Reproductive efficiency is a key element of profitability in dairy herds. However, the genetic evaluation of fertility traits is often challenged by the presence of high censorship rates due to various reasons. An easy approach to address this challenge is to remove the censored data from the dataset. However, removing data might bias the genetic evaluation. Therefore, addressing this issue is crucial, particularly for small populations and populations with limited size. This study uses a Moroccan Holstein dataset to compare two Gaussian linear models and a threshold linear model to handle censored records of days open (DO). Data contained 8646 records of days open across the first three parities of 6337 Holstein cows. The pedigree file comprised 11,555 animals and 14.51% of the dataset was censored. The genetic parameters and breeding values of DO were computed using three different methods: a linear model where all censored records were omitted (LM), a penalty method in which a constant equal to one estrus cycle in cattle was added to the maximum value of DO in each contemporary group to impute the censored records (PLM), and a bivariate threshold model with a penalty (PTM). The heritability estimates were equal to 0.021 ± 0.01 (PLM), 0.029 ± 0.01 (LM), and 0.033 ± 0.01 (PTM). The penalty method and the threshold linear model with a penalty showed better prediction accuracy calculated using the LR method (0.21, and 0.20, respectively). PLM and PTM had a high Spearman correlation (0.99) between the estimated breeding values of the validation dataset, which explains the high percentage of common animals in the top 20% of selected animals. The lack of changes in the ranking of animals between PLM and PTM suggests that both methods can be used to address censored data in this population.
