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Measures of strength of association (view source)
Revision as of 08:15, 5 May 2011
, 08:15, 5 May 2011no edit summary
(a<sub>1</sub>/n<sub>1</sub>) / (a<sub>0</sub>/n<sub>0</sub>)<br>
(a<sub>1</sub>/n<sub>1</sub>) / (a<sub>0</sub>/n<sub>0</sub>)<br>
As mentioned above, the output from a case control study will be the ''odds of exposure'' amongst diseased and nondiseased animals. It can be shown that (as long as the ''[[Sampling strategies#Sampling fraction|sampling fraction]]'' is different for cases and controls), the ''exposure odds ratio'' comparing diseased to non diseased animals is identical to the ''odds ratio for disease'', comparing exposed to nonexposed animals. This is why the odds, rather than any other measure, is used in these types of studies. Although, strictly speaking, the exposure odds ratio is calculated as (a<sub>1</sub>/a<sub>0</sub>) / (b<sub>1</sub>/b<sub>0</sub>), it is often reformulated into the following equation (known as the '''cross products formula'''):<br>
As mentioned above, the output from a case control study will be the ''odds of exposure'' amongst diseased and nondiseased animals. It can be shown that (as long as the ''[[Sampling strategies#Sampling fraction|sampling fraction]]'' is different for cases and controls), the ''exposure odds ratio'' comparing diseased to non diseased animals is identical to the ''odds ratio for disease'', comparing exposed to nonexposed animals. This is why the odds, rather than any other measure, is used in these types of studies. Although, strictly speaking, the exposure odds ratio is calculated as (a<sub>1</sub>/a<sub>0</sub>) / (b<sub>1</sub>/b<sub>0</sub>), it is often reformulated, for ease of calculation, into the following equation (known as the '''cross product ratio'''):<br>
(a<sub>1</sub>×b<sub>0</sub>) / (b<sub>1</sub>×a<sub>0</sub>)
(a<sub>1</sub>×b<sub>0</sub>) / (b<sub>1</sub>×a<sub>0</sub>)<br>
These ratio measures of strength of association vary from approximately 0 to +∞, with an estimate of 1 indicating no association. It should be noted that although the odds ratio for disease is a useful measure of strength of association, its value will differ from the equivalent prevalence or risk ratio, with a tendency towards more extreme (more positive in the case of prevalence/risk ratios greater than 1, or smaller in the case of prevalence/risk ratios less than 1) values when the disease under investigation is common in the population. This may not be a problem when using case control studies, as these are often used when the disease in question is rare. However, odds ratios are commonly used in more advanced statistical methods (particularly [[Logistic regression|logistic regression]] - in which case, care must be taken when interpreting odds ratios.
[[Category:Veterinary Epidemiology - Statistical Methods|B]]
[[Category:Veterinary Epidemiology - Statistical Methods|B]]