---
title: "Relative risk (risk ratio), cohort 2x2"
method_id: SM.REL.RSK.2X2.RR
family: Relationship
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/relative_risk.md
source: Clarus method library
---

# Relative risk (risk ratio), cohort 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 ratio; RR; cumulative incidence ratio; rate ratio (2x2 cohort).

## Hypotheses

- **Null (H0):** RR = 1 (the risk of {outcome} is the same in the exposed and unexposed groups).
- **Alternative (H1):** RR != 1 (the risk of {outcome} differs between the exposed and unexposed groups).

## When to use it

Use this method when your goal is to:
- quantify outcome risk ratio between exposed and unexposed
- estimate relative risk in a cohort
- report effect of a binary exposure on a binary outcome in prospective data

## Data it expects

- **dependent:** 1 binary outcome (event / no event), counted prospectively
- **independent:** 1 binary exposure (exposed / unexposed) — the two rows of a 2x2 cohort table
- **pairing:** independent (each subject contributes to exactly one cell); cohort/prospective design with known denominators in each exposure arm

## Assumptions Clarus checks

- **cohort design** (severity: critical; on violation: reroute)
- **independence of observations** (severity: critical; on violation: warn_only)
- **adequate cell counts** (gate: expected_frequency; severity: warning; on violation: correct)

## Effect size reported

- **relative risk** (Rothman, Greenland & Lash (2008), Ch. 4; RR = (a/(a+b)) / (c/(c+d)))

## Honest limitations

- Relative risk is only valid for cohort (prospective) data where genuine risks can be measured; in case-control studies use the odds ratio instead.
- A large relative risk on a very low baseline risk can still affect few people in absolute terms — always read the risk difference alongside the ratio.
- Few outcome events make the estimate unstable and the confidence interval wide; precision, not just the point estimate, must be reported.
- A relative risk away from 1 is not evidence of causation unless exposure was randomly assigned; observational cohorts can be confounded.
- If a zero cell forced a continuity correction, the relative risk and its interval are approximate.
- If the 95% CI includes 1, this is absence of evidence for a risk difference, not proof that exposure carries no risk; the interval shows which effects remain plausible.
- Relative risk depends on which outcome level is called the 'event' and which group is 'exposed'; reversing them gives a different (reciprocal or complementary) number, so the orientation must be stated.

## Primary sources

- Rothman, K. J., Greenland, S., & Lash, T. L. (2008). Modern Epidemiology (3rd ed.). Lippincott Williams & Wilkins, Ch. 4 & 8.
- Katz, D., Baptista, J., Azen, S. P., & Pike, M. C. (1978). Obtaining confidence intervals for the risk ratio in cohort studies. Biometrics, 34(3), 469-474. https://doi.org/10.2307/2530610
- Agresti, A. (2013). Categorical Data Analysis (3rd ed.). Wiley, Ch. 2-3.
- Haldane, J. B. S. (1956). The estimation and significance of the logarithm of a ratio of frequencies. Annals of Human Genetics, 20(4), 309-311. https://doi.org/10.1111/j.1469-1809.1955.tb01285.x
- Szklo, M., & Nieto, F. J. (2019). Epidemiology: Beyond the Basics (4th ed.). Jones & Bartlett.

## 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, "Relative risk (risk ratio), cohort 2x2", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/relative_risk.md

**APA**

Clarus. (2026). Relative risk (risk ratio), cohort 2x2 (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/relative_risk.md

**BibTeX**

```bibtex
@misc{clarus-relative-risk,
  author       = {Clarus},
  title        = {Relative risk (risk ratio), cohort 2x2},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/relative_risk.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.RR · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library