How do you calculate absolute risk reduction and relative risk reduction?

Absolute risk reduction is the control event rate minus the experimental event rate, for example 0.20 minus 0.12 equals 0.08. Relative risk reduction is the absolute risk reduction divided by the control event rate, or equivalently one minus the relative risk, so 0.08 divided by 0.20 equals 0.40, a 40 percent reduction.

How do you calculate absolute risk reduction?

Subtract the event rate in the treatment group from the event rate in the control group. If 20 percent of control patients and 12 percent of treated patients have the event, the absolute risk reduction is 20 minus 12, which is 8 percentage points, or 0.08 as a proportion.

What is the formula linking absolute risk reduction and number needed to treat?

The number needed to treat is the reciprocal of the absolute risk reduction: NNT equals 1 divided by the absolute risk reduction. With an absolute risk reduction of 0.08, the number needed to treat is 1 divided by 0.08, which is 12.5, so about 13 patients must be treated to prevent one event.

What is absolute risk?

Absolute risk is the plain probability of an event occurring in a defined group over a defined period, such as 3 percent if 30 of 1,000 people have an event in a year. It is the basis for the control and experimental event rates from which risk reductions are calculated.

Absolute Risk Reduction Explained

Absolute risk reduction is the difference between the event rate in the control group and the event rate in the treatment group: the control event rate minus the experimental event rate. If 20 percent of untreated patients have an event and 12 percent of treated patients do, the absolute risk reduction is 8 percentage points, or 0.08. It tells you how much the actual risk fell in real terms, which is the figure a patient and clinician most need, and it is the direct route to the number needed to treat. Relative measures, by contrast, describe proportional change and can make a tiny absolute benefit look dramatic.

Why absolute and relative measures tell different stories

Take the same example. The risk fell from 20 percent to 12 percent. The relative risk reduction is the proportional fall, 8 divided by 20, which is 0.40 or 40 percent. Both statements are true of the identical data, yet “a 40 percent reduction” sounds far larger than “an 8 percentage-point reduction”. The danger appears when the baseline risk is small. If a treatment cuts risk from 2 percent to 1 percent, the relative risk reduction is still a headline 50 percent, but the absolute risk reduction is only 1 percentage point, and a hundred people would need treating to prevent a single event. This is why guidelines and honest reporting insist on the absolute measure alongside the relative one: the relative figure is the same whether the baseline is 2 percent or 50 percent, so it hides the thing that determines whether a treatment is worth giving. The trade-offs between ratio measures themselves are covered in our comparison of the odds ratio and the risk ratio.

The formulae, worked through

Write the control event rate as the proportion with the event in the control arm and the experimental event rate as the proportion in the treated arm. Then:

Absolute risk reduction equals the control event rate minus the experimental event rate. With rates of 0.20 and 0.12, that is 0.20 − 0.12 = 0.08.
Relative risk equals the experimental event rate divided by the control event rate, here 0.12 ÷ 0.20 = 0.60.
Relative risk reduction equals one minus the relative risk, here 1 − 0.60 = 0.40, or 40 percent. Equivalently it is the absolute risk reduction divided by the control event rate, 0.08 ÷ 0.20 = 0.40.

Two cautions follow. First, the sign convention: when treatment lowers risk, the absolute risk reduction is positive; when it raises risk, the same calculation yields a negative number, sometimes reported as an absolute risk increase. Second, never confuse relative risk reduction with the relative risk itself; a relative risk of 0.60 corresponds to a relative risk reduction of 40 percent, not 60 percent. You can compute the underlying risk ratio and its confidence interval directly with our odds ratio and risk ratio calculator.

From absolute risk reduction to number needed to treat

The most useful thing the absolute risk reduction unlocks is the number needed to treat, the average number of patients you must treat to prevent one additional event. It is simply the reciprocal of the absolute risk reduction: one divided by 0.08 is 12.5, so about 13 patients must be treated to prevent one event. A small absolute risk reduction means a large number needed to treat, and therefore a less impressive treatment in practical terms, however flattering its relative risk reduction. The full interpretation, including the number needed to harm and how to read confidence intervals around it, is set out in our guide to interpreting the number needed to treat, and you can convert directly with the number needed to treat calculator.

What absolute risk means on its own

Absolute risk is the plain probability of an event in a defined group over a defined period: if 30 of 1,000 people have an event in a year, the absolute risk is 3 percent. It is the foundation on which the reductions are built, because both the control and experimental event rates are themselves absolute risks. A relative measure compares two absolute risks; an absolute measure reports the risks, or their difference, on the original scale. Keeping the distinction clear is the single most important habit in communicating evidence, because a patient understands “3 in 100 instead of 5 in 100” far better than “a 40 percent reduction”, and the former cannot mislead them about scale.

Why absolute measures matter for pooled effects

Meta-analyses almost always pool a relative measure, usually a risk ratio, an odds ratio, or a hazard ratio from time-to-event data, because relative effects tend to be more stable across populations with different baseline risks, which makes them more suitable for combining. That stability is exactly why a pooled relative effect is hard for a reader to act on: a risk ratio of 0.60 means something very different for a high-risk and a low-risk patient. The standard solution is to apply the pooled relative effect to an assumed baseline risk to produce an absolute effect for a chosen population, which is precisely the step the GRADE summary-of-findings table formalises when it reports the anticipated absolute effects. The choice of which effect measure to pool in the first place is discussed in our guide to selecting an effect size for synthesis. The lesson is consistent: pool in relative terms for stability, then translate back to absolute terms for interpretation, so the final statement reflects how much real risk actually changed.

Common mistakes

A handful of errors recur. The first is reporting only the relative risk reduction, which inflates the apparent benefit when the baseline risk is low and is the classic way a marginal treatment is oversold. The second is confusing relative risk with relative risk reduction, two numbers that always sum to one but are forever mixed up. The third is computing a number needed to treat from a relative measure rather than from the absolute risk reduction, which is simply invalid. The fourth is ignoring the confidence interval on the absolute risk reduction, which can be wide enough to include zero even when the point estimate looks worthwhile. Report the control event rate, the absolute risk reduction with its interval, and the number needed to treat together, and the evidence becomes both honest and usable.