Lameness is the most visible animal welfare issue of the modern North American dairy industry and arguably the second most important cause of economic losses.1 Dairy cows affected with lameness are less profitable because of increased likelihood of culling and death, decreased reproductive performance, and decreased milk production.2,3 Consumer awareness about the welfare of food animals has created a demand for food-animal products from animal-friendly production systems. To genuinely meet this consumer demand, North American dairy farmers will have to substantially decrease the prevalence and incidence of lameness in dairy cows. Sole ulcers (pododermatitis circumscripta) and white line diseases are widespread in dairy cattle, and once an animal is affected, lameness can persist for > 30 days.4,5 Therefore, efforts should be directed toward decreasing the incidence of these diseases.
The ability to predict the incidence of diseases is an invaluable tool for their prevention. In human medicine, predictive models are commonly used to quantify the risk of disease as well as the probability of success of specific treatments. The risk of coronary heart disease is predicted by use of a multivariable-adjusted model that includes blood pressure values and cholesterol concentrations.6 With regard to dairy cattle, prevention of lameness is the most important step to reduce its welfare implications and associated economic losses.7 Hence, it is important to develop a model that accurately predicts the occurrence of lameness, allowing farmers to apply preventive strategies on targeted high-risk groups.
The objective of the study reported here was to develop a parsimonious statistical model that could accurately predict the incidence of lameness in the subsequent lactation by use of information available during hoof trimming at the cessation of lactation in dairy cows. The hypothesis was that DCT, BCS, age, and CHDLs at cessation of lactation are associated with the incidence of sole ulcers and white line disease in the subsequent lactation.
Materials and Methods
Farm and management—Data were collected from a dairy farm located near Ithaca, NY, from September 11, 2008, until June 15, 2009. This farm was selected because of its long history of a working relationship with the Ambulatory and Production Medicine Clinic at Cornell University. The farm milked 2,800 Holstein cows 3 times daily in a double 52-stall parallel milking parlor. The cows were housed in freestall barns with concrete stalls covered with mattresses and bedded with waste paper pulp. The feed alleys had grooved concrete flooring and were cleaned with automatic scrapers. All walkways to and from the milking barn and the holding pen were covered with rubber, including the holding pen. Each individual cow was scheduled to receive routine hoof trimming twice yearly; a protocol was created with specific dairy farm record database softwarea that identified lactating cows for routine trimming when 150 days had passed since their last routine hoof trimming. Furthermore, all cows received a regular hoof trimming at cessation of lactation, which reset the 150-day schedule. Lame cows were identified by the farm employees using visual detection of asymmetric gait (lameness) in cows returning from the milking parlor; a systematic lameness scoring system was not used. Treatment of lame cows was also performed by trained farm employees.
All cows were offered a total mixed ration consisting of approximately 55% forage (corn silage, haylage, and wheat straw) and 45% concentrate (cornmeal, soybean meal, canola, cotton seed, and citrus pulp) on a dry-matter basis. The diet was formulated to meet or exceed the National Research Council nutrient requirements for lactating Holstein cows weighing 650 kg and producing 45 kg of 3.5% fat-corrected milk.
Nonlactating cows were grouped on the basis of days from parturition: a far-off group (> 30 days from parturition) and a close-up group (≤ 30 from parturition). Nonlactating cows were housed in 6-row freestall barns bedded with sand, and the alleys were scraped with a skid steer twice daily.
Study design and data collection—A prospective cohort study design was used. Data were collected at cessation of lactation by the authors and throughout the subsequent lactation by trained farm employees. The following data were collected at cessation of lactation: BCS that was scored on a scale from 1 to 5 with a quarter-point system as described by Edmonson et al,8 cow height measurement assessed as the distance in centimeters from the floor to the dorsal aspect of the caudal sacral joint, and visual locomotion score as described by Bicalho et al.2 Additionally, all cows' hooves were trimmed by one of the authors, and DCT and digital lesions including CHDLs were recorded. Cattle were restrained for hoof trimming with a standing hoof trimming chute. After hoof trimming, the cows underwent digital ultrasonographic B-mode examination with an ultrasonography machineb equipped with a curved-array, dual-frequency probe (set at 7.5 MHz) to assess the DCT. The examination was always performed at zone 4 of the weight-bearing surface,9 assessing the distance from the inner margin of the sole (identified as a thin echogenic line) to the distal edge of the tuber-culum flexorum of the third phalanx (identified as a thick echogenic line). Before beginning the study, the technique was evaluated in a study10 (by use of slaughterhouse-acquired foot specimens) that assessed the association of ultrasonographic measurement and the actual measurement of the middle digital cushion pad after dissection of hooves, which revealed no significant differences between the measurements.
After the onset of lactation, cows were monitored on a daily basis for visual signs of lameness (presence of a limp) by 2 trained farm employees. Employees were trained by veterinarians of the Cornell Ambulatory and Production Medicine Clinic and received a refresher course once per year. They observed cows walking to the parlor, and those that were limping were taken to the hoof trimming chute for therapeutic hoof trimming. Treatment was applied according to the diagnosed foot disorder, and a protocol designed by the Cornell Ambulatory and Production Medicine Clinic was followed; data were recorded and entered into dairy farm record database software.a
Statistical analysis—To predict the incidence of CHDLs in the subsequent lactation, logistic regression models were fitted to the data by use of a statistical software program.c The following independent variables were entered into the model: DCT, BCS, CHDLs at cessation of lactation, height of the cow at cessation of lactation, age in days, calving season, days of milk production at cessation of lactation, and days of pregnancy at cessation of lactation. Variables were removed from the model manually and in a stepwise manner at a value of P > 0.10. All possible 2-way interactions between the independent variables were added to the model; none were significant. After variable selection steps, the following variables were considered relevant (P ≤ 0.10): DCT, BCS, CHDLs at cessation of lactation, and age. To select the most economical logistic regression model with good predictability of CHDLs in the subsequent lactation, 3 models were evaluated. The first model included all 4 significant variables (DCT, BCS, CHDLs at cessation of lactation, and age); the second model included DCT, CHDLs at cessation of lactation, and age; and the third model only included BCS, CHDLs at cessation of lactation, and age. The probability equation of the logistic regression model was used to calculate the predicted probabilities of CHDLs during the subsequent lactation.
To assess the model fit and the overall predictability of the final logistic regression models, ROC analyses were performed by use of the predicted probability estimates (from all logistic regression models) and the presence or absence of CHDLs diagnosed at hoof trimming in the subsequent lactation. Furthermore, the log likelihood and pseudo R2 estimates from each model were used to assess and compare the model fit. All statistical analyses were performed with statistical software.c The variables and their respective interaction terms were retained in the model at values of P < 0.05.
Results
Descriptive statistics—All of the 574 cows for which lactation was ended on the study farm between September 11, 2008, and January 2, 2009, were enrolled in the study and were available for analysis, of which 140 (24%) had a diagnosis of and were treated for CHDLs at cessation of lactation: 114 with sole ulcers and 26 cows with white line disease. Cows had a mean ± SD follow-up period after the onset of parturition of 77 ± 43 days. All cows were multiparous, and the mean ± SD parity number was 2.92 ± 1.21, with a range of 2 to 8 parities. Mean ± SD age at enrollment was 1,580 ± 468 days, ranging from 1,095 to 3,639 days. Mean ± SD length of the nonlactation period was 63 ± 10 days.
Cows that had CHDLs at cessation of lactation had an incidence of CHDLs of 43.8% in the subsequent lactation, whereas for cows that were free of CHDLs at cessation of lactation, the incidence of CHDLs in the subsequent lactation was 9.6% (P < 0.001). The incidence of CHDLs in the subsequent lactation was highly related to BCS at cessation of lactation. Digital cushion thickness at cessation of lactation was also associated with CHDL incidence in the subsequent lactation; the incidence of CHDLs was 26.6% and 9.7% for the lowest and highest quartile of DCTs, respectively. The incidence of CHDLs was lower as BCS increased, even when analyzing only the cows that were free of CHDLs at cessation of lactation; the incidence of CHDLs was 33%, 22%, 9%, 9%, 7%, and 12% for BCSs of 2, 2.5, 3, 3.5, 4, and 4.5, respectively. Mean ± SD age for the entire study population was 1,581 ± 468 days. Mean age for cows detected with CHDLs at cessation of lactation was 1,847 days (95% CI, 1,774 to 1,921 days), and mean age for cows free of CHDLs was 1,494 days (95% CI, 1,453 to 1,536 days).
Body condition score was significantly (P < 0.001) associated with DCT; mean DCT was 0.94, 1.00, 1.03, 1.07, 1.09, and 1.11 for BCSs of 2, 2.5, 3, 3.5, 4, and 4.5, respectively. Cows with sole ulcers and white line disease at cessation of lactation had mean ± SE DCTs of 0.097 ± 0.02 and 0.096 ± 0.03, respectively, which were significantly lower than that of cows without CHDLs at cessation of lactation (DCT, 1.06 ± 0.01). A similar association of CHDLs and mean DCT was found for cows with CHDLs in the subsequent lactation; mean ± SE DCT for cows that were not detected with CHDLs in the subsequent lactation was 1.05 ± 0.01, and mean DCTs for cows with sole ulcers and white line disease in the subsequent lactation were 0.98 ± 0.02 and 0.99 ± 0.03, respectively.
Comparison of logistic regression models—All 3 logistic regression models predicted the incidence of CHDLs in subsequent lactation with good accuracy, and the area under the ROC curves was 0.76, 0.76, and 0.77 for the first, second, and third logistic regression models, respectively (Figure 1 [P > 0.05]). Results of 3 logistic regression models were determined (Table 1). When the recommended probability cutoffs were used to dichotomize cows into high risk and low risk for lameness groups in the subsequent lactation, an overall accuracy of 0.74, 0.76, and 0.76 was estimated for models 1, 2, and 3, respectively (Table 2). The dynamics of the sensitivity and specificity as the probability cutoff is increased from 0 to 1 and was illustrated graphically for the third logistic regression model (Figure 2). Sensitivity, specificity, overall accuracy, and percentage of cows with values greater than the suggested probability cutoff were estimated for each hypothetical probability cutoff (Table 3).
Receiver-operator characteristic curves for 3 logistic regression models for evaluation of CHDLs in dairy cows. The first, second, and third models are represented by the light gray line, black line, and dark gray line, respectively. The straight line indicates the line of no discrimination.
Citation: American Journal of Veterinary Research 72, 10; 10.2460/ajvr.72.10.1338
Sensitivity (gray line) and specificity (black line) analysis for a logistic regression model that included BCS, age, and CHDL at cessation of lactation in dairy cows as independent variables. Notice the increase in specificity and decrease in sensitivity as the model's predicted probability cutoff value increases. The intersection of the sensitivity and specificity lines indicates the recommended cutoff probability value for defining lameness.
Citation: American Journal of Veterinary Research 72, 10; 10.2460/ajvr.72.10.1338
Results of 3 logistic regression models used to predict incidence of CHDLs in dairy cows.
| Model and variable* | Adjusted incidence of CHDL | Coefficient | SE | P value |
|---|---|---|---|---|
| Model 1 | ||||
| DCT 0–25 (quartile) | 27.1 | −1.09 | 0.64 | 0.04 |
| DCT 25–50 (quartile) | 22.2 | |||
| DCT 50–75 (quartile) | 12.6 | |||
| DCT 75–100 (quartile) | 10.8 | |||
| BCS | ||||
| 2 | 38.9 | −0.52 | 0.24 | 0.03 |
| 2.5 | 32.6 | |||
| 3 | 16.5 | |||
| 3.5 | 14.5 | |||
| 4 | 11.6 | |||
| 4.5 | 6.7 | |||
| CHDL | 43.8 | 1.54 | 0.26 | 0.01 |
| No CHDL | 9.6 | |||
| Age (d) | NA | 0.0005 | 0.0002 | 0.05 |
| Model 2 | ||||
| DCT | NA | −1.27 | 0.63 | 0.04 |
| Age (d) | NA | 0.0004 | 0.0002 | 0.10 |
| CHDL | NA | 1.67 | 0.25 | 0.01 |
| Model 3 | ||||
| BCS | NA | −0.57 | 0.24 | 0.02 |
| Age (d) | NA | 0.0005 | 0.0002 | 0.06 |
| CHDL | NA | 1.64 | 0.25 | 0.01 |
Variables were measured at the time of cessation of lactation.
NA = Not appicable.
Model fit evaluation parameters for 3 logistic regression models used to predict CHDLs in dairy cows.
| Parameter | Model 1 | Model 2 | Model 3 |
|---|---|---|---|
| Log likelihood | −234.95 | −237.35 | −236.40 |
| Pseudo R2 | 0.148 | 0.139 | 0.143 |
| Area under the ROC curve | 0.77 (0.73–0.80) | 0.759 (0.72–0.79) | 0.758 (0.72–0.79) |
| Probability cutoff | 0.14 | 0.146 | 0.153 |
| Sensitivity | 71.0 (61.5–79.4) | 65.4 (55.6–74.4) | 65.4 (55.6–74.4) |
| Specificity | 75.3 (71.1–79.2) | 78.5 (74.5–82.2) | 78.3 (74.3–82.0) |
| Positive predictive value | 67.3 | 65.4 | 65.4 |
| Negative predictive value | 75.3 | 78.3 | 78.1 |
| Overall accuracy | 0.74 | 0.76 | 0.76 |
Sensitivity = Sensitivity of CHDL detection in the subsequent lactation when lameness was defined by a predicted probability greater than the estimated cutoff value. Specificity = Specificity of CHDL detection in the subsequent lactation when lameness was defined by a predicted probability greater than the estimated cutoff value.
Outcome of curve analysis for logistic regression model 3 in Tables 1 and 2. Sensitivity, specificity, overall accuracy, and percentage of cows with values greater than the suggested probability cutoff value were estimated for each hypothetical probability cutoff value.
| Probability cutoff value* | Sensitivity (% [95% CI]) | Specificity (% [95% CI]) | Overall accuracy (%) | Cows > cutoff value (%) |
|---|---|---|---|---|
| > 0.096 | 90.6 (83.5–95.4) | 32.2 (28.0–36.6) | 43.5 | 71.7 |
| > 0.097 | 87.8 (80.1–93.4) | 40.1 (35.6–44.7) | 47.3 | 67.5 |
| > 0.100 | 85.0 (76.9–91.2) | 50.0 (45.4–54.6) | 56.2 | 57.2 |
| > 0.103 | 80.3 (71.6–87.4) | 54.1 (49.4–58.7) | 59.3 | 52.0 |
| > 0.111 | 78.5 (69.5–85.9) | 60.1 (55.5–64.6) | 63.5 | 47.1 |
| > 0.130 | 70.0 (60.5–78.6) | 72.1 (67.8–76.1) | 71.7 | 35.8 |
| > 0.153* | 65.4 (55.6–74.4) | 78.3 (74.3–82.0) | 75.8 | 30.0 |
| > 0.180 | 60.7 (55.6–74.4) | 81.3 (77.5–84.8) | 77.5 | 26.9 |
| > 0.365 | 49.5 (39.7–59.4) | 87.1 (83.7–90.0) | 80.1 | 19.7 |
Probability cutoff value suggested by curve analysis.
Further analysis and predictions were completed for the third logistic regression model. Predicted probabilities calculated with the probability equation (Table 4) had a bimodal distribution, likely because of the effect of the binomial independent variable CHDL at cessation of lactation (Figure 3). Older cows with low BCS at cessation of lactation and a CHDL detected during hoof trimming at the time of cessation of lactation had the highest probability of a CHDL in the subsequent lactation (predicted probability, 0.65; 95% CI, 0.49 to 0.78). However, the lowest predicted probability of lameness was for a young cow with a high BCS and without CHDLs at cessation of lactation (predicted probability, 0.03; 95% CI, 0.01 to 0.08).
Frequency distribution plot of the predicted probabilities from a logistic regression model that included BCS, age, and CHDL at cessation of lactation in dairy cows as independent variables. Notice that the distribution of the predicted probability is bimodal, illustrating the importance of CHDL at cessation of lactation in the model. The curved line is a fitted Gaussian distribution curve indicating the skewed distribution of predicted lameness probabilities.
Citation: American Journal of Veterinary Research 72, 10; 10.2460/ajvr.72.10.1338
Predicted probabilities of CHDLs in dairy cows in the subsequent lactation and respective 95% CIs calculated with the logistic regression probability equation of the third logistic regression model in Tables 1 and 2.
| BCS | Age (d) | CHDL at cessation of lactation | Predicted probability of CHDL | 95% CI |
|---|---|---|---|---|
| 2 | 2,501 | 1 | 0.65 | 0.49–0.78 |
| 0 | 0.26 | 0.14–0.44 | ||
| 2.5 | 1,892 | 1 | 0.51 | 0.41–0.6 |
| 0 | 0.17 | 0.11–0.24 | ||
| 3 | 1,618 | 1 | 0.41 | 0.32–0.49 |
| 0 | 0.12 | 0.09–0.15 | ||
| 3.5 | 1,458 | 1 | 0.32 | 0.23–0.44 |
| 0 | 0.08 | 0.06–0.12 | ||
| 4 | 1,267 | 1 | 0.25 | 0.14–0.4 |
| 0 | 0.06 | 0.03–0.10 | ||
| 4.5 | 1,199 | 1 | 0.19 | 0.09–0.37 |
| 0 | 0.04 | 0.02–0.09 | ||
| 5 | 1,141 | 1 | 0.15 | 0.05–0.35 |
| 0 | 0.03 | 0.01–0.08 |
The model included BCS, age (d), and presence (1) or absence (0) of CHDL at cessation of lactation.
Discussion
Although the biomechanical importance of the digital cushion in alleviating compression under the tuberculum flexorum of the distal phalanx has been acknowledged,11–13 little is known about how digital cushion properties are associated with the pathogenesis of CHDLs and how digital cushion properties are altered by the cows' nutrition, health, management, and environment. The incidence of sole ulcers and white line diseases was significantly associated with DCT; cows with low DCT were at a higher risk of CHDLs. Body condition scores were positively associated with DCT. Recently, the authors reported the results of a cross-sectional observational study,10 indicating that the DCT was associated with CHDL, BCS, and stage of lactation. Cross-sectional studies are generally quick and cheap and provide important insights regarding the association of risk factors and disease; however, a known problem with such studies is the limited ability to differentiate cause and effect from a simple association.14 Hence, one of the motivations for the present study arose from the need to confirm the findings from our previous cross-sectional study10 with the use of a more credible longitudinal observational cohort study. In the present study, a strong positive association between BCS and DCT was observed, which is in agreement with our previous findings.10 Additionally, cows that had CHDLs at cessation of lactation as well as in the subsequent lactation had a mean DCT that was significantly lower than that of cows without CHDLs. This finding is also in agreement with our previous study,10 giving further support to the concept that lesions are prevented by thicker digital cushions.
The incidence of CHDLs in the subsequent lactation was strongly associated with BCS, even when analyzing solely the cows that were free of CHDLs at cessation of lactation. It has been reported that cows with low BCSs at parturition are at 9.4 times the risk of developing lameness throughout the lactation, compared with better-conditioned cows.15 In another study,16 the risk of foot problems after parturition increased by 7 times for cows that were considered underconditioned at cessation of lactation. Additionally, it has been hypothesized that the aggravated negative energy balance that causes decreased BCS is the cause of increased risk of lameness.17 We hypothesize that the increased incidence of CHDLs in increasingly thinner cows is a result of loss of pressure-dampening capacity of the digital cushion structures of thinner cows, given that thinner cows have lower DCTs.
The DCT seems to play an important role in the pathogenesis of CHDLs; however, it is important to note that the occurrence of claw contusions is likely the ultimate cause of CHDLs.11,18 There is a wide variation of lameness incidence among different freestall farms, indicating that housing and management differences among dairy farms influence the pathogenesis of lameness.19 Results of several herd-level risk factor studies indicate that poor housing and management strategies are linked with a higher incidence of lameness: overstocking freestall facilities significantly increases the incidence of lameness and decreases lying time,20 total daily milking time is positively associated with prevalence of lameness,21 and the prevalence of lameness in sand-bedded freestall herds is significantly lower than other freestall herds.22 Therefore, housing and management strategies that target cow well-being will ultimately increase the time cows spend resting (stocking density and total milking time) or increase the comfort of the cows (sand bedding), consequently decreasing claw contusions and, ultimately, lameness. The present study as well as our previous study10 provide compelling evidence that low BCS is an important component of the pathogenesis of CHDLs in dairy cows. Contrarily, there is little evidence that CHDLs are caused by subclinical ruminal acidosis.19 Nutritional strategies that are targeted toward the prevention of underconditioned cows are likely to differ from the current nutritional strategies for the prevention of subclinical ruminal acidosis; the first should require denser diets, and the second should require higher fiber diets (lower nutritional density). The paradox of lameness prevention through nutrition is puzzling and certainly needs further investigation; the prevention of subclinical ruminal acidosis at the expense of maintaining proper BCS may induce more lameness instead of preventing it.
The prevalence of lameness increases linearly with parity number.2 In the present study, age at cessation of lactation was used as an independent variable for all 3 logistic regression models. When BCS and DCT were removed from the models, age was significantly associated with CHDLs. The authors believe that much of the variability explained by age is also explained by BCS and DCT because older cows have lower BCS16 and consequently lower DCT10; hence, when all 3 variables are added together in the multivariable model, age loses significance. The variable that was the strongest predictor of a CHDL in the subsequent lactation was a lesion at cessation of lactation; cows detected with sole ulcers or white line disease at cessation of lactation had an incidence of CHDLs of 43.8% in the subsequent lactation, whereas the incidence for cows without lesions was only 9.6%. Sole ulcers and white line diseases are chronic disease processes with a high recurrence rate, and once an animal is affected, lameness can persist for > 30 days.4 Sole ulcers and white line diseases are prevalent in North America; a combined incidence of those lesions of 23.3% has been reported.2
The major objective of the present study was to develop an accurate economical logistic regression model for prediction of lameness in the subsequent lactation by use of data that are readily available at cessation of lactation. Evaluation of 3 models indicated that lameness could be predicted with good accuracy with any of the 3 models. The first model included all significant variables (DCT, BCS, CHDL at cessation of lactation, and age); because DCT and BCS are strongly associated, inclusion of these 2 variables in the model is likely to be redundant and potentially undesirable because of multicoliniarity between the 2 variables. Additionally, the ROC analysis revealed no significant difference in the accuracies of the 3 models, and disease-predictive models are more likely to be implemented if fewer variables are used. It is common practice to trim the hooves of dairy cows close to the time of cessation of lactation; therefore, information such as BCS, presence of CHDLs, and age is readily available. The DCT measurements are reliable and provide consistent data10; however, they require the use of expensive ultrasonography equipment. Determination of BCS is easy and inexpensive and has good agreement between trained observers.8 The authors believe that BCS performed by trained observers could successfully replace DCT. Therefore, the third logistic regression model (including presence of CHDLs, age, and BCS at cessation of lactation) could be used to predict the incidence of CHDLs on dairy farms.
An overall accuracy of approximately 75% was attained for all 3 logistic regression equations. It is important to acknowledge that the outcome variable used in this study (CHDL) was the lameness data that were based on the farm's detection and treatment of lameness cases. Thus far, it is understood that lameness diagnosis by any available means is faulty (ie, it has low accuracy).23 Additionally, dairy farmers and employees often underestimate the true incidence of lameness; the prevalence of lameness estimated by researchers was 2.5 times that estimated by the herd managers.24 Therefore, the accuracies achieved in the present study could be higher or lower given the imperfect gold standard of CHDL detection in the subsequent lactation. However, the authors believe that because of the painful and chronic nature of sole ulcers and white line disease, most affected cows would be identified. Therefore, a concern regarding the ability to replicate the findings of this study exists and the use of locomotion scoring systems to detect lameness in the subsequent lactation may fail to yield similar results given the imperfection of these detection systems.23
The ability to predict lameness will facilitate the implementation of lameness prevention strategies by targeting cows with predicted probabilities of lameness greater than the suggested cutoff value. For instance, high-risk cows could be housed in a specified pen after parturition and the pen could be kept with low stocking density and perhaps bedded with sand; sand is known to provide better comfort for lame cows.25 However, before lameness prediction models can be effectively implemented on commercial dairy farms, it would be prudent to validate the model in a multifarm study that could account for known farm-level risk factors such as bedding type, stocking density, milk production, and others.5
Evaluation of 3 models indicated that lameness could be predicted with good accuracy by use of any of them. The incidence of CHDLs was predicted with good overall accuracy (> 74%) by use of all 3 logistic regression equations. The authors concluded that the third logistic regression equation, which included BCS, age, and CHDL at cessation of lactation, was the best equation for on-farm use because it contains only information that could be easily gathered by a trained employee.
ABBREVIATIONS
| BCS | Body condition score |
| CHDL | Claw horn disruption lesion |
| CI | Confidence interval |
| DCT | Digital cushion thickness |
| ROC | Receiver operating characteristic |
Dairy Comp 305, Valley Agricultural Software, Tulare, Calif.
Aquila Vet ultrasound machine, Esaote Europe BV, The Netherlands.
Stata, StataCorp LP, College Station, Tex.
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