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Measures of strength of association (view source)
Revision as of 08:01, 5 May 2011
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The measures of disease frequency which can be extracted from this table will depend on the [[Study design|study design]] used, which will be [[Study design#Analytic studies|analytic]] in nature, as data regarding exposure have been collected.<br>
The measures of disease frequency which can be extracted from this table will depend on the [[Study design|study design]] used (which will be [[Study design#Analytic studies|analytic]] in nature, as data regarding exposure have been collected).<br>
In the case of a [[Study design#Cross sectional studies|cross sectional study]], the '''[[Measures of disease frequency#Prevalence|prevalence]]''' can be estimated amongst exposed individuals as (a<sub>1</sub>/n<sub>1</sub>), and amongst unexposed individuals as (a<sub>0</sub>/n<sub>0</sub>).<br>
In the case of a [[Study design#Cross sectional studies|cross sectional study]], the '''[[Measures of disease frequency#Prevalence|prevalence]]''' can be estimated amongst exposed individuals as (a<sub>1</sub>/n<sub>1</sub>), and amongst unexposed individuals as (a<sub>0</sub>/n<sub>0</sub>).<br>
In the case of a [[Study design#Cohort studies|cohort study]] or a [[Study design#Experimental studies|experimental study]], the disease status of individuals will relate only to ''new'' cases of disease (i.e. those which were not diseased at the start of the study. In these cases, the '''[[Measures of disease frequency#Incidence risk|incidence risk]]''' can be estimated amongst exposed individuals as (a<sub>1</sub>/n<sub>1</sub>), and amongst unexposed individuals as (a<sub>0</sub>/n<sub>0</sub>). Alternatively, the [[Measures of disease frequency#Incidence rate|incidence rate]] can be estimated, if the total animal-time for each exposure group is known, as (a<sub>1</sub>/[total number of animal-time units in exposed group]) amongst exposed animals and (a<sub>1</sub>/[total number of animal-time units in unexposed group]) amongst unexposed animals.<br>
In the case of a [[Study design#Cohort studies|cohort study]] or a [[Study design#Experimental studies|experimental study]], the disease status of individuals will relate only to ''new'' cases of disease (i.e. those which were not diseased at the start of the study. In these cases, the '''[[Measures of disease frequency#Incidence risk|incidence risk]]''' can be estimated amongst exposed individuals as (a<sub>1</sub>/n<sub>1</sub>), and amongst unexposed individuals as (a<sub>0</sub>/n<sub>0</sub>). Alternatively, the [[Measures of disease frequency#Incidence rate|incidence rate]] can be estimated, if the total animal-time for each exposure group is known, as (a<sub>1</sub>/[total number of animal-time units in exposed group]) amongst exposed animals and (a<sub>1</sub>/[total number of animal-time units in unexposed group]) amongst unexposed animals.<br>
In the case of a [[Study design#Case control studies|case control study]], no [[Measures of disease frequency|measures of disease frequency]] can be calculated, as selection of individuals was based upon their disease status. However an analytic study can still be conducted. This is achieved by looking at the '''odds of exposure''' in the different disease groups. It can be shown that (as long as the ''[[Sampling strategies#Sampling fraction|sampling fraction]]'' is different for cases than controls), the exposure odds ratio comparing diseased to non diseased animals is identical to the odds ratio for disease, comparing exposed to nonexposed animals. The odds ratio amongst diseased individuals is calculated as (a<sub>1</sub>/a<sub>0</sub>), and amongst nondiseased individuals as (b<sub>1</sub>/b<sub>0</sub>).<br>
In the case of a [[Study design#Case control studies|case control study]], no [[Measures of disease frequency|measures of disease frequency]] can be calculated, as selection of individuals was based upon their disease status. However an analytic study can still be conducted. This is achieved by looking at the '''odds of exposure''' in the different disease groups. This may seem incorrect (as we are more interested in the relative probabilities of disease amongst exposure groups than the odds of exposure amongst disease groups), but will be explained further below. The odds ratio amongst diseased individuals is calculated as (a<sub>1</sub>/a<sub>0</sub>), and amongst nondiseased individuals as (b<sub>1</sub>/b<sub>0</sub>).<br>
For study designs apart from case-control studies, once estimates of the prevalences, risks or rates of disease amongst different exposure groups have been calculated, the ratio of these can be calculated by dividing the estimates for the different groups with each other. In most cases, the frequency of disease amongst exposed animals is divided by the frequency of disease amongst unexposed animals (although the opposite approach can be taken if desired). Therefore, the prevalence or risk ratio can be calculated using teh following equation:<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>
(a<sub>1</sub>×b<sub>0</sub>) / (b<sub>1</sub>×a<sub>0</sub>)