Understanding Relative and Absolute Risk

“Raises the risk by 50%.” “Cuts the risk by a quarter.” Statements like these are accurate and still leave out the thing you most need to know: 50% of what? The answer lies in the difference between two ways of describing the same finding.

Two definitions

The US National Cancer Institute (NCI) describes absolute risk as the risk a person has of developing a disease over a certain period of time, for example so many cases in every 100,000 people in one year. Relative risk compares two groups: the percentage of people affected in one group is divided by the percentage affected in the other.

Cancer Research UK, a UK charity, put the same distinction in everyday terms in a 2013 article on media stories. The absolute risk is the actual risk itself. The relative risk says how much more, or less, likely something is in one group than in another.

Relative risk on its own does not tell you how likely the event is in the first place. A large relative change in something very rare can amount to very little. A small relative change in something common can affect many people.

One example, followed all the way through

Imagine a headline: “Daily habit raises risk of Condition X by 50%”.

Step 1. Find the starting point

Suppose that among 1,000 people who do not have the habit, 2 develop Condition X over ten years. That is the baseline absolute risk: 2 in 1,000, or 0.2%.

Step 2. Apply the relative change

A 50% increase means half as much again. Half of 2 is 1, so the figure for people with the habit is 3 in 1,000, or 0.3%.

Step 3. Work out the absolute difference

3 minus 2 is 1. Among 1,000 people with the habit, there is 1 extra case over ten years.

Step 4. Say it in whole people

“A 50% higher risk”, “from 0.2% to 0.3%” and “1 extra case in every 1,000 people” all describe the same invented finding. They leave very different impressions, and only the last two let you judge the size of the effect.

The same percentage on a different baseline

Now keep the 50% and change the starting point. Suppose Condition Y affects 200 in 1,000 people without the habit. A 50% increase takes that to 300 in 1,000, which is 100 extra cases per 1,000 people.

The relative risk is identical and the consequences are a hundred times apart. This is the point Cancer Research UK makes with real studies: the starting absolute risk is what gives a relative figure its meaning, and a modest-sounding percentage can matter across a whole population when the condition is common.

It works the same way for benefits

Suppose a treatment is described as “reducing the risk of an event by 25%”. If 20 in 1,000 untreated people have the event over five years, a 25% reduction brings that to 15 in 1,000. The absolute reduction is 5 in 1,000: of every 1,000 people treated for five years, 5 avoid the event, 15 have it anyway, and 980 would not have had it with or without the treatment. Again, these are invented numbers.

A fair comparison describes benefits and harms in the same way, for the same number of people. If the benefit is quoted as a relative figure and the side effects as absolute ones, or the other way round, the two cannot be weighed against each other. The Harding Center for Risk Literacy in Germany designs “fact boxes” for this purpose: tables that set the most important benefits and harms of a medical measure side by side, so that people without statistical training can compare them.

Why headlines prefer the relative figure

Often because it is the more striking number. Sense about Science, a UK charity, lists “reporting a relative increase in risk without including the absolute change” among the ways statistics get hyped. Cancer Research UK warns readers to be wary of headlines built on a relative figure, and points out that a phrase such as “ten times more likely” means little until you know the underlying numbers.

This is not always deliberate. Relative risk is a standard measure in research studies, as the NCI notes, and summaries tend to repeat it. The absolute numbers are sometimes in the study itself.

Five questions to ask of any risk figure

1. Compared with what? Who is in the comparison group?
2. What is the baseline? How many people in 1,000 are affected to begin with?
3. Over how long? A year, ten years, a lifetime?
4. In whom? People of what age and with what circumstances, and how like you are they?
5. How sure is the link? A difference between two groups does not show by itself that one thing caused the other. See our explainer on association and causation.

Cancer Research UK adds two practical tips. Convert figures to a common base, such as “per 1,000” or “per 10,000”, before comparing them. And remember that a risk is a chance, not a certainty: it describes what happens across a group, not what will happen to one person.

Using this in an appointment

The same idea applies when a test or treatment is offered. An NCI article on cancer screening statistics quotes a professor of medicine whose advice to patients is to ask for the right numbers: what is my chance of dying from the disease if I am screened, and if I am not? That is a request for absolute figures.

Your clinician may not have exact figures, and population numbers never fit one person perfectly. An approximate answer in whole people is still more useful than a precise percentage with no baseline. More questions of this kind are in questions to ask when a test or treatment is suggested.

A small absolute change is not automatically unimportant. One extra case in 1,000 matters a great deal if the outcome is serious and the exposure is easy to avoid, and it may matter less if avoiding it is costly to you. The numbers do not make that decision. They let you make it knowing the size of what is at stake.