---
title: "Absolute risk difference / NNT, 2x2"
method_id: SM.REL.RSK.2X2.ARD
family: Relationship
version: 1.0.0
date_modified: 2026-06-21
canonical: https://clarus.ofrencber.com/library/risk_difference.md
source: Clarus method library
---

# Absolute risk difference / NNT, 2x2

> A classical statistical method in the Clarus library (Relationship family).
> Clarus selects, assumption-checks and runs this method on your data with a
> deterministic rule engine and real numerical libraries (scipy / statsmodels);
> it never generates numbers, citations or results.

**Also known as:** risk difference; RD; absolute risk reduction; ARR; attributable risk; number needed to treat; NNT.

## Hypotheses

- **Null (H0):** RD = 0 (the absolute risk of {outcome} is the same in the two groups).
- **Alternative (H1):** RD != 0 (the absolute risk of {outcome} differs between the two groups).

## When to use it

Use this method when your goal is to:
- quantify the absolute difference in outcome risk between two groups
- report absolute risk reduction and number needed to treat from a 2x2 table
- express the clinical consequence of a treatment or exposure on the original probability scale

## Data it expects

- **dependent:** 1 binary outcome (event / no event), counted with known denominators per group
- **independent:** 1 binary group / exposure / treatment (group 1 / group 2) — the two rows of a 2x2 table
- **pairing:** independent (each subject contributes to exactly one cell); a design with genuine per-group risks (cohort / randomized trial), so an absolute risk can be computed in each arm

## Assumptions Clarus checks

- **genuine per group risk** (severity: critical; on violation: reroute)
- **independence of observations** (severity: critical; on violation: warn_only)
- **adequate cell counts** (gate: expected_frequency; severity: warning; on violation: warn_only)

## Effect size reported

- **risk difference** (Laupacis, Sackett & Roberts (1988), NEJM 318(26):1729; ARR = risk(group 1) - risk(group 2))

## Honest limitations

- The risk difference is an ABSOLUTE (percentage-point) measure; the same RD can correspond to very different relative changes depending on the baseline risk, so report the per-arm risks alongside it.
- The number needed to treat is the reciprocal of the risk difference; when the risk difference is near zero the NNT is enormous and unstable, and a confidence interval for the NNT that spans the no-difference point is non-finite (Laupacis et al. 1988; Altman 1998).
- Absolute risk and the risk difference can only be measured in cohort / randomized designs; case-control data require the odds ratio instead.
- Few outcome events make the Wald confidence interval imprecise and possibly out-of-range near 0 or 1; for very sparse data a Newcombe / Agresti-Caffo interval is preferable.
- A risk difference away from 0 is not evidence of causation unless the groups were formed by random assignment; observational cohorts can be confounded.
- If the 95% CI includes 0, this is absence of evidence for a difference, not proof that the groups carry equal risk; the interval shows which differences remain plausible.
- The sign of the risk difference and the meaning of the NNT depend on which row is 'group 1' and which outcome is the 'event'; the orientation must be stated.

## Primary sources

- Laupacis, A., Sackett, D. L., & Roberts, R. S. (1988). An assessment of clinically useful measures of the consequences of treatment. New England Journal of Medicine, 318(26), 1728-1733. https://doi.org/10.1056/NEJM198806303182605
- Altman, D. G. (1991). Practical Statistics for Medical Research. Chapman & Hall, Ch. 10 (difference between two proportions).
- Newcombe, R. G. (1998). Interval estimation for the difference between independent proportions: comparison of eleven methods. Statistics in Medicine, 17(8), 873-890. https://doi.org/10.1002/(SICI)1097-0258(19980430)17:8<873::AID-SIM779>3.0.CO;2-I
- Altman, D. G. (1998). Confidence intervals for the number needed to treat. BMJ, 317(7168), 1309-1312. https://doi.org/10.1136/bmj.317.7168.1309
- Rothman, K. J., Greenland, S., & Lash, T. L. (2008). Modern Epidemiology (3rd ed.). Lippincott Williams & Wilkins, Ch. 4 & 8.

## How to cite this

To cite this Clarus method page (the page itself — for the method's own primary sources, see above):

**Plain text**

Clarus, "Absolute risk difference / NNT, 2x2", version 1.0.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/risk_difference.md

**APA**

Clarus. (2026). Absolute risk difference / NNT, 2x2 (Version 1.0.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/risk_difference.md

**BibTeX**

```bibtex
@misc{clarus-risk-difference,
  author       = {Clarus},
  title        = {Absolute risk difference / NNT, 2x2},
  howpublished = {Clarus method library},
  version      = {1.0.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/risk_difference.md}
}
```

_No DOI is minted for Clarus method pages yet; this citation uses the canonical URL, version and date. Cite the primary sources above for the method's scientific provenance._

---

METHOD SM.REL.RSK.2X2.ARD · VERSION 1.0.0 · UPDATED 2026-06-21 · SOURCE Clarus method library