Converting estimated breeding values from the observed to probability scale for health traits

Dairy cattle health traits are paramount from a welfare and economic viewpoint, and modern breeding programs therefore prioritize the genetic improvement of these traits. Estimated breeding values for health traits are published as the probability of animals staying healthy. They are obtained using threshold models, which assume that the observed binary phenotype (i.e., healthy or sick) is dictated by an underlying normally distributed liability exceeding or not exceeding a threshold. This methodology requires significant computing time and faces convergence challenges, as it implies a nonlinear system of equations. Linear models have more straightforward computations and provide a robust approximation to threshold models; thus, they could be used to overcome these challenges. However, linear models yield estimated breeding values on the observed scale, requiring an approximation to the liability scale analogous to that from threshold models to later obtain the estimated breeding values on the probability scale. In addition, the robustness of the approximation of linear to threshold models depends on the amount of information and the incidence of the trait, with extreme incidence (i.e., ≤5%) deviating from optimal approximation. Our objective was to test a transformation from the observed to the liability, and then to the probability scale, in the genetic evaluation of health traits with moderate and very low (extreme) incidence. Data comprised displaced abomasum (5.1 million), ketosis (3.6 million), lameness (5 million), and mastitis (6.3 million) records from a Holstein population with a pedigree of 6 million animals, of which 1.7 million were genotyped. Univariate threshold and linear models were performed to predict breeding values. The agreement between estimated breeding values on the probability scale derived from threshold and linear models was assessed using Spearman rank correlations and comparison of estimated breeding values distributions. Correlations were at least 0.95, and estimated breeding value distributions almost entirely overlapped for all the traits but displaced abomasum, the trait with the lowest incidence (2%). Computing time was ∼3 times longer for threshold than for linear models. In this Holstein population, the approximation was suboptimal for a trait with extreme incidence (2%). However, when the incidence was ≥6%, the approximation was robust, and its use is recommended along with linear models for analyzing categorical traits in large populations to ease the computational burden.