# What researchers mean by... absolute and relative risk

When a doctor says that a woman has a 15 per cent risk of developing a particular cancer over a lifetime, or a new drug can reduce the risk of heart disease by 20 per cent over an old drug, what exactly does that mean?

The media often mentions risk when reporting on research, but this can sometimes be misleading. Understanding how risk is expressed can help determine a study's significance, or a person's chance of illness, injury or recovery. Risk can be explained in terms of absolute or relative risk. Here's a look at the difference between these terms.

## Absolute Risk

Let's say a study of 100 workers in factory A revealed that 20 workers experienced back pain on the job. In factory B, 30 workers in a similar workplace of 150 workers developed back pain. The absolute risk of developing back pain is simply the percentage of people affected. This is 20 per cent in both groups. In scientific terms, absolute risk is the number of people experiencing an event in relation to the population at risk.

## Relative Risk

Relative risk is a comparison between two groups of people, or in the same group of people over time. It can be expressed as a ratio. In the example above, the relative risk of developing back pain — comparing factory A and factory B — is 20:20 or one. That is, workers in factory A are no more (or less) likely to have back pain than workers in factory B. It's 20 per cent for both groups.

Now suppose workers in factory A were to receive exercise therapy for half an hour each day. One year later, we find that only eight of 100 workers have back pain, while the rate in factory B remains the same at 20 per cent.

The ratio now changes to 8:20. Eight is the risk per 100 workers in factory A. Twenty is the risk per 100 workers in factory B. If we divide eight by 20, this gives us 0.40, or 40 per cent. In other words, the relative risk of developing back pain in factory A is now 40 per cent of the risk in factory B.

## Risk Reduction

How much did the risk of back pain change due to the exercise therapy intervention? Again, this can be calculated two ways, using absolute and relative risk reduction.

Absolute risk reduction is the difference in the percentage of people who are affected. Again, recall that before the intervention, 20 per cent of workers in factory A developed back pain. Afterwards, eight per cent did. The difference is 12. Therefore, the intervention resulted in an absolute risk reduction of 12 per cent.

The relative risk reduction is the change in relative risk. Recall that before the intervention, the relative risk was one for both factory A and B. After the intervention, it dropped to 0.40. The difference is 0.60. In other words, the intervention resulted in a 60 per cent reduction in relative risk.

## Which is better?

Risk expressed either way is correct. In our example, the relative risk reduction of 60 per cent appears larger than the absolute risk reduction of 12 per cent. It often helps to look at both types of risk to see how significant a change is.

For example, say the absolute risk of a work injury is two per 100 workers. Due to an intervention, it drops to one injury per 100 workers. This yields a relative risk reduction of 50 per cent. Overall, in absolute terms, this means one less injured worker per 100.

In another case, say the absolute risk of injury is 50 per 100 workers, but drops to 25 injuries per 100 workers. This will also result in relative risk reduction of 50 per cent. However, this translates to 25 fewer injured workers per 100. Even though the relative risk reduction is the same in both cases, the second intervention has a greater impact overall.

Let's revisit the examples from the start of the article. The doctor is describing the absolute risk of the woman developing cancer, in relation to all women at risk, over a lifetime. On the other hand, the reduction in risk of the new heart disease drug is relative, compared with the older drug.

The figures quoted are fictional. However, a 2005 study by Institute for Work & Health researchers did show that some forms of exercise therapy for back pain can be helpful.

Source: At Work, Issue 46, Fall 2006: Institute for Work & Health, Toronto