SELECTING LINEAR-SCORE DISTRIBUTIONS FOR MODELING 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 Feb ruary, 1993 and March, 1995. The objective was to identify probability distributions of logarithmically transformed somatic-cell counts (lin ear 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 composite-milk samp les culture negative and culture positive for the pathogens Streptococ cus agalactiae, Streptococcus non-agalactiae, Staphylococcus aureus, a nd coagulase-negative staphylococci for the complete dataset and by bu lk-tank somatic-cell count group (<500 000, greater than or equal to 5 00 000 SCC/ml). Based on the rankings of three goodness-of-fit tests ( Anderson-Darling, Kolmogorov-Smirnov and chi(2)), the Weibull distribu tion (among the three top-ranking distributions for 14 out of 15 cases ) may be used to model the individual-cow linear-score response by cul ture-result-specific bulk-tank somatic-cell count group. A beta distri bution was among the three top-ranking distributions for nine out of 1 5 culture-result-specific bulk-tank somatic-cell count groups and has a logical relationship to linear score because it is defined on a fixe d interval. On the other hand, the normal distribution had a poorer fi t than the Weibull and at least two other distributions far all cultur e negative and coagulase-negative staphylococci samples. We do not ass ume that the underlying biological processes are fully explained by ei ther Weibull or beta distribution-but modelling the Linear score for t he above culture results with these distributions provided an adequate fit to the survey data, reduced the need for two-sided truncation tha t open intervals needed, and had errors that did not appear to be syst ematically positive or negative. (C) 1998 Elsevier Science B.V.