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Department of Animal Science, Iowa State University, Ames 50011-3150
Corresponding author: P. J. Berger; e-mail: pjberger{at}iastate.edu.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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Key Words: birth weight • dystocia • Holstein • perinatal mortality
Abbreviation key: AIC = Akaike’s Information Criterion, CE = calving ease, MRR2 = max-rescaled R2, OR = odds ratio, PA = pelvic area, PM = perinatal mortality
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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Currently in the United States, there is a genetic evaluation of sires and maternal grandsires for dystocia, but there is no formal evaluation for PM. Calving ease is a trait considered to be correlated with PM. In spite of the availability of calving ease evaluations, Meyer et al. (2001a) observed an increasing phenotypic trend in PM from 1985 to 1996. In first-parity cows, the incidence of stillbirths increased from 9.5 to 13.2%, and in later parity cows it increased from 5.0 to 6.6%. Meyer et al. (2001b) also found an increasing genotypic trend among US sires. Either 1) producers are ignoring the evaluations and are more interested in selecting for milk yield, 2) the evaluations are inadequate to produce favorable genetic changes, or 3) a reduction in difficult births is not resulting in a reduction in PM. Whatever the reason, PM is becoming a problem and should not be neglected any longer.
Associated Traits
Meijering (1984) extensively reviewed of traits that are associated with dystocia and stillbirth. Meyer et al. (2000, 2001a, 2001b) studied traits that were collected from field data. In addition to traits found in field data, this study investigates several factors that may be associated with PM and dystocia that are not commonly measured in field data. Table 1 lists all effects considered in the analysis; however, not all the traits were found to be significant. Therefore, only significant effects were included in the final models. McDermott et al. (1992) found that birth weight is the most important factor in predicting dystocia. As for PM, Berger et al. (1992) noted that calves that are lighter and heavier than average tend to have more PM. Unfortunately, birth weight is not commonly measured in field data for Holsteins. Meijering (1984) concluded that birth weight’s impact on incidence of dystocia is nonlinear, but it sometimes is mistakenly modeled as a linear effect. One of the primary interests of this study is to determine the impact of birth weight.
The objectives of this study are: 1) to determine the best model to predict PM and dystocia given the information available in field data and additional variables with more intensive data recording on research farms and 2) to determine the value of birth weight in the predicted model.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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After editing, the incidence of perinatal mortality was 7.1%. The incidence of dystocia was 23.7%. The dataset used to model perinatal mortality contained 4528 calvings, and the dataset used to model dystocia contained 4111 calvings. Perinatal mortality is defined as a death of the calf within the first 48 h after parturition. The protocol for providing assistance is to give the cow 2 h without assistance after the appearance of the calf’s feet. If the cow does not make progress after the 2-h waiting period, assistance is then provided. The primary difference in the total number of observations was because pelvic area is found to be significant in the model for dystocia, but not significant in the model for PM. The analysis procedure automatically drops records with missing values when those values are needed for the analysis. There were 402 records missing pelvic area measurements. These records were included in the first analysis of PM (when pelvic area was not included in the model), but omitted from the second analysis of dystocia (when pelvic area was included in the model).
Table 1
has all factors that were considered to be potentially valuable predictors of PM and dystocia. Note that not all of these factors were found to have significant effects on dystocia or PM. Table 2 has summary statistics for the continuous traits used in the final model. Table 3 has the incidences of dystocia and PM by parity.
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Odds ratio.
Odds ratios (OR) are another useful way to interpret results from a logistic regression analysis (Kleinbaum, 1994; Hosmer and Lemeshow, 2000). An OR compares two opposing probabilities to determine which is more problematic. For example, we may want to compare dystocia in male calves versus dystocia in female calves. If the OR is exactly equal to 1, then there is no difference between the sexes for the odds of dystocia. In that case, sex of the calf would not be a good predictor of dystocia. If the OR is 1.5, we interpret this value as meaning male calves have a 50% greater chance of dystocia than female calves given that all other variables are the same. An OR of 2 is double the risk.
The OR above was for a discrete variable such as sex of calf. An OR can also be calculated for a continuous variable. This type of OR can be interpreted as a linear trend over the range of the variable. For example, an OR of 1.05 for year is interpreted as a 5% increase in the OR for dystocia for the next year while the other variables are held constant. Suppose all calves born in 1988 have a 10% chance of needing assistance, then all calves born in 1989 have a 10.5% (10% x 1.05) chance of needing assistance.
In our analysis, some of our variables are included as quadratic effects. In this scenario, the OR is not constant over the full range of values for the continuous variable, and, therefore, cannot be calculated directly. For variables of this sort, we plotted the probability curves for dystocia and PM (Figures 1, 2, and 3). This gives us a good representation of how the impact of the variable changes throughout its range of values.
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where k represents the number of response levels minus one and s is the number of predictive effects (SAS, 1999).
Max-rescaled R2.
The coefficient of determination, denoted as R2, is a familiar term used in traditional linear regression. It describes the amount of variation that is accounted for by the regression model. Because logistic regression is a nonlinear regression, we cannot calculate an R2 value. However, Nagelkerke (1991) describes a generalization of R2 to logistic regression called the Max-Rescaled R2 (MRR2) that has the same interpretation as the traditional R2 value.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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Perinatal Mortality Model Analysis
Logistic regression model.
Using score and stepwise procedures in SAS, the most parsimonious model was found to include the effects of year, season, dystocia, parity, linear and quadratic effects of ratio of calf to cow weights, linear and quadratic effects for birth weight of calf, and linear and quadratic effects of gestation length. Table 4 shows a few of the models investigated for predicting PM. Model 1 includes the sex of calf effect, which was expected to be an important factor in the model, but its importance is diminished when birth weight is included in the model (Meijering, 1984; McDermott et al., 1992). Sex of calf is then no longer a significant effect. model 2, which drops sex of calf from the model, results in the best model with the highest MRR2 value (15.7%) and the lowest AIC value. Model 3 represents what would happen if we have birth weights but not the BW of the cows, which might be a possible scenario in the field. In such a scenario, we could not calculate the ratio effect. Model 3 has a relatively small loss of fit. This indicates that the ratio effect is not as valuable as the birth weight effect. Model 4 represents the absence of both birth weight and cow weight, which would be the case if we did not have birth weight records. This model has a large loss of fit. Without birth weight and cow weight in the model (See model 4 in Table 4), we lose approximately 1/3 of our predictive ability, dropping the MRR2 down from 15.7 to 10.9%. Dystocia differences between sexes may depend primarily on birth weight, because male calves are larger than female calves at birth (Meijering, 1984; McDermott et al., 1992). Because the birth weight effect appears to account for the sex difference, model 5 puts the sex effect back into the model to see if the sex effect can account for the missing birth weight effect. There is only a slight increase in the value of MRR2. Therefore, the birth weight effect explains more than just the sex effect. Clearly, birth weight is a better predictor of PM than the sex of the calf. The best logistic regression model (See model 2 in Table 4) is given in equation [1] as:
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 | ([1]) |
where 
PM is the probability of perinatal mortality, BW is birth weight, and GL is gestation length. Table 5 has significant parameters along with their estimates from the best model (model 2; Table 4
). The ratio of calf weight to cow weight is clearly correlated with the calf’s birth weight alone; however, it appears that ratio and birth weight explain different sources of variation. It is a well-known fact that the sex of the calf has an effect on PM (Meijering, 1984; McDermott et al., 1992), but with the inclusion of birth weight and ratio effects, sex is no longer significant. Apparently, effect due to sex of calf is accounted for by including ratio and birth weight effects.
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has estimates for the odds ratios for significant factors in the PM analysis. Although the effect of year is significant, there is a rather small increasing trend in the odds ratio for PM. The estimate of the odds ratio for year, 1.02, tells us that there is a 2.1% increase in the odds ratio for PM per year. For example, if the incidence of PM is 7.1% in a given year, then it will increase to 7.24% (0.071 x 1.02) the next year. Season has a noticeable effect on PM. Calves born in the winter are 36% more likely to die in the first 48 h than calves born in the summer. The effect of dystocia gives the largest OR. The OR for dystocia can be interpreted to mean if a calf needs assistance, it has a 2.7 times greater chance of dying than a calf that is unassisted, given that all other factors are held constant. The effect of parity has a similar magnitude of effect as dystocia. Primiparous cows tend to have 2.4 times more PM in their calves than their multiparous counterparts.
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Ratio.
Figure 1 shows the effect of the ratio of calf to cow weights. The ratio is calculated by dividing the calf’s birth weight by the cow’s weight measured 2 or 3 d after parturition. The graph shows ratios ranging over approximately two standard deviations from 4.5 up to 9.3% with a mean of 6.9% and a standard deviation of 1.2%. In spite of having smaller calves (38.2 vs. 41.7 kg, respectively), primiparous cows have a larger average ratio (7.5%) compared with multiparous cows (6.5%) (from Table 2). Jersey cattle tend to be excellent for calving ease with a ratio tightly distributed around 6% (Howard Tyler, personal communication). It appears that Holsteins’ best survival rate occurs when the ratio is close to 7.2%. As the ratio gets small, the chance of PM for assisted calves becomes very large. This may be slightly exaggerated due to extrapolation of the model when there are very few observations. Most of the small ratios will be due to very small birth weights, and very few small calves need assistance. That being said, the effect of ratio on dystocia is strong. For all cows, ratios of calf to cow weight of 4.5, 5.7, 6.9, 8.1, and 9.3% yield probabilities of mortality at 8.2, 4.2, 3.1, 3.5, and 5.7%, respectively. The intermediate optimum for ratio is 7.2%. Therefore, an average calf with a birth weight of 40.3 kg (88.7 lbs) should be born to a cow weighing 559.7 kg (1231.4 lbs) to minimize the calf’s chance of death (40.3 kg/559.7 kg = 7.2%).
Birth weight.
Figure 2 shows the impact of birth weight on probability of PM. The graph shows birth weights ranging over approximately two standard deviations from 29 to 52 kg with a mean of 40.3 kg and a standard deviation of 5.7 kg. Primiparous cows tended to have smaller calves (38.2 kg) than multiparous cows (41.7 kg) (see Table 2). Once ratio is considered in the model, smaller birth weights tend to have lower risk of mortality. Birth weights above the average of 40.3 have an exponentially increasing risk of mortality. Probabilities of perinatal mortality for birth weights of 29, 35, 40, 46, and 52 kg were 2.1, 2.5, 3.4, 5.1, and 9.6%, respectively, when other factors were set at their average value.
Gestation length.
Figure 3 demonstrates the impact of gestation length on risk of mortality. The mean gestation length is 278.7 d with a standard deviation of 5.6 d. First-parity cows had a shorter gestation length than later-parity cows at 277.9 and 279.2 d, respectively (Table 2). The graph shows gestation length ranging over approximately two standard deviations from 268 to 290 d. Similar to the findings of Meyer et al. (2000), short gestation lengths are the most problematic. Gestation lengths of 268, 273, 279, 284, and 290 d yield probabilities of mortality of 5.5, 3.9, 3.1, 3.1, and 3.6%, respectively. The graph indicates the intermediate value that minimizes the risk of PM is 282 d, which is longer than the accepted breed average of 280 d.
Dystocia Model Analysis
Logistic regression model.
Similar to the procedure done for PM, the most parsimonious model for dystocia was found to include year, season, sex, perinatal mortality, parity, birth weight (only a linear effect), and pelvic area (PA). We chose to include PM in the model for dystocia to adjust for the average difference in incidence of PM associated with each level of dystocia. If a dairy producer wants to know that a cow is at high risk for a difficult calving, he cannot know in advance if the calf will die. In this case, PM is not helpful in the model. However, future genetic evaluations of sires for calving ease could conceivably incorporate PM in the model to enhance the evaluation of sires for calving ease. Perinatal mortality will be known at the same time as calving ease and will be easy to incorporate in revised sire evaluation procedures. Therefore, PM was retained in one model and deleted from another model to evaluate the effect of including or ignoring PM. Table 7 compares a few of the models for dystocia. Model 1 is the best model with the highest MRR2 value of 26.6% and the lowest AIC value. Similar to the models for PM, model 1 includes all significant effects. Model 2 ignores the effect of PM, assuming that PM is unknown prior to birth according to the discussion earlier in this paragraph. Model 2 is a slightly less efficient predictor of dystocia than model 1; it has 1.1% less predictive value and the AIC is larger. Model 3 ignores the effect of birth weight. Without birth weight in the model, we lose approximately 1/5 of our predictive ability, dropping the MRR2 down to 20.0%. This model has fewer significant factors than the model for PM making this model slightly simpler. The best logistic regression model for dystocia is given as
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where DYS is the probability of dystocia and BW is birth weight. Table 8 gives significant parameters along with their estimates. The first thing that one may notice is the significant differences in this model compared with the model for PM. Factors contributing to PM may not be contributing to an increase in incidences of dystocia. Here, in contrast with PM, sex of calf is a significant factor, whereas ratio is not. For analyzing dystocia, the effect of pelvic area accounts for the size of the cow better than ratio does. Also note that the quadratic term for birth weight is not necessary to predict dystocia. This is due to the fact that smaller than average birth weights do not need assistance as often as larger than average birth weights. The linear trend of birth weight is sufficient to model the increase in dystocia.
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has estimates of the OR for the factors in the dystocia model. The estimate of the OR for year tells us that there is a 4.7% decrease in dystocia per year. For example, if the incidence of dystocia is 23.7% in a given year, then it will decrease to 22.52% (0.237 x 0.95) the next year. The effect of season on dystocia is about half that for PM. Calves born in the winter are 15% more likely to need assistance than calves born in the summer. Male calves tend to need assistance 25% more often than female calves. The effect of PM means that if a calf died in the first 48 h, then it had a 2.5 times greater chance that it needed assistance given that all other factors are held constant. The most noteworthy OR estimate is for parity. A first-parity cow has 4.7 times higher risk of dystocia than later-parity cows. A 1-kg increase in birth weight corresponds to a 13% increase in dystocia. Finally, a 1-dm2 increase in pelvic area means that there is an 11% decrease in incidence of dystocia.
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), there is only a slight change in the OR estimates, which is as we would expect from the small drop in MRR2 value of this model. The OR estimates for the model without PM are 0.95 for year, 1.17 for season, 1.26 for sex, 5.02 for parity, 1.13 for birth weight, and 0.88 for pelvic area. Compare these with the OR estimates in Table 9. |
CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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APPENDIX |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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lists three permutations and their respective estimate of PM at each tenth of a percentile. We can see that the model can give us a wide range of estimates from 0.8% to 69.1%. For example at the sixtieth percentile, we can use equation [1] and the parameter estimates in Table 7 to calculate the estimate of PM.
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Then solve for PM to get PM = 0.132. Finally, multiply 0.132 by 100% to get the estimate of 13.2%. Following this example, one can calculate the estimate of PM for any situation one might encounter.
As is the case with most predictive models, concern arises when one uses the model to predict a situation where any one variable is an outlier. With this particular model, special caution is needed when both ratio and birth weight are outliers. Consider, for example, the situation where PM is maximized in Table 10. A ratio of 4.5%, which is 2 standard deviations below average, and a birth weight of 52 kg, which is 2 standard deviations above average, implies the cow’s weight is 1156 kg (2542 lb), which is very unlikely.
Also, one should note that some factors might compensate for other factors. For the first example in the 60% of Table 10, a calf with low birth weight (29 kg) and average GL (279 d) would normally have a low risk for PM, but this example also has a need for assistance of a small ratio scenario in the first parity, which substantially raises the risk of PM.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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FOOTNOTES |
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Received for publication January 29, 2003. Accepted for publication June 20, 2003.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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