Relative Risk Reduction

Relative risk reduction (RRR) is the proportional decrease in the risk of an event in the treatment group compared to the control group, calculated as one minus the relative risk and typically expressed as a percentage. It quantifies the fraction of baseline risk that is removed by the intervention.

RRR is widely used to communicate treatment benefits in clinical trials, drug advertising, and media coverage of medical research. Its appeal lies in its ability to express the treatment effect as a single, often impressive sounding percentage. However, RRR can be misleading when interpreted without reference to the baseline risk, because the same relative reduction corresponds to very different absolute benefits depending on how common the outcome is. Understanding both RRR and absolute risk reduction (ARR) is essential for evidence based clinical decision making.

RRR is calculated as (control group risk minus treatment group risk) divided by control group risk, or equivalently, one minus the relative risk. If the event rate in the control group is 8% and in the treatment group is 6%, the relative risk is 0.75 and the RRR is 25%. This means the treatment reduces the risk of the event by 25% relative to the control group's risk.

The corresponding absolute risk reduction is the arithmetic difference between the two risks: 8% minus 6% = 2 percentage points. The number needed to treat (NNT) is the reciprocal of the ARR: 1 divided by 0.02 = 50, meaning 50 patients must be treated to prevent one event.

The critical insight is that RRR is often assumed to stay roughly constant across baseline risk levels, while the ARR then changes in proportion to the baseline risk. A drug that reduces relative risk by 25% will produce a large absolute benefit in a high risk population (25% RRR applied to a 40% baseline risk = 10 percentage point ARR, NNT = 10) but a much smaller absolute benefit in a low risk population (25% RRR applied to a 4% baseline risk = 1 percentage point ARR, NNT = 100). This is why clinical decision making should incorporate both relative and absolute measures.

Report RRR alongside ARR and NNT when communicating the results of intervention studies to provide a complete picture of the treatment's impact. RRR is useful for describing the proportional size of an intervention's effect (how much of the underlying risk it removes), while ARR and NNT translate that effect into the absolute number of patients who benefit. Avoid using RRR alone to make claims about clinical significance, as it can overstate the practical importance of the treatment for low risk populations.

A common and consequential mistake is reporting RRR without the corresponding ARR, leading clinicians and patients to overestimate the treatment's benefit. Pharmaceutical advertising is frequently criticized for emphasizing impressive RRR figures while omitting ARR data. Another error is applying a RRR from a trial population to a clinical population with a very different baseline risk without recalculating the ARR for that population. Researchers sometimes confuse RRR with ARR, or use the terms interchangeably, which can lead to orders of magnitude errors in the interpretation of treatment effects. Finally, reporting a confidence interval for the RRR but not for the ARR or NNT provides incomplete uncertainty characterization.

A randomized trial of a new blood thinner for stroke prevention in atrial fibrillation reports that the annual stroke rate is 1.8% in the treatment group and 3.0% in the control group. The RRR is 40% (1 minus 0.60), which sounds substantial. The ARR is 1.2 percentage points, and the NNT is 84 (1 ÷ 0.012 = 83.3, rounded up), meaning 84 patients must be treated for one year to prevent one stroke. A clinician counseling a patient with a very low baseline stroke risk (0.5% per year) notes that the same drug, assuming constant relative efficacy, would yield an ARR of only 0.2 percentage points and an NNT of 500.