L . Wallin et al. Livestock Production Science 63 2000 275 –289
277
Fig. 1. Questionnaire response: number of horses in Riding Horse Quality Test, distributed by birth year and sex. Table 1
compared with 5 of the coldbloods. Information
Use of horses that participated in the Riding Horse Quality Tests
about the horses was available up to 1989.
Area of activity Number
Percentage of horses
2.3. Swedish Warmblood brood-mare data
n 51847 Competition
1563 85
A third population was included in the study, stud
Show jumping 1201
65
book mares of the Swedish Warmblood breed, in
Dressage 892
48
order to compare two groups of females of the same
Eventing 187
10
breed. All brood-mares born between 1965 and 1967
Driving 23
1
a
Breeding 521
28
and registered with a foal for the first time in the
Leisure riding 497
27
1971 stud book were included. The mares were then
Riding school 78
4
4–6 years old. It was important to find mares as
Miscellaneous 54
3
young as possible when they entered the stud book in
a
Twelve of 74 stallions were used for breeding.
order to identify those that could have died early at an age of just 4 years or over, thereby allowing a
reasonable estimate of length of life. The last stud Swedish Cavalry Horse Foundation CHF. Among
book included information up to 1991. The study the warmblood horses, the cavalry had preferred
included 481 brood-mares, 266 of whom were dead. buying geldings. Thus, their material included only
There was no information on the causes of culling or 38 mares, whereas the distribution between sexes
death in this material. among the coldblood horses was more even: 115
RHQT horses represented in general sport horses geldings and 89 mares. Both groups of horses were
while the last two populations represented riding born between 1970 and 1975. The CHF bought the
school horses and brood-mares within the same horses as 3-year-olds.
breed. Thus, possible differences in longevity and or The cavalry in Sweden needed horses for various
causes of death depending on population area of purposes, but because many cavalry regiments had
activity were covered in the study. been disbanded and the need for the horses was
concentrated to short periods during the year, horses were loaned out after 1 year of training. Riding
3. Methods
schools or private persons were able to hire the horses for long periods of time. About half of the
A failure time survival analysis was used to take warmbloods were used as riding school horses,
account of the censoring in the RHQT, CHF and
278 L
. Wallin et al. Livestock Production Science 63 2000 275 –289
brood-mare data. In addition to the probability times. In our data, however, failure time is measured
density function ft and the cumulative density to the nearest year only. Therefore, there are several
function Ft, in this type of analysis, two other horses having exactly the same length of life so-
functions are defined. If T is the failure time length called ties. According to Kalbfleisch and Prentice
of life then the survivor function, St, is 1980, the above models do not deal well with data
having many ties. Therefore, the following approxi- St 5 PT t 5 1 2 Ft
0 , t , 1 ` 1
mation was applied: all horses having a certain non-censored failure time e.g. 6 years were given a
The survivor function expresses the proportion of random deviation to this failure time. The deviation
horses still alive at time t. The other function, the was sampled from a uniform distribution between
hazard function, ht, is 20.005 and 0.005. Therefore, instead of all horses
having the failure time of for example 6 years, they ht 5 ft St
2 would range from 5.995 to 6.005. Horses being
where ht is the probability of death at time t , given
reported as dead in the same year as tested were survival up to time t. This is sometimes referred to as
given only positive deviations to avoid negative life the relative risk of death.
lengths. The normal distribution is not good for describing
The survival and median length of life was studied the probability density function for length of life, for
using
PROC LIFEREG
in SAS, 1989. This procedure of at least two reasons. Firstly, a normal distribution
generating random numbers was replicated 100 times would range from 2` to 1`, but survival times
with different starting values for the random numbers cannot be negative. Secondly, life lengths are usually
generator and the effect on the estimated parameters skewed to the right, i.e. there is a longer right tail of
was studied. This procedure of randomly breaking the distribution than for the normal distribution. A
the tied failure times was shown in a simulation to common distribution used is the Weibull distribution
work very well. Failing to account for ties would Kalbfleisch and Prentice, 1980, where the Weibull
have resulted in an overestimation of the median survivor function, St, is
length of life Strandberg, 1997. Of the total of 1847 horses participating in the
p
St 5 exph 2 lt j
3 RHQT, 503 were reported dead and their length of
life was known. For the remaining 1344 horses it The corresponding hazard function, ht, is
was only known that they were alive at the end of
p 21
data collection, viz. 1990. Because all horses in- ht 5
lp lt 4
cluded in this material had participated in the test, it where
l and p are non-negative parameters. When was also known that they were at least 4 years old.
p 51, the Weibull distribution becomes an exponen- Therefore, the measure of length of life studied was
tial distribution with constant hazard throughout life. length of life after test, defined as year of death or
When p .1, the hazard increases with increasing censoring, minus year of test. After the analysis, 4
length of life. The parameter l reflects the general
years were added to the estimates of length of life level of risk of death, but a change in
l is dependent after test in order to achieve length of life.
on the value of p. The survival of males and mares of the RHQT
To study the effect of various explanatory vari- data was studied using model 5 with sex as an
ables on the length of life, such as effects of sex or explanatory variable. The trend in life length over
year of birth, the model can be expanded to birth years was studied also using model 5 with
birth-year group as the explanatory variable, but
ht; z 5 h t exphz9 bj
5 analysed for each sex separately. The males and
where h t is the baseline hazard from 4, z is the mares were divided into three different groups
design vector for the explanatory variables, and b is
according to year of birth. Standard errors of median the vector of these variables.
length of life were averaged from the standard errors The above models assume truly continuous failure
of the 100 replicates.
L . Wallin et al. Livestock Production Science 63 2000 275 –289
279
The survival of warmblood and coldblood horses Table 2. The probabilities of death for the males
in the CHF data was studied using model 4 without were higher for almost all ages compared with the
any explanatory variable, but analysed separately for mares. A slightly higher probability of death was
each sex. The dependent variable was length of life, noted for the age group 11 years than for other ages
defined as year of death or censoring, minus year of of the mares. Thus, the tendency was that mares
birth. The same procedure was applied to the stud lived longer than males. The mares had a 14-years
book data of brood-mares. survival rate of 72 compared with 51 for the
Frequencies of diseases leading to death were males.
2
tested for sex differences by x -analysis using SAS,
Among the CHF warmblood geldings few died 1989.
before the age of 7, Table 3. Higher probabilities of death were seen in the age groups 7 to 9 years for
geldings. The 14-years survival rate was 53. It was
4. Results difficult to interpret the figures on numbers of dead
