus, linear models are widely used to obtain genomic estimated breeding values (GEBV); however, these are on the observed scale (phenotypic). This creates the need for a robust method to approximate GEBV from linear models to the liability scale. A recently proposed approximation showed good concordance for low-prevalence traits (<5%) but has not yet been tested for a wider range of prevalence values and for models with more than one random effect. We aimed to evaluate the performance of this approximation for pig binary traits with prevalences ranging from <5% to >86%, in both animal and maternal animal models. Data were available for five fitness traits (FT1-FT5), with up to 233k animals with phenotypes, of which 204k animals were genotyped with a 25k SNP array. Variance component estimates were obtained using threshold models. Classical animal models were used for FT1-FT3, and maternal animal models for FT4 and FT5. Variance components on the observed scale were then obtained by multiplying estimates from a threshold model by the square of the height of the standard normal density evaluated at the threshold. GEBV were predicted using single-step genomic best linear unbiased prediction under both linear and threshold models. The approximation tested involved scaling the GEBV using the height of the ordinate of the standard normal distribution evaluated at the threshold as a scaling factor. The agreement between GEBV from the scaled linear model and the threshold model on the probability scale was evaluated using Pearson and Spearman correlations, mean squared error (MSE), regression parameters, overlapping coefficient (OVL), distribution overlap, and classification accuracy (CACC). Correlations between linear and threshold GEBV ranged from 0.94 (low-prevalence traits) to 0.99 (high-prevalence traits) for the direct GEBV and were 0.99 for the maternal GEBV. MSE were close to zero. The OVL exceeded 0.83 for all traits. CACC ranged from 95.10% to 98.33% for the direct GEBV and from 92.54% to 97.42% for the maternal GEBV. Regardless of model and trait prevalence, this approximation yielded GEBV that are highly consistent with threshold model GEBV, providing a reliable, practical approach for large-scale pig genetic evaluations for binary traits using linear models.