Evaluating somatic cell scores with a Bayesian Gaussian linear state-space model

Because accurate characterization of health state is important for managing dairy herds, we propose to validate the use of a linear state-space model (LSSM) for evaluating monthly somatic cell scores (SCSs). To do so, we retrieved SCS from a dairy database and collected reports on clinical mastitis collected in 20 farms, during the period from January 2008 to December 2011 in the Walloon region of Belgium. The dependent variable was the SCS, and the independent variables were the number of days from calving, year of calving and parity. The LSSM also incorporated an error-free underlying variable that described the trend across time as a function of previous clinical and subclinical status. We computed the mean sum of squared differences between observed SCS and median values of the posterior SCS distribution and constructed the receiver operating characteristic (ROC) curve for SCS thresholds going from 0 to 6. Our results show SCS estimates are close to observed SCS and area under the ROC curve is higher than 90%. We discuss the meaning of the parameters in light of our current knowledge of the disease and propose methods to incorporate, in LSSM, this knowledge often expressed in the form of ordinary differential equations.