Investigating clustering in interval-censored udder quarter infection times in dairy cows using a gamma frailty model

Udder infections in dairy cows are observed at udder quarter level. Therefore, the best strategy to study infection dynamics of particular bacteria causing mastitis is to follow up and model individual udder quarter infection times. Udder quarter infection times, however, are not independent as they are clustered within a cow and herds. Another challenge in modelling infection times is that the exact infection time is unknown; it is only known that the infection has taken place in the interval between the last negative and the first positive sample. We applied a technique based on the gamma frailty model which handles the clustering and interval censoring simultaneously. Parameter estimates can be obtained analytically and their variance is obtained by the inverse of the hessian matrix. The proposed technique was applied to udder quarter infection times for Corynebacterium bovis, Staphylococcus aureus and Streptococcus uberis. Multiparous cows were more likely to get infected earlier in lactation with C. bovis or S. uberis than primiparous cows. The times to infection of all three bacteria were highly clustered at cow level and the results of a stratified model on a subset of herds suggested a high clustering on herd level for C. bovis and S. uberis.