174 R
. Rupp, D. Boichard Livestock Production Science 62 2000 169 –180
scores SCS were defined in a classical way through computed using Kaplan–Meier’s formula 8. This
a logarithmic-transformation of test day SCC: SCS5 plot displayed a straight line, which validated the
log SCC 100,00013 and a lactation mean of all assumption of Weibull proportional hazard model.
2
test day SCS was computed for each cow. As for Likelihood ratio tests are shown in Table 1 for the
herd mastitis frequency, herd SCS mean was calcu- complete data set. All factors were found to be
lated from data of all parities and all cows in each highly significant.
herd. Separate analyses allowed to account for possible differences in the baseline hazard function
3.1. Estimates of the Weibull parameters and of and changes in effects of covariates.
the explanatory covariates Table 2 presents the estimates of Weibull parame-
3. Results ters
r and r logl. For all analyses, r estimates were similar and close to 1. In general, values were
In the complete original data set, 20 of lactations slightly lower than one, reflecting a monotonous
were affected by at least one clinical mastitis event. slight decrease in hazard, i.e., in risk of occurrence
However, out of the 20,422 selected cows and over of first clinical mastitis, with time. However, this is
the 19 months under study, only 2649 13 had true only within defined period of lactation stage 5
clinical mastitis recorded, because of the editing levels. Indeed, as the lactation stage effect depends
strategy. Out of the 2649 first clinical mastitis cases on time, it interacts with the general shape of the
recorded, 64 1693 events occurred in first lacta- baseline hazard function and only this interaction
tion and 36 956 events occurred in the beginning should be interpreted. This is illustrated in Fig. 2,
of the second lactation. Fig. 1 displays the dis- which displays the hazard rate of a cow calving in
tribution of failure times i.e. time to first clinical September in an average herd, and with ISCC
mastitis. Mean failure time was 246 days. Failure between 50,000 and 75,000 cells ml, IMY between
time was quite high because clinical mastitis cases 25.5 and 27.5 kg and 360 days calving interval. The
occurring before day 35 were not included in the hazard slightly decreased from 35 days to the end of
analysis, and because cases occurring in the begin- first lactation and strongly increased around second
ning of the second lactation were considered. Mean calving. When compared with first lactation, the
censoring time of unaffected cows 87 reached relative increase around second calving was more
362 days. Mean SCC at first test day was 101,500 pronounced in herds with low clinical mastitis
and 89,500 c ml, for cows with and without clinical frequency than in herds with high clinical mastitis
mastitis, respectively, and 91,000 c ml in the whole frequency Fig. 2, but no difference was observed
selected population. between herds with low or high SCS level not
The adequacy of the Weibull distribution to the shown. However, it should be noted that the hazard
density of the failure times observed in the data was function drawn is left truncated in first lactation, as
ˆ checked by plotting the log[2S
t] against logt, selection of data required edit of cows censored
KM
ˆ where S
t is the empirical survivor function before 35 days, i.e. cows with a clinical mastitis
KM
Table 1 Results of the likelihood ratio test: comparison of the full model with models excluding one effect at a time
Models tested Change in
df P value
22 log-likelihood
a
Full Model excluding ISCC 104.0
5 0.0001
Full Model excluding IMY 53.3
5 0.0001
Full Model excluding MC 51.1
11 0.0001
Full Model excluding ST 1431.0
4 0.0001
a
Full model includes effects of Herd-Year HY, Month of First Calving MC, Stage of Lactation ST, Initial Somatic Cell Count ISCC, and Initial Milk Yield IMY.
R . Rupp, D. Boichard Livestock Production Science 62 2000 169 –180
175 Table 2
Estimates of r, r logl standard errors and g parameters for global all herds and separated subgroups of herds analyses
Subgroups Number of cows
Number of herds r
r logl g
All herds 20,317
2611 0.91 0.02
27.95 0.17 2.21
a
CM1 11,781
1468 1.04 0.05
29.16 0.33 4.99
b
CM2 8536
1143 0.87 0.03
27.22 0.20 4.81
c
SCS1 10,183
1270 0.93 0.05
28.17 0.26 2.67
d
SCS2 10,134
1341 0.90 0.05
27.69 0.23 2.08
a
CM15group of herds with low mastitis frequency.
b
CM25group of herds with high mastitis frequency.
c
SCS15group of herds with low somatic cell score average.
d
SCS25group of herds with high somatic cell score average.
Fig. 2. Hazard rate of cow over time, estimated in global solid line and separate analyses according to mastitis frequency: subgroups of herds with low dot line or high bold dot line frequency.
]] Œ
event or a SCC higher than 400,000 cells ml during exp 12
0.5554.43. As expected, g estimates
the first 35 days of lactation. For these discarded increased to 4.99 and 4.81 i.e., variances decreased
cows 4719, clinical mastitis frequency was high to 0.22 and 0.23, respectively when strata were
51.2 and 90 of these clinical events occurred defined according to mastitis frequency, i.e., in
before 100 days after first calving. Therefore, be- subgroups with less and more than 20 of clinical
cause of selection of data, the hazard was likely to be cases within herds, respectively Table 2.
underestimated from 35 days to the end of first Table 3 displays estimates of relative first mastitis
lactation. hazard for month of first calving. A large increase in
The estimate of the g parameter for herd year
risk was observed for first calving occurring in effect distribution is in Table 2. Its value was equal
summer and, to a smaller extent, in spring. This to 2.21 in the overall analysis. This rather low value
month effect was the same in both herd groups based indicated a high variability of mastitis frequency
on SCS level, whereas relative increase in risk was among herds. On the log-scale, the corresponding
more less pronounced in herds with low high herd-year expected mean was
C2.212log2.215 mastitis frequency.
1
2 0.24 and the herd-year variance was C
2.215 Table 3 and Fig. 3 show the influence of initial
0.55. Thus, relative mastitis rates for different herd- milk yield on mastitis frequency. Increased milk
]] Œ
years varied roughly from exp22 0.5550.23 to
production at first test day was generally associated
176 R
. Rupp, D. Boichard Livestock Production Science 62 2000 169 –180 Table 3
Relative hazard ratio for effects of month of first calving, initial SCC, and initial milk yield Effects and levels
Relative hazard ratio All herds
Subgroups
a b
c d
CM1 CM2
SCS1 SCS2
Month of first calving September 95
1.00 1.00
1.00 1.00
1.00 October 95
1.19 1.40
1.08 1.27
1.09 November 95
1.35 1.35
1.36 1.36
1.31 December 95
1.13 1.23
1.08 1.21
1.04 January 96
1.16 1.46
1.05 1.11
1.16 February 96
1.13 1.41
1.01 0.99
1.21 March 96
1.01 1.28
0.92 0.92
1.03 April 96
1.15 1.90
0.90 1.42
0.93 May 96
1.09 1.44
0.93 0.91
1.17 June 96
1.52 2.47
1.17 1.48
1.47 July 96
1.56 1.78
1.47 2.12
1.11 August 96
1.79 2.48
1.58 1.73
1.79 Initial SCC
in 1000 cells ml Less than 35
1.00 1.00
1.00 1.00
1.00 35–50
1.17 1.03
1.27 1.13
1.14 50–75
1.28 1.06
1.38 1.26
1.21 75–150
1.39 1.31
1.41 1.48
1.24 150–215
1.86 2.00
1.73 1.79
1.75 215,000–400,000
1.88 1.51
2.06 1.80
1.76 Initial milk yield
kg Less than 21.5
1.00 1.00
1.00 1.00
1.00 21.5–23.5
1.14 1.11
1.12 1.29
1.04 23.5–25.5
1.14 1.12
1.12 1.18
1.12 25.5–27.5
1.32 1.12
1.40 1.36
1.32 27.5–29.5
1.24 1.09
1.25 1.23
1.27 More than 29.5
1.57 1.46
1.50 1.78
1.42
a
CM15group of herds with low mastitis frequency.
b
CM25group of herds with high mastitis frequency.
c
SCS15group of herds with low somatic cell score average.
d
SCS25group of herds with high somatic cell score average. P 0.10 different from 1.00.
P 0.05 different from 1.00.
with increased risk of first mastitis. However, this lower SCS level than in herds with greatest SCS
effect was not uniform. It was especially large for level. On the other hand, first milk yield had less
greatest yields: cows producing more than 29.5 kg of impact in the group of herds with lower mastitis
milk were 1.5 times more likely to be affected than frequency than in the overall analysis.
the lowest producing cows less than 21.5 kg. Table 3 and Fig. 4 present the relationship be-
However, cows above the average for milk pro- tween initial somatic cell count and risk of first
duction, but not in the highest category, appeared to mastitis. In the overall analysis, the relative hazard
be less affected than average cows. The unfavorable gradually increased with ISCC. Cows with the
effect of the highest yield was larger in herds with lowest ISCC, i.e., less than 35,000 cells ml, were at
R . Rupp, D. Boichard Livestock Production Science 62 2000 169 –180
177
Fig. 3. Relative hazard ratio for initial milk yield effect IMY estimated in global s and separate analyses according to mastitis frequency: subgroups of herds with low j or high m mastitis frequency.
Fig. 4. Relative hazard ratio for initial SCC effect ISCC in global s and separate analyses according to mastitis frequency: subgroups of herds with low j or high m mastitis frequency.
lowest risk. When compared with cows with the with fewer clinical cases. In the latter herds, cows
lowest ISCC, the relative hazard ratio reached 1.75 with the lowest ISCC remained at the lowest risk,
for cows with the highest ISCC, i.e., between but no significant increase in risk was observed until
215,000 and 400,000 c ml. Estimates of the ISCC up to 75,000 cells ml. Relative hazard was sig-
effect were similar for groups of herds with low or nificantly higher for ISCC from 75,000 to 215,000
high SCS level. In contrast, estimates of ISCC effect cells ml, and seemed to decrease for the highest
revealed somewhat different patterns for herds with class, i.e., from 215,000 to 400,000 cells ml. This
high mastitis frequency when compared with herds decrease was significant P 0.05, i.e., cows with
178 R
. Rupp, D. Boichard Livestock Production Science 62 2000 169 –180
ISCC in the highest class, were 0.75 times as likely latter study are similar to the estimates of risk of first
to have first mastitis as cows with ISCC from 75,000 case obtained in this paper. These results, obtained in
to 215,000 cells ml. natural conditions, do not support earlier observa-
tions of increased risk of low SCC cows for infection after experimental challenge Schalm et al., 1964a;
4. Discussion and conclusion Schukken et al., 1994. Hence, the latter authors
