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The numbers I have for fatalities in associated with AERC rides the 
through 2003 through 2006 is for 34 deaths, 20 of which are colic. I 
could not find the 2007 numbers – the website hasn't been updated for 
over a year. I have a copy of the 2003 numbers (10) which were put 
together prior to the organization of the WOTH committee. During that 
four year period there have been over 89,000 starts in endurance rides.

There are two questions. The first is "is the fatality rate of horses 
associated with doing an endurance ride the same as that of the normal 
population?" The second relates to the how the horses die. That is "Is a 
horse that dies associated with competing in an endurance ride more 
likely to die of colic than is the case in the normal population of 
horses at large?" The second question is addressed first.

In order to address these issues data on the normal horse population is 
needed. The following reference was used. 
http://www.aphis.usda.gov/vs/ceah/ncahs/nahms/equine/equine05/equine05_infosheet_part_one_highlights.pdf. 
This article is also of interest 
http://www.aphis.usda.gov/vs/ceah/ncahs/nahms/equine/equine98/colic.PDF.

Colic: It is reported in the above reference that 14.6% of the deaths 
are a result of colic. The first null hypothesis to test is: A 
proportion of horses that die at an endurance ride from colic is no 
different than in the general horse population.

The mean number of horses that die from colic from an endurance ride is 
mu=20/34=.588 (58.8%). The standard error is .0844 (8.44%). The 95% 
confidence interval for the proportion of horses that die from colic as 
a result of an endurance ride is .4228 to .7537 (42.28% to 75.37%). From 
the reference the proportion of equine fatalities from colic in the 
general population is 14.6%. Therefore, the null hypothesis can be 
rejected with 95% confidence (that it can be rejected with a probability 
of .95 of being correct). Or to restate with a confidence of 95% it can 
be concluded that equine deaths associated with an endurance ride are 
the result of colic at a higher rate than deaths of horses in the 
general population as result from colic.

Fatality Rate: The next question is more interesting. As will be 
discussed below there is not sufficient data in any one year to 
effectively address this issue to a reasonable statistical confidence. 
However, with four year of data the issue can be addressed to a 
reasonable (95%) confidence. The reason is a single year sample space is 
not very large for the proportions being considered.

The general population of interest is horses between the ages of 5 and 
20 years. The mortality rate (from the stated reference) is 1.2 horses 
per 100 horses per year. Since the impact of an endurance ride is just a 
couple of days (we will use two – the day of and day after the ride). 
After that time the endurance horse re-enters the general population as 
the effects of the endurance ride diminishes. The mortality rate for the 
general population will need to be scaled for that time span. The 
mortality rate for the normal population is .0000329 (0.00329%) per day. 
That on any given day a horse has the probability of .0000329 of dying. 
For the two day period of interest a horse in the normal population has 
the probability of .0000658 of dying.

The data for fatalities from 2003 through 2006 is

number of fatalities = 34
number of starts (sample size) = 89294

The mean number of horses that die in the general population (in 5 – 20 
age range) in a two day period in a sample size of 89294 horses is 6. 
The question remains is the significance of the difference between the 6 
that would be expected to die in a sample that size and the 34 that died 
associated with endurance rides.

In order to address that the null hypothesis to be tested is: The 
fatality rate of horses associated with doing an endurance ride is the 
same as that of horses in the normal population? This hypothesis will 
now be tested to a confidence of 95%.

The sample proportion of horses that die at an endurance ride is 
34/89294=.000381 (0.0381%). The standard error for the estimate is 
0.0000653 (.006653%). The 95% confidence interval is then .000253 
(.0253%) to .000509 (.0509%). That confidence interval translates to 
between 22 and 46 equine deaths in 89294 starts. The 22 is far in excess 
of the 6 predicted from the mortality rate of the normal horse population.

To say this more precisely, from the reference the scaled proportion of 
horses that die in the normal population is 0.0000658 (0.00658%) which 
is less than the lower end of the confidence interval. This formally 
says the same thing as above reference to 6 and 22. Therefore the null 
hypothesis can be rejected with a 95% confidence. In other words, the 
mortality rate of horses associated with endurance rides is greater than 
that of the 5 – 20 year old horses in the general population with a 95% 
confidence.

The beauty of taking four years of data is with a sample size of in 
excess of 89000 starts, hypothesis concerning small proportions can be 
tested. If one were to calculate the 95% confidence interval for any 
single year one would have the expected number to die in the sample size 
of a single year is 2. The 95% confidence interval for a single year 
would be 1 to 15. The predicted number of deaths of 2 is within this 
confidence so the null hypothesis cannot be rejected. However, the extra 
data provides statistical separation and in fact it becomes clear that 
to a 95% confidence that horses after competing in an endurance ride die 
at a higher rate than the same age group of horses die in the general 
population.


Truman
--

"Mathematics may be defined as the subject in which we never know what 
we are talking about, nor whether what we are saying is true." Bertrand 
Russell


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