A semi-parametric model for lactation curves: development and application

We propose a semi-parametric model for lactation curves that, along with stage of lactation, accounts for day of the year at milk recording and stage of gestation. Lactation is described as having 3 different phases defined by 2 change points of which the second is a function of gestation stage. Season of milk recording is modelled using cosine and sine functions. As an application, the model is used to estimate the association between intramammary infections (IMI) dynamics as measured by somatic cell count (SCC) over the dry period and the shape of the lactation curve. Milk recording data collected in 2128 herds from England and Wales between 2004 and 2007 were used in the analysis. From a random sample of 1000 of these herds, smoothed milk production was used to test the behaviour of the model and estimate model parameters. The first change point was set at 60 days in milk. The second change point was set at 100 days of gestation or 200 days in milk when the latter was not available. Using data from the 1128 remaining herds, multilevel models were then used to model individual test-day milk production within lactations within herds. Average milk production at 60 days in milk for cows of parities 1, 2, 3 and greater than 3 were 26.9 kg, 31.6 kg, 34.4 kg and 34.7 kg respectively and, after this stage, decreases in milk production per 100 days milk of lactation were 3.1 kg, 5.1 kg, 6.3 kg and 6.7 kg respectively. Compared to cows that had an SCC below 200,000 cells/mL on both the last milk recording in a lactation and the first milk recording in the following lactation, cows that had an SCC greater than 200,000 cells/mL on their first milk recording after calving had an estimated loss of milk production of between 216 and 518 kg depending on parity. These estimates demonstrate the impact of the dynamics of SCC during the dry period on milk production during the following lactation.