Heather G. Allore

Optimizing replacement of dairy cows: modeling the effects of diseases

We modified an existing dairy management decision model by including economically important dairy cattle diseases, and illustrated how their inclusion changed culling recommendations. Nine common diseases having treatment and veterinary costs, and affecting milk yield, fertility and survival, were considered important in the culling decision process. A sequence of stages was established during which diseases were considered significant: mastitis and lameness, any time during lactation; dystocia, milk fever and retained placenta, 0-4 days of lactation; displaced abomasum, 5-30 days; ketosis and metritis, 5-60 days; and cystic ovaries, 61-120 days. Some diseases were risk factors for others. Baseline incidences and disease effects were obtained from the literature. The effects of various disease combinations on milk yield, fertility, survival and economics were estimated. Adding diseases into the model did not increase voluntary or total culling rate. However, diseased animals were recommended for culling much more than healthy cows, regardless of parity or production level. Cows in the highest production level were not recommended for culling even if they contracted a disease. The annuity per cow decreased and herdlife increased when diseases were in the model. Higher replacement cost also increased herdlife and decreased when diseases were in the model. Higher replacement cost also increased herdlife and decreased the annuity and voluntary culling rate.

Approaches to modeling intramammary infections in dairy cattle.

In this paper, three approaches (Markov processes, discrete-event simulation, and differential equations) to modeling intramammary infections (IMI; focusing on the dynamic changes between uninfected, subclinical, and clinical udder health states) are described. The objectives were to describe the various approaches to modeling intramammary infections, determine if simulations of the examples of the three approaches yield stable prevalences, and discuss the approaches limitations. The literature review showed that there is no agreement on the proportion of animals that change health states. The approach of discrete-event simulation modeling included the most cow-level risk factors and udder-health states (hence, was judged to replicated best the dynamics of the infection process) and yielded stable prevalences for all udder-health states. However, there remain parts of the dynamics that need further research. These include the pathogen-specific probabilities and times of occurrence for: regression of clinical IMI to subclinical IMI, flare-up of subclinical IMI to clinical IMI, and incidence of subclinical IMI. Also, the assumption in all current approaches of homogeneous mixing is violated because the primary contact structure for contagious pathogens during milking is either between cows through residual infectious milk in the milking machine or within a cow by vacuum fluctuations or teat-cup liner slips. Better contact structures should be incorporated so that the effects of control strategies can be better-estimated. Moreover, the three modeling approaches discussed assumed that all non-infected quarters are susceptible to infection--which might be denied by work in genetic resistance.

Censoring in survival analysis: a simulation study of the effect of milk yield on conception.

Survival-analysis methods often are used to analyze data from dairy herds where the outcome of interest is the interval from calving to conception. The purpose of this study was to determine whether an association between milk yield and culling biases the estimation of the effect of milk yield on conception. This was done by simulating four different scenarios modeling dairy-cattle milk yield and reproductive performance with known relationships among study factors. Coxs proportional-hazards model was used to analyze the effect of milk yield on days open under the following four scenarios: (1) no association between milk yield and culling or between milk yield and conception; (2) association between milk yield and culling only; (3) association between milk yield and conception only; (4) associations between milk yield and both culling and conception. The analyses also were repeated for data sets with an association between milk yield and culling, but with probabilities of culling ranging from 0.01 to 0.4. An effect of milk production on culling appeared to cause a small increase in the parameter estimates for the association of milk yield and days open - particularly when the probability of culling was high. The effect of high milk production on median days open (as estimated by survival functions) changed by 2 to 4 days when an association between milk yield and culling was programmed in the simulated data sets.

Simulated effects on dairy cattle health of extending the voluntary waiting period with recombinant bovine somatotropin.

We simulated the effect of extending the voluntary wait period by 100 days on disorder-frequency measures that were based on cow-years (from lactations completed during the 4-year simulation horizon), metric tons of milk yield, and lactational incidence risks. A dynamic stochastic discrete-event simulation model that focuses on clinical and subclinical intramammary infections (IMI), plus clinical metabolic (left-displaced abomasum, ketosis, milk fever) and reproductive (cystic ovarian disease, dystocia, retained placenta, twinning, uterine infection) disorders in dairy herds was used. Although the voluntary wait period was increased by 100 days (50 vs. 150), the predicted difference in simulated days to conception was only 89 days for the extended voluntary wait-period group (which we attributed to higher fertility later in lactation). Herds that had a voluntary wait period of 150 days (compared to the control herds voluntary wait period of 50 days) were predicted to have significantly lower rates of metabolic and reproductive disorders and clinical mastitis on both cow-year and milk-yield bases. Simulated control herds, on average, produced 8539 kg of milk in an average lactation of 325 days and simulated herds with a 150-day voluntary wait period 10893 kg of milk in an average lactation of 409 days. There was a significantly lower predicted rate and risk of culling for reproductive failure in the extended voluntary wait period group. The predicted lactational incidence risks for subclinical IMI were 18% higher for the extended voluntary wait period group - but extending the voluntary wait period by 100 days was predicted not to increase the risk of any of the other 10 disorders.

Disease management research using event graphs

Event Graphs, conditional representations of stochastic relationships between discrete events, simulate disease dynamics. In this paper, we demonstrate how Event Graphs, at an appropriate abstraction level, also extend and organize scientific knowledge about diseases. They can identify promising treatment strategies and directions for further research and provide enough detail for testing combinations of new medicines and interventions. Event Graphs can be enriched to incorporate and validate data and test new theories to reflect an expanding dynamic scientific knowledge base and establish performance criteria for the economic viability of new treatments. To illustrate, an Event Graph is developed for mastitis, a costly dairy cattle disease, for which extensive scientific literature exists. With only a modest amount of imagination, the methodology presented here can be seen to apply modeling to any disease, human, plant, or animal. The Event Graph simulation presented here is currently being used in research and in a new veterinary epidemiology course.

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 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.