A treatment can look dramatic or trivial depending entirely on which number you report. Absolute risk reduction (ARR), relative risk reduction (RRR), and number needed to treat (NNT) are three different ways of expressing the same clinical trial result, and they are not interchangeable — reporting only the relative measure is one of the most common and well-documented ways trial results get made to look bigger than they are. This guide works through one illustrative worked example and carries it through every measure, including where confidence intervals and reporting standards come in.
The illustrative example used throughout this guide
The numbers below are illustrative only — a constructed example for demonstrating the arithmetic, not a real trial or real intervention. Do not cite these figures as evidence for any actual treatment.
| Outcome occurred | Total in arm | Risk | |
|---|---|---|---|
| Control arm | 200 | 1,000 | 200/1,000 = 20% (0.20) |
| Treatment arm | 150 | 1,000 | 150/1,000 = 15% (0.15) |
This is a standard 2×2 trial-results table: a fixed number of participants randomized to a control group or a treatment group, followed for a defined period, with a binary outcome (event happened / did not happen) counted in each arm. Every measure below is derived from just these four numbers.
Absolute risk in each arm
Absolute risk is simply the proportion of participants in a given arm who experienced the outcome over the study’s follow-up period — control-arm risk (CER, control event rate) 20%, treatment-arm risk (EER, experimental event rate) 15% in the example above. Absolute risk is the only one of these measures with a direct real-world interpretation on its own: “20% of untreated patients had the event” is a complete statement. Relative and ratio measures, by contrast, only make sense in reference to a baseline.
Absolute risk reduction (ARR): the risk difference
ARR = control-arm risk − treatment-arm risk.
In the example: ARR = 20% − 15% = 5 percentage points (0.05). ARR is also called the risk difference — it is reported in the same units as the outcome rate itself (percentage points, or events per however many patients), which is exactly why it is harder to make sound more impressive than it is. It answers a concrete question: “if I treat a population like this one, what fraction of them will be spared the outcome because of treatment, over and above what would have happened anyway?”
Relative risk (RR) and relative risk reduction (RRR)
Relative risk (risk ratio) = treatment-arm risk ÷ control-arm risk. In the example: RR = 15% ÷ 20% = 0.75 — treated patients had 75% of the risk of control patients.
Relative risk reduction (RRR) = 1 − RR, which is algebraically identical to RRR = ARR ÷ control-arm risk. In the example: RRR = 1 − 0.75 = 25% (equivalently, 5% ÷ 20% = 25%). Framed as “a 25% reduction in risk,” this sounds substantially larger than “a 5-percentage-point reduction in risk” — even though both describe exactly the same trial result.
Why the same RRR can mean wildly different things
This is the core reason ARR and RRR need to be reported together, not the relative measure alone: RRR is a ratio, so it says nothing about the size of the baseline risk it is being applied to. A 50% RRR sounds identical whether it is being applied to a common outcome or a rare one — but the number of people actually helped is completely different.
| Scenario (illustrative) | Baseline (control) risk | RRR | Resulting ARR | Resulting NNT |
|---|---|---|---|---|
| Low-baseline-risk population | 2% | 50% | 1 percentage point | 100 |
| High-baseline-risk population | 40% | 50% | 20 percentage points | 5 |
Both rows report an identical, genuinely accurate “50% relative risk reduction.” One describes a treatment that helps 1 in 100 people treated; the other describes a treatment that helps 1 in 5. A press release, abstract, or headline that reports only the RRR cannot distinguish between these two situations — and RRR is systematically the larger, more attention-grabbing number precisely because dividing by a small baseline risk inflates it. This is a recognised, well-documented form of reporting spin in trial publications and press coverage, not a hypothetical concern: it is the specific reason reporting guidelines (below) require the absolute measure alongside the relative one.
The practical corollary: always ask what the underlying baseline (control-arm) risk was before treating a relative-risk headline as meaningful. A large RRR applied to a rare outcome can still mean very few people actually benefit from treatment.
Number needed to treat (NNT)
NNT = 1 ÷ ARR (with ARR expressed as a decimal, not a percentage). In the example: NNT = 1 ÷ 0.05 = 20 — twenty patients need to be treated, on average, for one additional patient to avoid the outcome who would not have avoided it under the control condition. The concept was introduced by Laupacis, Sackett, and Roberts in 1988 as a way of translating a risk difference into a single, clinically intuitive number of patients.
Two practical rules that are easy to get wrong:
- NNT is always rounded up to the next whole integer, never rounded to the nearest one. An NNT of 20.4 is reported as 21 — rounding down would imply benefit for a fraction of a patient that the data doesn’t actually support; rounding up is the conservative, correct convention.
- NNT is meaningless without stating the follow-up period the underlying trial used. An NNT of 20 over 5 years of follow-up is a very different clinical claim from an NNT of 20 over 30 days — the same ARR, and therefore the same NNT, can arise from very different absolute rates of event accrual. Always report NNT alongside the outcome definition and the time horizon it was measured over; a bare “NNT = 20” without either is not a complete or reusable statement.
Number needed to harm (NNH), and weighing it against NNT
Number needed to harm (NNH) is the mirror-image calculation applied to a harmful outcome (an adverse event) instead of a beneficial one: NNH = 1 ÷ absolute risk increase, where the absolute risk increase is the excess rate of the adverse event in the treatment arm versus control. A treatment with NNT = 20 for its primary benefit and NNH = 200 for a serious adverse event is, all else equal, a much more favourable trade-off than one with NNT = 20 and NNH = 25 — the raw NNT number alone says nothing about this balance. A complete appraisal of a treatment’s clinical value requires both figures, over the same follow-up period and ideally in the same population, side by side — never NNT reported in isolation as though it were the whole picture.
Odds ratio vs. risk ratio
A fourth measure, the odds ratio (OR), is frequently confused with relative risk but is calculated differently: odds ratio compares the odds of the outcome (events ÷ non-events) between arms, rather than the risk (events ÷ total). In the worked example: control-arm odds = 200/800 = 0.25; treatment-arm odds = 150/850 ≈ 0.176; OR ≈ 0.706 — close to, but not identical to, the RR of 0.75 calculated above.
When the outcome is rare (roughly under 10%), OR closely approximates RR, which is why the two are often used loosely as if interchangeable. When the outcome is common, they diverge substantially, and OR always overstates the effect relative to RR in the direction away from 1 (an OR further from 1 than the corresponding RR). This matters most for case-control studies, which by design sample participants based on outcome status rather than exposure status — meaning true absolute risk in the source population generally cannot be estimated from a case-control design, so odds ratio is the measure such studies can validly report, not risk ratio or ARR. Logistic regression models — a common way of estimating an adjusted effect while controlling for covariates — likewise produce odds ratios natively rather than risk ratios; see the logistic regression (logit model) guide for how that coefficient-to-odds-ratio conversion works.
Confidence intervals on ARR and NNT
Every point estimate above — ARR, RR, RRR, OR, NNT — is calculated from a finite sample and carries sampling uncertainty that should be reported as a confidence interval, not stated as though it were exact. CONSORT (below) specifically requires the confidence interval alongside the point estimate for every primary and secondary outcome, not a bare p-value or point estimate in isolation.
ARR’s confidence interval is usually straightforward — an interval around the risk difference, symmetric on the percentage-point scale for large samples. NNT’s confidence interval is not straightforward, because NNT is the reciprocal of ARR, and the reciprocal transform behaves badly whenever the ARR interval crosses zero. If a trial’s true effect is not statistically significant, the ARR confidence interval spans zero — for example, ARR 10% with 95% CI −5% to 25% — and taking the reciprocal of an interval that includes zero mathematically produces an interval that passes through infinity, not a normal finite range. Altman (BMJ, 1998) addressed this directly and proposed reporting such cases using both NNT-for-benefit (NNTB) and NNT-for-harm (NNTH) explicitly, joined at infinity — the example above would be reported as NNTB 10 (95% CI NNTH 20 to ∞ to NNTB 4), rather than as a single misleadingly finite-looking NNT confidence interval. Any NNT reported without checking whether its underlying ARR confidence interval crosses zero should be treated cautiously — a “significant-looking” NNT can hide a genuinely non-significant underlying effect.
Where baseline risk comes from — and why it doesn’t transport automatically
The control-arm risk in a trial is a property of the specific population enrolled — their disease severity, age, comorbidities, background care, and the specific follow-up period used — not a fixed constant of the disease itself. This is closely related to the distinction between prevalence and incidence: a trial’s control-arm event rate is an incidence measure specific to that trial’s population and duration, and it will differ from the incidence in a different population with a different risk profile.
Applying a trial’s ARR directly to a different-risk population is a common and consequential error. Because ARR = RR × baseline risk (approximately, for small effects), and because clinical trial populations are frequently enriched for higher baseline risk than the general population a clinician is treating, naively applying a trial’s published ARR/NNT to a lower-risk real-world patient overstates the expected benefit — sometimes substantially. The RR (or OR) is generally assumed to be more transportable across risk strata than the ARR is, which is why guideline developers typically recombine a trial’s relative effect estimate with a patient’s or population’s own baseline risk, rather than reusing the trial’s published ARR/NNT unadjusted. This is also why NNTs quoted for the “same” intervention can differ several-fold across published sources — they usually reflect different baseline-risk populations, not different treatment effects.
Reporting standards: what CONSORT requires
The CONSORT 2010 statement, the standard reporting guideline for parallel-group randomized controlled trials, addresses this directly. CONSORT checklist item 17b states that for binary outcomes, trials should report both absolute and relative effect sizes, each with its confidence interval — the explicit rationale being that neither measure alone gives a complete picture of a treatment’s effect and its clinical implications, and binary-outcome event rates/denominators should be reported so readers can verify how the ratios and differences were derived. A results section, abstract, or press release that reports RRR (or OR) without the corresponding ARR is not meeting this standard, even where a percentage change is technically accurate.
The same underlying logic — full transparency of the numbers behind a summary statistic — is why CONSORT also expects effect sizes and their precision (confidence intervals) reported for every primary and secondary outcome, rather than significance stated via p-value alone.
Frequently asked questions
Is a lower NNT always better?
Generally yes for benefit — a lower NNT means fewer patients need to be treated for one to benefit — but NNT must always be read against NNH for the same intervention, and against the seriousness/reversibility of both the benefit and the harm being weighed, not compared as a bare number across unrelated interventions or outcomes.
Can NNT be negative, or less than 1?
An NNT less than 1 would imply more than one patient benefits per patient treated, which is not meaningful for a single binary outcome — in practice NNT is ≥1 (after rounding up). A negative ARR (treatment arm risk higher than control) indicates net harm rather than benefit, and is properly reported as an NNH for that outcome rather than a negative NNT.
Why do case-control studies report odds ratios instead of risk ratios or ARR?
Because case-control studies sample participants by outcome status (a fixed number of cases and controls, not a representative cohort followed forward in time), the true incidence/absolute risk in the source population generally cannot be recovered from the sampled data — only the odds ratio can be validly estimated. Risk ratio and ARR require a cohort or trial design where absolute risk is directly observable.
What does it mean when an NNT’s confidence interval includes infinity?
It means the underlying ARR confidence interval crosses zero — the trial has not established statistical significance for that outcome, even if the point-estimate NNT looks like a clean, clinically meaningful number. Report both the NNTB and NNTH bounds explicitly in that case, per Altman’s 1998 recommendation, rather than a single point-estimate NNT.
Is a large RRR always more informative than the ARR?
No — RRR alone cannot distinguish a treatment that helps a large fraction of patients from one that helps very few, because it says nothing about the baseline risk it was calculated from. ARR (or NNT, its reciprocal) is the measure that reflects real-world impact on a specific population; RRR is most useful as a secondary, comparative figure once ARR is already reported.
