on July 22, 2011 by Georgina Moulton in Statistical Methods, Comments (0)

# Basic Statistics for Epidemiology: Risk

Author: Sara Muller, University of Keele

(based on Health Knowledge materials)

Risk has a very similar meaning in epidemiology as it does in everyday usage – it is about chance. It is defined by Unwin et al, as *“the probability that an event will occur *

It is often used to compare the risk of an event between groups. There are lots of ways to define the groups you might want to compare. For example, socio-demographic factors, or exposure to factors that may cause the disease.

There are several measures of risk, and we will deal with each in turn in this article.

- Absolute risk = incidence rate
- Relative risk
- Attributable risk
- Odds Ratio

A worked example deals with the association between smoking and cancer.

Lung Cancer |
|||

Yes | No | ||

Ever Smoked | Yes | 70 | 60 |

No | 20 | 90 |

Absolute Risk

Absolute risk of lung cancer by smoking status

Smokers: \[70/70+60 = 70/130\] \[=0.538\]

Non-smokers: \[20/20+90 = 20/110\] \[=0.181\]

Relative Risk

The relative risk is the ratio of absolute risk (incidence rates). Relative risk measures the strength of association between an exposure and a disease. Groups are usually defined by exposure to a potential determinant/cause of the disease, but can be similar things, such as gender.

\[incidence rate of disease in group with exposure/incident rate of disease in group without exposure\]

If the result is:

<1 exposure decreases risk of disease

0 exposure has no effect on risk of disease

>1 exposure increases risk of disease

Using the absolute risks above the relative rate would be:

\[0.538/0.181 = 2.97\]

Those people who have ever smoked are 3 times more likely to die of lung cancer over a 15 year period than those who have never smoked.

Attributable Risk

Attributable risk measures the **proportion** of disease in the population (or just in the exposed group) that can be ‘attributed’ to the exposure. It can be expressed in any of the same ways as a proportion.

AR population = incidence rate population – incidence rate non-exposed

AR exposed = incidence rate exposed – incidence rate non-exposed

An example of attributable risk is below:

Population incidence rate = \[70+20/70+20+60+90 = 90/240 = 0.375\]

AR population = \[0.375 – 0.181 = 0.194\]

AR exposed = \[0.538 – 0.181 – 0.357\]

This suggest that in the 15 year follow up period, 19% of lung cancer deaths in the population and 36% in smokers can be attributed to smoking.

Odds Ratio

Compare the odds of an event of interest between two groups using a ratio. It is not the same as a risk ratio, although it will give similar results if the disease is rate. It is often used in case-control studies.

Odds of exposure among cases/odds of exposure among controls.

If we to continue the example above the odds ratio calculation would be as follows:

Odds of disease in exposed = \[70/20\]

Odds of disease in unexposed = \[60/90\]

Odds ratio = \[70/20/60/90 = 70*90/20*60 = 5.25\]

Those people how have ever smoked had 5.25 times the odds of developing lung cancer in the 15 year follow up period those who had never smoked.

Tags: epidemiology, odds ratio, public health, risk

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