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# Association

## Definition of Association

• Relationship between two or more events or variables.

## Measuring Disease Association

Usually we want to look at the relationship between an exposure (risk factor, predictor) and the outcome.

The measures that are used to show association beween an exposure or treatment and disease are called measures of association.

## Summary of Measures of Association

The following table shows all the possible ratio and difference measures that can be calculated from cross-sectional, cohort data, and case control study.

Study Type Ratio Difference
Cross-sectional Study prevalence ratio prevalence difference
Cross-sectional Study odds ratio odds difference
Cohort Study risk ratio risk difference
Cohort Study rate ratio rate difference
Cohort Study odds ratio odds difference
Case Control Study case control odds ratio

All of the ratios are commonly seen, but the difference measures are rare except for the risk difference and possibly the rate difference.

• Odds differences are almost never seen as most find them hard to interpret.

## Ratio Measures Limited by Type of Study

The type of study limits the kind of ratio measure that can be calculated.

• The cohort study allows calculation of all three measures, but the risk and rate ratio measures are more easily understood than the odds ratio and are therefore the measures reported in cohort studies rather than the odds ratio.
• The prevalence ratio looks like a risk ratio, but one should always keep in mind that it is risk based on existing, or prevalent, disease rather than incident disease.
• The odds ratio from a cross-sectional study is not usually described as a prevalence odds ratio, but of course it is also based on a prevalent sample. Prevalence odds ratio is a more precise way to characterize what is being reported.
• The case-control study only allows calculation of the odds ratio, a major reason for the importance of the odds ratio in clinical research.

## Relative Measures and Strength of Association

In practice many risk factors have a relative measure in the range of 2 to 5: Some very strong risk factors may have a relative measure in the range of 10 or more
• For example, asbestos and lung cancer
Relative measures < 2.0 may still be valid but are more likely to be the result of bias
• For example, second-hand smoke relative risk < 1.5
These ranges for ratio measures can be used as a kind of rough rule of thumb. There is certainly nothing absolute about them.

They suggest that it is more difficult to demonstrate an etiologic role for exposures that have associated ratios less than 2.0.

• This is one reason it took a very long time to convince the medical and public health community that there were risks associated with second-hand smoking.

Topic revision: r14 - 03 Feb 2012 - 17:10:59 - PeterBacchetti

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