Selecting linear-score distributions for modelling milk-culture results

The data for this cross-sectional retrospective study are from surveys of 65 dairy-cattle herds in central New York, USA sampled between February, 1993 and March, 1995. The objective was to identify probability distributions of logarithmically transformed somatic-cell counts (linear score) for use in a simulation model of mastitis and milk quality. Probability density functions were estimated using maximum-likelihood estimators for the linear score of individual-cow compositemilk samples culture negative and culture positive for the pathogens Streptococcus agalactiae, Streptococcus non-agalactiae, Staphylococcus aureus, and coagulase-negative staphylococci for the complete dataset and by bulk-tank somatic-cell count group (< 500 000, ≥ 500 000 SCC/ml). Based on the rankings of three goodness-of-fit tests (Anderson-Darling, Kolmogorov-Smirnov and x²), the Weibull distribution (among the three top-ranking distributions for 14 out of 15 cases) may be used to model the individual-cow linear-score response by culture-result-specific bulk-tank somatic-cell count group. A β distribution was among the three top-ranking distributions for nine out of 15 culture-result-specific bulk-tank somatic-cell count groups and has a logical relationship to linear score because it is defined on a fixed interval. On the other hand, the normal distribution had a poorer fit than the Weibull and at least two other distributions for all culture negative and coagulase-negative staphylococci samples. We do not assume that the underlying biological processes are fully explained by either Weibull or β distribution—but modelling the linear score for the above culture results with these distributions provided an adequate fit to the survey data, reduced the need for two-sided truncation that open intervals needed, and had errors that did not appear to be systematically positive or negative.