Absolute risk reduction:
formula and worked example

The plain gap between two event rates

Absolute risk reduction (ARR) answers a direct question: out of every 100 people, how many fewer have the outcome because of the intervention? You subtract the event rate in the treated group from the event rate in the control group and report the difference in percentage points.

This is the figure that matters when someone has to weigh a benefit against a cost, a side effect or an inconvenience. A relative statement such as 'cuts risk by a third' sounds large whatever the baseline. The absolute gap tells you how much actually changes for a person standing in front of the decision.

The idea is not limited to medicine. Any programme with a measurable bad outcome, such as machine breakdowns, customer churn or late deliveries, can be summarised the same way.

Because it is expressed on the same scale as the original risks, ARR is also easy to scale up. Multiply by the number of people in a programme and you have the number of events avoided: a 4-point reduction across 5,000 people is 200 fewer events. That kind of back-of-envelope projection is what planners, insurers and public health teams actually need when they decide whether a measure is worth rolling out.

The formula and its inputs

• Risk control: the share of the untreated or standard-care group that had the outcome during follow-up.
• Risk treatment: the share of the treated group that had the same outcome over the same period.

Both proportions must come from comparable groups and the same time window. A control risk of 0.12 means 12 events per 100 people.

Worked example: 12% falls to 8%

In an imagined trial, 12 of 100 people in the control arm had an event and 8 of 100 in the treatment arm did.

1. 1Write the risks as proportions: control 0.12, treatment 0.08.
2. 2Subtract: 0.12 - 0.08 = 0.04.
3. 3Multiply by 100 to express the gap in percentage points: 4.
4. 4Interpret: for every 100 people treated, 4 fewer have the event.

How to read 4 percentage points

The same trial can be described in two ways. The absolute reduction is 4 percentage points. The relative reduction is 4 divided by 12, about 33%, meaning the treated group's risk is a third lower than the control group's. Both are correct; they answer different questions, and mixing them up is one of the commonest errors in reporting.

Context decides whether 4 points is worth chasing. For a mild, short-lived outcome it may not justify cost or side effects. For a serious outcome, 4 fewer events per 100 people is substantial. There is no universal cut-off, and thresholds used by guideline bodies differ by condition and country.

The inverse of the ARR, 1 / 0.04 = 25, is the number needed to treat: roughly 25 people must be treated to avoid one event over the follow-up period.

Why baseline risk drives the absolute gain

Raising the control risk from 0.12 to 0.132 lifts the reduction from 4 to 5.2 points. Note what the table does and does not show: it holds the treated risk fixed, so it describes a different scenario rather than the same drug applied to a sicker population. If the treatment kept its one-third relative effect, a control risk of 0.132 would give a treated risk near 0.088 and an ARR of about 4.4 points. Either way, the absolute benefit grows with baseline risk, which is why a treatment can be worthwhile for a high-risk group and marginal for a low-risk one.

Where absolute risk reduction goes wrong

• Calling the answer a percent. A drop from 12% to 8% is 4 percentage points, while the relative drop is 33%; writing '4% reduction' invites readers to guess which one is meant.
• Pooling groups with different follow-up lengths, so the two risks are not measured over the same period.
• Ignoring uncertainty. A 4-point gap from 50 people per arm may be well within chance; the interval around it matters.
• Applying a trial's ARR to a population with a very different baseline risk and expecting the same absolute benefit.
• Treating a negative value as an error. It signals harm, and should be reported as an absolute risk increase.

Most of these slips come from the same source: the reader sees one tidy number and forgets that it summarises two proportions drawn from two samples. Ask for the group sizes and event counts behind the rates before relying on the gap. A difference of 4 points between groups of 5,000 is firm evidence, while the same difference between groups of 40 is not.

Putting the figure to work

Suppose a clinic is choosing between two preventive options. Option A cuts risk from 12% to 8%. Option B cuts it from 3% to 1%. Option B has the larger relative effect, a two-thirds reduction, yet its absolute gain is only 2 points against 4 for Option A. A planner who looked only at relative figures would pick the wrong one.