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### [RC] Colic rates and death rates at endurance rides compared to thosein the general population - Truman Prevatt

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.

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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