Absolute risk reduction (ARR) is the simple difference between two event rates: the rate of a bad outcome in a control group minus the rate of that same outcome in a treatment group. The formula is ARR = control event rate − treatment event rate. It’s considered the most useful way to present research results for real-world decision-making because it tells you, in plain percentage points, how much a treatment actually lowers your chance of a specific outcome.
The Formula and How to Use It
The calculation itself is straightforward subtraction. You need two numbers: the event rate in the group that didn’t receive the treatment (the control group) and the event rate in the group that did (the treatment group).
ARR = Control Event Rate − Treatment Event Rate
Say a clinical trial tests a new blood pressure medication. Over five years, 8% of people in the control group have a heart attack, compared to 5% of people taking the medication. The absolute risk reduction is 8% − 5% = 3 percentage points. That means the treatment lowered the risk of heart attack by 3 percentage points in absolute terms.
If the control group’s event rate were higher, say 20%, and the treatment group’s rate were 14%, the ARR would be 6 percentage points. Same drug, same relative effect, but a bigger absolute benefit because the starting risk was higher. This is a critical concept: people at greater baseline risk stand to gain more from the same intervention.
Why ARR Matters More Than Relative Risk Reduction
Relative risk reduction (RRR) describes how much a treatment reduces risk compared to the control group’s risk. It often sounds more impressive than the absolute numbers. Using the first example above, the RRR would be 3/8 = 37.5%. A 37.5% reduction in heart attacks sounds dramatic. A 3 percentage point reduction sounds modest. Both describe the same data.
The problem is that relative risk reduction stays roughly the same regardless of a person’s baseline risk, while absolute risk reduction shifts depending on how likely the bad outcome was in the first place. If your baseline risk of heart attack is only 2% instead of 8%, that same 37.5% relative reduction translates to an ARR of just 0.75 percentage points. The treatment helps far fewer people in that low-risk group, even though the relative number looks identical.
This is why drug advertisements and even some study abstracts tend to favor relative numbers. They’re not wrong, but they can inflate the perceived benefit of a treatment. ARR keeps things grounded in what actually happens to real groups of people.
Turning ARR Into Number Needed to Treat
One of the most practical things you can do with ARR is convert it into a number called the “number needed to treat,” or NNT. This tells you how many people need to receive the treatment for one person to benefit. The formula is simple:
NNT = 1 / ARR
If the ARR is 3% (or 0.03 as a decimal), the NNT is 1 / 0.03 = 33.3, which you’d round up to 34. That means 34 people would need to take the medication for one additional person to avoid a heart attack compared to taking nothing. If the ARR were 6%, the NNT drops to about 17, meaning the treatment is twice as efficient in that higher-risk group.
NNT puts treatment effects into tangible terms. An NNT of 5 means a treatment is quite effective on a population level. An NNT of 100 means the vast majority of people taking the treatment won’t personally benefit from it, even if it works well for the few who do. Neither number is automatically “good” or “bad” since context matters. An NNT of 100 for preventing a fatal outcome might still be worthwhile, while an NNT of 10 for reducing mild symptoms might not justify serious side effects.
A Step-by-Step Calculation Example
Imagine you’re reading a study about a new screening program for colon cancer. Here’s how to work through the numbers:
- Step 1: Find the event rate in the control group. In the study, 1.5% of people who weren’t screened died of colon cancer over 10 years. This is your control event rate (CER): 0.015.
- Step 2: Find the event rate in the treatment group. Among those who were screened, 1.0% died of colon cancer. This is your experimental event rate (EER): 0.010.
- Step 3: Subtract. ARR = 0.015 − 0.010 = 0.005, or 0.5 percentage points.
- Step 4: Calculate NNT. NNT = 1 / 0.005 = 200. That means 200 people need to be screened for one colon cancer death to be prevented over 10 years.
For comparison, the relative risk reduction here would be 0.005 / 0.015 = 33%. “Screening reduces colon cancer death by 33%” and “200 people need screening to prevent one death” describe the same finding, but they feel very different. The ARR and NNT give you the full picture.
Adding Confidence Intervals
Any ARR calculated from a study is an estimate based on a specific group of participants. Confidence intervals tell you the range where the true ARR likely falls. If a study reports an ARR of 10% with a 95% confidence interval of 5% to 15%, you can be reasonably confident the real reduction is somewhere in that range.
You can convert those confidence interval boundaries into NNT the same way you convert the ARR itself, just take the reciprocal of each boundary and reverse their order. For an ARR confidence interval of 5% to 15%, the NNT confidence interval would be 100/15 to 100/5, giving you roughly 6.7 to 20. So the true number needed to treat likely falls between 7 and 20 people. Wide confidence intervals suggest the study was small or the results were variable. Narrow intervals mean you can trust the estimate more.
When to Use ARR vs. RRR
Neither measure is inherently better. They answer different questions. Relative risk reduction is useful for understanding whether a treatment works at all and whether its effect is consistent across different populations. Absolute risk reduction is what you need when deciding whether a specific treatment is worth it for a specific group of people.
If you’re reading about a treatment and only see relative numbers, you can calculate the ARR yourself as long as you know the baseline event rate. Multiply the baseline risk by the relative risk reduction to get the absolute benefit. For example, if your baseline risk is 4% and the treatment offers a 25% relative reduction, the ARR is 4% × 0.25 = 1 percentage point. That single percentage point of benefit is the number that should guide your thinking, not the 25%.