Writing about risk

Writing about risk is challenging because the same risk can be expressed in different ways. You need to think about how to express the risk in a way that your audience will easily understand.

For example, if you are talking about the risk of someone developing a disease, you can express the risk in at least 3 different ways:

  • number of individuals in a given sample – a 1 in 10 risk of developing the disease (commonly expressed as a number in 10, 100 or 1000)
  • percentage – a 10% chance of developing the disease
  • decimal between 0 and 1 – a 0.1 risk of developing the disease.

Types of risk

Absolute risk is risk stated without any context:

You have a 50% chance of flipping a coin and getting heads.

This risk is not compared with any other risk: it is just the probability of something occurring.

We all have absolute risks of developing various diseases (eg heart disease or cancer) – the absolute risk is just the population-based probability of getting the disease (eg 1 person in every 100).

Relative risk is a comparison between different risk levels; it is usually used to compare the risk in 2 different groups of people:

Your relative risk for lung cancer is (approximately) 10 if you have ever smoked, compared with a nonsmoker.

This means that a smoker is 10 times more likely to get lung cancer than a nonsmoker. If the absolute risk is about 1% for a nonsmoker, that for a smoker is about 10%. In medical research, groups are often compared to see whether belonging to a certain group increases or decreases the risk of developing a disease. However, relative risk figures are meaningless when given without reference to the absolute risk:

Is stir-fried broccoli good for you?

Consider these (totally hypothetical) statements:

  • Eating an apple a day reduces your risk of having a heart attack by 40%.
  • Eating stir-fried broccoli twice a week reduces your risk of having a heart attack from 0.5% to 0.3%.

Question: Which is better for you – an apple a day or stir-fried broccoli twice a week?

The first statement gives the risk reduction for eating an apple a day as 40%, which makes eating apples sound like a very good idea. However, this figure is the relative risk reduction. It is impossible to know what this means for an individual without knowing what the 40% reduction actually refers to – that is, what is the risk of heart disease for a person who doesn’t eat an apple a day?

The information on broccoli gives the risk reduction as 0.2 percentage points (from 0.5% to 0.3%), which sounds less impressive. However, this is the absolute risk reduction, and, because 0.2 relative to 0.5 is 40%, it is exactly the same as a relative risk reduction of 40%.

To make a valid comparison of apples and broccoli, you would need to know the absolute figures for apples.

To understand risk information, you need to know the actual numbers of people involved.

For the stir-fried broccoli example, imagine that a clinical trial gives the following results:

  • Control group: 5 in 1,000 subjects had a heart attack.
  • People eating stir-fried broccoli twice a week: 3 in 1,000 subjects had a heart attack.

These results are shown in the following table, which defines the terms commonly used in the academic literature relating to risk.




Absolute risk (AR)

The risk of an event (eg having a heart attack)

Control: 5/1,000 = 0.005 (0.5%)

Broccoli: 3/1,000 = 0.003 (0.3%)

People in the control group had a 0.5% chance (1 in 200 chance) of having a heart attack. People who ate broccoli had a 0.3% chance (1 in 333 chance) of having a heart attack

Absolute risk reduction (ARR) (absolute risk difference)

The difference in risk between the control and treatment groups

0.005 – 0.003 = 0.002 (0.2%)

The chance of having a heart attack in the broccoli-eating group was 0.2 percentage points lower than in the control group

Relative risk (RR)

The risk in the treatment group relative to the risk in the control group

0.003/0.005 = 0.6 (60%)

People who ate broccoli were 0.6 times as likely to have a heart attack as those who did not eat broccoli

Relative risk reduction (relative risk difference)

The reduction in the risk due to the treatment. Calculated as 1 – RR or ARR/risk in control group

1.0 – 0.6 = 0.4 (40%) or 0.002/0.005 = 0.4 (40%)

Eating broccoli reduced the risk of having a heart attack by 40%

Number needed to treat (NNT)

The number of people that need to be treated to prevent 1 adverse event. Calculated as 1/ARR

1.0/0.002 = 500

For every 500 people who ate broccoli, 1 heart attack was prevented

Note: These figures are made up and in no way represent the health effects of eating apples or broccoli!

Source: The table is adapted from Glasziou et al (2007).

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