title: Selecting linear-score distributions for modelling milk-culture results.
abstract: 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 composite-milk 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, > or = 500,000 SCC/ml). Based on the rankings of three goodness-of-fit tests (Anderson-Darling, Kolmogorov-Smirnov and chi 2), 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 beta 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 beta 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.
authors.affiliation: Department of Animal Science, College of Agriculture and Life Sciences, Cornell University, Ithaca, NY 14853, USA. hga1@cornell.edu
authors.forename: H G
authors.initials: HG
authors.lastname: Allore
authors.forename: D J
authors.initials: DJ
authors.lastname: Wilson
authors.forename: H N
authors.initials: HN
authors.lastname: Erb
authors.forename: P A
authors.initials: PA
authors.lastname: Oltenacu
mesh_terms: D000818:Animals; D002417:Cattle; D002452:Cell Count / Q000662:veterinary; D015169:Colony Count, Microbial; D003430:Cross-Sectional Studies; D003612:Dairying / Q000706:statistics & numerical data*; D005260:Female; D007774:Lactation; D016013:Likelihood Functions; D016014:Linear Models; D008414:Mastitis, Bovine / Q000453:epidemiology* / Q000517:prevention & control; D008892:Milk / Q000166:cytology / Q000382:microbiology / Q000592:standards*; D008954:Models, Biological; D009518:New York / Q000453:epidemiology; D015995:Prevalence; D011336:Probability; D012189:Retrospective Studies; D013211:Staphylococcus aureus / Q000302:isolation & purification; D013291:Streptococcus / Q000302:isolation & purification; D013292:Streptococcus agalactiae / Q000302:isolation & purification