Relative Risk Reduction Calculator

Relative Risk Reduction (RRR) measures the proportional decrease in adverse event risk in the treatment group compared to the control group. It is expressed as a percentage and tells you by how much the treatment reduced the risk of the bad outcome relative to the baseline (control) risk. For example, an RRR of 40% means the treatment reduced the event rate by 40% relative to the control group.

RRR is calculated using the formula: RRR = ((ARC − ART) / ARC) × 100, where ARC is the event rate in the control group (events ÷ total in control) and ART is the event rate in the treatment group (events ÷ total in treatment). The result is expressed as a percentage.

Absolute Risk Reduction (ARR) is the simple arithmetic difference between the control event rate and the treatment event rate (ARC − ART). Relative Risk Reduction (RRR) expresses that same difference as a proportion of the control event rate. RRR can appear much larger than ARR, so both values together give a more complete picture of treatment benefit.

Relative Risk (RR), also called risk ratio, is the ratio of the event rate in the treatment group to the event rate in the control group. An RR of 1.0 means no difference between groups. An RR less than 1 indicates the treatment reduces risk, while an RR greater than 1 indicates increased risk in the treatment group.

The Number Needed to Treat (NNT) tells you how many patients need to receive the treatment for one additional adverse event to be prevented, compared to the control group. It is calculated as 1 / ARR (where ARR is expressed as a decimal). A lower NNT indicates a more effective treatment.

RRR can be misleading because it doesn't reflect the baseline risk. A treatment that reduces a 1% risk to 0.5% has the same RRR (50%) as one that reduces a 40% risk to 20%, but the clinical impact is very different. Always consider ARR and NNT alongside RRR for a fuller understanding of treatment benefit.

RRR is commonly reported in randomised controlled trials (RCTs) and meta-analyses to communicate the effectiveness of an intervention. It helps clinicians and patients understand how much a treatment reduces the relative likelihood of a bad outcome compared to no treatment or a placebo.

If the treatment event rate (ART) is higher than the control event rate (ARC), the RRR will be negative. A negative RRR indicates that the treatment actually increased risk rather than reducing it — this is sometimes called relative risk increase (RRI). The ARR would also be negative in this case, and NNT would become the Number Needed to Harm (NNH).