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.

1. Absolute risk = incidence rate
2. Relative risk
3. Attributable risk
4. 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.