Deaths observed in Medicare beneficiaries: average attributable fraction and its longitudinal extension for many diseases

Calculating the longitudinal extension of the average attributable fraction (LE-AAF) for many risk factors (RFs) requires a two-stage computational process using only those combinations of RFs observed in the dataset. We first screen candidates RFs in a Cox Model, and assuming piecewise constant hazards, use pooled logistic regression to model the probability of death as a function of combinations of selected RFs. We average the iterative differencing of the attributable fractions calculated for all overlapping subsets of co-occurring RFs to obtain a LE-AAF for each RF that is additive and symmetrical. We illustrate by partitioning the additive proportions of death from 10 different groupings of acute and chronic diseases, on a national sample of older persons from the US (Medicare Beneficiary Survey) over a 4-year period and compare with results reported by the National Center for Healthcare Statistics. We conclude that careful screening of RFs with analysis restricted to extant combinations greatly reduces computational burden. LE-AAF accounted for a cumulative total of 66% of the deaths in our sample, compared with the 83% accounted for by the National Center for Healthcare Statistics.

Designing phenotyping studies for genetically engineered mice

A phenotyping study records physiologic or morphologic changes in an experimental animal resulting from an intervention. In mice, this intervention is most frequently genetic, but it may be any type of experimental manipulation. Accurate representation of the human condition under study is essential if the model is to yield useful conclusions. In this review, general approaches to the design of phenotyping studies are considered. These approaches take into account major sources of reduced model validity, such as unexpected phenotypic variation in mice, evolutionary divergence between mice and humans, unanticipated sources of variation, and common design errors. As poor design is the most common reason why studies fail to yield enduring results, emphasis is placed on reduction of bias, sampling, controlled study design, and appropriate statistical analysis.

Bayesian hierarchical modeling for a non-randomized, longitudinal fall prevention trial with spatially correlated observations

Because randomization of participants is often not feasible in community-based health interventions, non-randomized designs are commonly employed. Non-randomized designs may have experimental units that are spatial in nature, such as zip codes that are characterized by aggregate statistics from sources like the U.S. census and the Centers for Medicare and Medicaid Services. A perennial concern with non-randomized designs is that even after careful balancing of influential covariates, bias may arise from unmeasured factors. In addition to facilitating the analysis of interventional designs based on spatial units, Bayesian hierarchical modeling can quantify unmeasured variability with spatially correlated residual terms. Graphical analysis of these spatial residuals demonstrates whether variability from unmeasured covariates is likely to bias the estimates of interventional effect. The Connecticut Collaboration for Fall Prevention is the first large-scale longitudinal trial of a community-wide healthcare intervention designed to prevent injurious falls in older adults. Over a two-year evaluation phase, this trial demonstrated a rate of fall-related utilization at hospitals and emergency departments by persons 70 years and older in the intervention area that was 11 per cent less than that of the usual care area, and a 9 per cent lower rate of utilization from serious injuries. We describe the Bayesian hierarchical analysis of this non-randomized intervention with emphasis on its spatial and longitudinal characteristics. We also compare several models, using posterior predictive simulations and maps of spatial residuals.

Treatment of death in the analysis of longitudinal studies of gerontological outcomes

BACKGROUND

Longitudinal studies in gerontology are characterized by termination of measurement from death. Death is related to many important gerontological outcomes, such as functional disability, and may, over time, change the composition of an older study population. For these reasons, treating death as noninformative censoring of a longitudinal outcome may result in biased estimates of regression coefficients related to that outcome.

METHODS

In a longitudinal study of community-living older persons, we analytically and graphically illustrate the dependence between death and functional disability. Relative to survivors, decedents display a rapid decline of functional ability in the months preceding death. Death's strong relationship with functional disability demonstrates that death is not independent of this outcome and, hence, leads to informative censoring. We also demonstrate the "healthy survivor effect" that results from death's selection effect, with respect to functional disability, on the longitudinal makeup of an older study population.

RESULTS

We briefly survey commonly used approaches for longitudinal modeling of gerontological outcomes, with special emphasis on their treatment of death. Most common methods treat death as noninformative censoring. However, joint modeling methods are described that take into account any dependency between death and a longitudinal outcome.

CONCLUSIONS

In longitudinal studies of older persons, death is often related to gerontological outcomes and, therefore, cannot be safely assumed to represent noninformative censoring. Such analyzes must account for the dependence between outcomes and death as well as the changing nature of the cohort.

Modeling repeated time-to-event health conditions with discontinuous risk intervals. An example of a longitudinal study of functional disability among older persons

OBJECTIVES

Researchers have often used rather simple approaches to analyze repeated time-to-event health conditions that either examine time to the first event or treat multiple events as independent. More sophisticated models have been developed, although previous applications have focused largely on such outcomes having continuous risk intervals. Limitations of applying these models include their difficulty in implementation without careful attention to forming the data structures.

METHODS

We first review time-to-event models for repeated events that are extensions of the Cox model and frailty models. Next, we develop a way to efficiently set up the data structures with discontinuous risk intervals for such models, which are more appropriate for many applications than the continuous alternatives. Finally, we apply these models to a real dataset to investigate the effect of gender on functional disability in a cohort of older persons. For comparison, we demonstrate modeling time to the first event.

RESULTS

The GEE Poisson, the Cox counting process, and the frailty models provided similar parameter estimates of gender effect on functional disability, that is, women had increased risk of bathing disability and other disability (disability in walking, dressing, or transferring) as compared to men. These results, especially for other disabilities, were quite different from those provided by an analysis of the first-event outcomes. However, the effect of gender was no longer significant in the counting process model fully adjusted for covariates.

CONCLUSION

Modeling time to only the first event may not be adequate. After properly setting up the data structures, repeated event models that account for the correlation between multiple events within subjects can be easily implemented with common statistical software packages.

Hierarchical models to evaluate translational research: Connecticut collaboration for fall prevention

BACKGROUND AND OBJECTIVE

Evidence-based second stage translational studies are necessary and difficult to evaluate. A quasi-experimental design is used to compare the rate of fall-related health care utilization of two geographically disparate areas in Connecticut, a small state in the northeastern United States, to evaluate an intervention designed to reduce fall-related injuries among older persons. This evaluation examines the two years immediately prior to intervention.

METHODS

The experimental units are postal (i.e., zip) code tabulation areas (ZCTAs) in which counts of fall-related health care utilization and demographic characteristics can be gathered from local and federal public health sources. We employ hierarchical modeling to determine whether there was a difference in fall-related health care utilization between the study arms prior to initiating the intervention. Geographic information systems are used to characterize neighboring ZCTAs and to graph model-adjusted rates of fall-related utilization.

RESULTS

After adjustment for covariates and spatial variation, we observed no significant difference between rates or temporal trends of fall-related health care utilization in the study arms over the two year pre-intervention period.

CONCLUSION

The study arms of the Connecticut Collaboration for Falls Prevention have equivalent rates and temporal trends of fall-related utilization over the two year pre-intervention period.

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.

A mathematical model of Staphylococcus aureus control in dairy herds

An ordinary differential equation model was developed to simulate dynamics of Staphylococcus aureus mastitis. Data to estimate model parameters were obtained from an 18-month observational study in three commercial dairy herds. A deterministic simulation model was constructed to estimate values of the basic (R0) and effective (Rt) reproductive number in each herd, and to examine the effect of management on mastitis control. In all herds R0 was below the threshold value 1, indicating control of contagious transmission. Rt was higher than R0 because recovered individuals were more susceptible to infection than individuals without prior infection history. Disease dynamics in two herds were well described by the model. Treatment of subclinical mastitis and prevention of influx of infected individuals contributed to decrease of S. aureus prevalence. For one herd, the model failed to mimic field observations. Explanations for the discrepancy are given in a discussion of current knowledge and model assumptions.

Cow- and quarter-level risk factors for Streptococcus uberis and Staphylococcus aureus mastitis

This study was designed to identify risk factors for intramammary infections with Streptococcus uberis and Staphylococcus aureus under field conditions. An 18-mo survey with sampling of all quarters of all lactating cows at 3-wk intervals was carried out in three Dutch dairy herds with medium bulk milk somatic cell count (200,000 to 300,000 cells/ml). Quarter milk samples were used for bacteriology and somatic cell counting. Data on parity, lactation stage, and bovine herpesvirus 4-serology were recorded for each animal. During the last year of the study, body condition score, and teat-end callosity scores were recorded at 3-wk intervals. A total of 93 new infections with Strep. uberis were detected in 22,665 observations on quarters at risk for Strep. uberis infection, and 100 new infections with Staph. aureus were detected in 22,593 observations on quarters at risk for Staph. aureus infection. Multivariable Poisson regression analysis with clustering at herd and cow level was used to identify risk factors for infection. Rate of infection with Strep. uberis was lower in first- and second-parity cows than in older cows, and depended on stage of lactation in one herd. Quarters that were infected with Arcanobacterium pyogenes or enterococci, quarters that had recovered from Strep. uberis- or Staph. aureus-infection in the past, and quarters that were exposed to another Strep. uberis infected quarter in the same cow had a higher rate of Strep. uberis infection. Teat-end callosity and infection with coagulase-negative staphylococci or corynebacteria were not significant as risk factors. Rate of Staph. aureus infection was higher in bovine herpesvirus 4-seropositive cows, in right quarters, in quarters that had recovered from Staph. aureus or Strep. uberis infection, in quarters exposed to other Staph. aureus infected quarters in the same cow, and in quarters with extremely callused teat ends. Infection with coagulase-negative staphylococci was not significant as a risk factor. The effect of infection with corynebacteria on rate of infection with Staph. aureus depended on herd, stage of lactation, and teat-end roughness. Herd level prevalence of Strep. uberis or Staph. aureus, and low quarter milk somatic cell count were not associated with an increased rate of infection for Strep. uberis or Staph. aureus.

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. Cox's 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.

Analysis of an outbreak of Streptococcus uberis mastitis

An outbreak of Streptococcus uberis mastitis was described to gain insight into the dynamics of Strep. uberis infections at a herd level. Data were obtained from a longitudinal observational study on a commercial Dutch dairy farm with good udder health management. Quarter milk samples for bacteriological culture were routinely collected at 3-wk intervals from all lactating animals (n = 95 +/- 5). Additional samples were collected at calving, clinical mastitis, dry-off, and culling. During the 78-wk observation period, 54 Strep. uberis infections were observed. The majority of infections occurred during a 21-wk period that constituted the disease outbreak. The incidence rate was higher in quarters that had recovered from prior Strep. uberis infection than in quarters that had not experienced Strep. uberis infection before. The incidence rate of Strep. uberis infection did not differ between quarters that were infected with other pathogens compared with quarters that were not infected with other pathogens. The expected number of new Strep. uberis infections per 3-wk interval was described by means of a Poisson logistic regression model. Significant predictor variables in the model were the number of existing Strep. uberis infections in the preceding time interval (shedders), phase of the study (early phase vs. postoutbreak phase), and prior infection status of quarters with respect to Strep. uberis, but not infection status with respect to other pathogens. Results suggest that contagious transmission may have played a role in this outbreak of Strep. uberis mastitis.

Teaching dairy herd health dynamics using a web-based program

INTRODUCTION

This course teaches veterinary students basic principles of epidemiology. Dynamic relationships of dairy herd performance parameters are demonstrated.

METHODOLOGY

Courseware combines lectures (both in-class and Web-based) and problem-based exercises using two computer simulation models. The format of this eight-week, one-credit course is a lecture followed by exercises in a computer laboratory working with simulation models. Currently, Cornell University and nine test sites use the courseware.

CURRENT STATUS

The course has been taught for two years, with students and experts providing evaluations and critical feedback for courseware modification.

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.

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.

Optimizing replacement decisions for Finnish dairy herds

The purposes of the study were to determine how "an optimal herd" would be structured with respect to its calving pattern, average herdlife and calving interval, and to evaluate how sensitive the optimal solution was to changes in input prices, which reflected the situation in Finland in 1998. The study used Finnish input values in an optimization model developed for dairy cow insemination and replacement decisions. The objective of the optimization model was to maximize the expected net present value from present and replacement cows over a given decision horizon. In the optimal solution, the average net revenues per cow were highest in December and lowest in July, due to seasonal milk pricing. Based on the expected net present value of a replacement heifer over the decision horizon, calving in September was optimal. In the optimal solution, an average calving interval was 363 days and average herdlife after first calving was 48.2 months (i.e., approximately 4 complete lactations). However, there was a marked seasonal variation in the length of a calving interval (it being longest in spring and early summer) that can be explained by the goal of having more cows calving in the fall. This, in turn, was due to seasonal milk pricing and higher production in the fall. In the optimal solution, total replacement percentage was 26, with the highest frequency of voluntary culling occurring at the end of the year. Seasonal patterns in calving and replacement frequencies by calendar month and variation in calving interval length or herdlife did not change meaningfully (< 1%-2% change in the output variables) with changes in calf, carcass or feed prices. When the price of a replacement heifer decreased, average herdlife was shorter and replacement percentage increased. When the price increased, the effect was the opposite.

Optimizing breeding decisions for Finnish dairy herds

The purpose of this study was to determine the effect of reproductive performance on profitability and optimal breeding decisions for Finnish dairy herds. We used a dynamic programming model to optimize dairy cow insemination and replacement decisions. This optimization model maximizes the expected net revenues from a given cow and her replacements over a decision horizon. Input values and prices reflecting the situation in 1998 in Finland were used in the study. Reproductive performance was reflected in the model by overall pregnancy rate, which was a function of heat detection and conception rate. Seasonality was included in conception rate. The base run had a pregnancy rate of 0.49 (both heat detection and conception rate of 0.7). Different scenarios were modeled by changing levels of conception rate, heat detection, and seasonality in fertility. Reproductive performance had a considerable impact on profitability of a herd; good heat detection and conception rates provided an opportunity for management control. When heat detection rate decreased from 0.7 to 0.5, and everything else was held constant, net revenues decreased approximately 2.6%. If the conception rate also decreased to 0.5 (resulting in a pregnancy rate of 0.25), net revenues were approximately 5% lower than with a pregnancy rate of 0.49. With lower fertility, replacement percentage was higher and the financial losses were mainly from higher replacement costs. Under Finnish conditions, it is not optimal to start breeding cows calving in spring and early summer immediately after the voluntary waiting period. Instead, it is preferable to allow the calving interval to lengthen for these cows so that their next calving is in the fall. However, cows calving in the fall should be bred immediately after the voluntary waiting period. Across all scenarios, optimal solutions predicted most calvings should occur in fall and the most profitable time to bring a replacement heifer into a herd was in the fall. It was economically justifiable to keep breeding high producing cows longer than low producing cows.

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.

Partial budget of the discounted annual benefit of mastitis control strategies

The objective of this study was to rank the benefits associated with various mastitis control strategies in simulated herds with intramammary infections caused by Streptococcus agalactiae, Streptococcus spp. other than Strep. agalactiae, Staphylococcus aureus, coagulase-negative staphylococci, and Escherichia coli. The control strategies tested were prevention, vaccination for E. coli, lactation therapy, and dry cow antibiotic therapy. Partial budgets were based on changes caused by mastitis control strategies from the mean values for milk, fat, and protein yields of the control herd and the number of cows that were culled under a fixed mastitis culling criterion. Each annual benefit (dollars per cow per year) of a mastitis control strategy was compared with the revenue for the control herd and was calculated under two different milk pricing plans (3.5% milk fat and multiple-component pricing), three net replacement costs, and three prevalences of pathogen-specific intramammary infection. Twenty replicates of each control strategy were run with SIMMAST (a dynamic discrete event stochastic simulation model) for 5 simulated yr. Rankings of discounted annual benefits differed only slightly according to milk pricing plans within a pathogen group but differed among the pathogen groups. Differences in net replacement costs for cows culled because of mastitis did not change the ranking of control strategies within a pathogen group. Both prevention and dry cow therapy were important mastitis control strategies. For herds primarily infected with environmental pathogens, strategies that included vaccination for mastitis caused by E. coli dominated strategies that did not include vaccination against this microorganism.

A simulation of strategies to lower bulk tank somatic cell count below 500,000 per milliliter

In the future, the Pasteurized Milk Ordinance may make milk quality standards more stringent by lowering the somatic cell count (SCC) limit on Grade A raw milk to 500,000/ml. Therefore, using a discrete event simulation model, we investigated the effects of the prevention of intramammary infection (as recommended by the National Mastitis Council), lactation therapy, and dry cow therapy (all seven possible combinations) on bulk tank SCC; milk, fat, and protein yields; prevalence of intramammary infection; and culling for mastitis. Untreated controls were also tested. Ten replicates of each intervention and each control were run for 2 simulated yr, including the daily sampling of 100 cows. The goal was to lower bulk tank SCC < 500,000/ml in the 2nd yr for herds that previously had stable bulk tank SCC between 500,000 and 750,000/ml. Although all strategies occasionally met this goal, on no occasion did all replicates perform without a violation in the 2nd yr of the study (median last month of violation ranged from mo 12 to 23). The combination of the prevention of intramammary infection, lactation therapy, and dry cow therapy resulted in the lowest bulk tank linear score, most replicated without a violation in the 2nd yr, fewest months with a bulk tank linear score > or = 5.3, and fewest mastitis culls. The combination of the prevention of intramammary infection and dry cow therapy also was favorably ranked (highest milk yield, fewest clinical intramammary infections during lactation, and highest percentage of uninfected cows).

Design and validation of a dynamic discrete event stochastic simulation model of mastitis control in dairy herds

A dynamic stochastic simulation model for discrete events, SIMMAST, was developed to simulate the effect of mastitis on the composition of the bulk tank milk of dairy herds. Intramammary infections caused by Streptococcus agalactiae, Streptococcus spp. other than Strep. agalactiae, Staphylococcus aureus, and coagulase-negative staphylococci were modeled as were the milk, fat, and protein test day solutions for individual cows, which accounted for the fixed effects of days in milk, age at calving, season of calving, somatic cell count (SCC), and random effects of test day, cow yield differences from herdmates, and autocorrelated errors. Probabilities for the transitions among various states of udder health (uninfected or subclinically or clinically infected) were calculated to account for exposure, heifer infection, spontaneous recovery, lactation cure, infection or cure during the dry period, month of lactation, parity, within-herd yields, and the number of quarters with clinical intramammary infection in the previous and current lactations. The stochastic simulation model was constructed using estimates from the literature and also using data from 164 herds enrolled with Quality Milk Promotion Services that each had bulk tank SCC between 500,000 and 750,000/ml. Model parameters and outputs were validated against a separate data file of 69 herds from the Northeast Dairy Herd Improvement Association, each with a bulk tank SCC that was > or = 500,000/ml. Sensitivity analysis was performed on all input parameters for control herds. Using the validated stochastic simulation model, the control herds had a stable time average bulk tank SCC between 500,000 and 750,000/ml.

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.

Effects of season, herd size, and geographic region on the composition and quality of milk in the northeast

Our objectives were to describe the milkshed comprising herds in New York, western New Jersey, and central and eastern Pennsylvania in regard to milk yield, composition, and quality and also to estimate the effects of season, herd size, and geographic area on those same variables. Data were collected from July 1993 through June 1994 from 3450 herds. The effect of a somatic cell count (SCC) limit of 500,000/ml on milk yield and the composition of monthly bulk tank milk for all marketed milk was estimated as was the frequency of deliveries of milk that contained SCC that were greater than this limit. All general linear models for mean monthly yield of milk and milk components (fat and protein) and SCC were significant for fixed effects of month and herd size within quartiles for herd size (defined by the number of lactating cows) and significant absorbed effects of herds within quartiles for herd size within subregion. Milk yield, milk components (kilograms), true protein percentage, and SCC were significantly higher in spring than in fall for both data files (complete data file and data file containing only herds with SCC < 500,000/ml). Thirty-five percent of herds with < 27 lactating cows but only 15.3% of herds with > 62 lactating cows had > or = 1 mo with an SCC > 500,000/ml. For herds in the subregions, percentages of shipments with an SCC > or = 500,000/ml ranged from 10.5 to 20.2%. Herds with < 27 lactating cows contributed to the milkshed a disproportionate percentage of SCC (11%) compared with their percentage of contribution of milk (5%).

A decision support system for evaluating mastitis information

A data-driven decision support system, MAST, was developed to summarize systematically the DHI data related to mastitis. MAST determines weaknesses and problems of a mastitis control strategy by pinpointing problem areas, highlighting the scope of the mastitis problem, providing reference values for comparison, offering potential solutions to problem areas, and monitoring changes in the control strategy. Advantages of a DHI data-driven system include accuracy of input data, fast execution speeds, access to untapped information available in DHI data, and a consistent analysis of data. An on-farm decision support system allows the evaluation of the mastitis control strategy at any time, which in turn increases the value of DHI information. The sequence of the graphical results allows users to understand intuitively the overall mastitis problems, find the potential origins, and assess their impact on the herd. Color-coded graphs with supplementary text allow for a rapid analysis of level and trends over time, as well as comparisons among parities, lactation stages, and active and culled cows.

An approach to summarize somatic cell score trends for a data-driven, decision support system

A set of analytical routines were developed to determine significant trends in values for herd DHI somatic cell scores. These trends were used as input to a data-driven, decision support system to aid mastitis management of dairy cattle. The trends of interest were those experienced over the last six DHI sample periods for the entire herd, for three parity groups, and for three stages of lactation. First, cows within the herd were split randomly into two equal groups to account for within-herd variation. For each group, linear regression was calculated for somatic cell score over time within each parity by stage of lactation group. The 18 slope estimates were then analyzed using a two-way ANOVA to test for main fixed effects of parity, stage of lactation, and their interaction. The results of the trend analyses were converted to facts that were asserted to an embedded expert system for further evaluation.