Piecewise modeling of the associations between dry period length and milk, fat, and protein yield changes in the subsequent lactation

Abstract

Our objective was to develop predictive models of 305-d mature-equivalent milk, fat, and protein yields in the subsequent lactation as continuous functions of the number of days dry (DD) in the current lactation. In this retrospective cohort study with field data, we obtained DHIA milk recording lactation records with the last DD in 2014 or 2015. Cows included had DD from 21 to 100 d. After editing, 1,030,141 records from cows in 7,044 herds remained. Three parity groups of adjacent (current, subsequent) lactations were constructed. We conducted all analyses by parity group and yield component. We first applied control models to pre-adjust the yields in the subsequent lactation for potentially confounding effects. Control models included the covariates mature-equivalent yield, days open, somatic cell score at 180 d pregnant, daily yield at 180 d pregnant, and a herd-season random effect, all observed in the current lactation. Days dry was not included. Second, we modeled residuals from control models with smooth piecewise regression models consisting of a simple linear, quadratic, and another simple linear equation depending on DD. Yield deviations were calculated as differences from predicted mature-equivalent yield at 50 DD. For validation, predictions of yield deviations from piecewise models by DD were compared with predictions from local regression for the DHIA field records and yield deviations reported in 38 experimental and field studies found in the literature. Control models reduced the average root mean squared prediction error by approximately 21%. Yield deviations were increasingly more negative for DD shorter than 50 d, indicating lower yields in the subsequent lactation. For short DD, the decrease in 305-d mature-equivalent milk yield ranged from 43 to 53 kg per DD. For mature-equivalent fat and protein yields, decreases were between 1.28 and 1.71 kg per DD, and 1.06 and 1.50 kg per DD, respectively. Yield deviations often were marginally positive and increasing for DD >50, so that the highest yield in the subsequent lactation was predicted for 100 DD. For long DD, the 305-d mature-equivalent milk yield increased at most 4.18 kg per DD. Patterns in deviations for fat and protein yield were similar to those for milk yield deviations. Predictions from piecewise models and local regressions were very similar, which supports the chosen functional form of the piecewise models. Yield deviations from field studies in the literature typically were decreasing when DD were longer, likely because of insufficient control for confounding effects. In conclusion, piecewise models of mature-equivalent milk, fat, and protein yield deviations as continuous functions of DD fit the observed data well and may be useful for decision support on the optimal dry period length for individual cows.