When a study reports that an exposure "doubles the risk", it has measured an association — and it has done so with one of three ratios. Knowing which ratio belongs to which design, and how to read it, is a reliable source of AKT marks.
The 2×2 table — where it all starts
Almost every measure of association is built from a four-cell table cross-classifying exposure against outcome. Label the cells a, b, c, d and the rest is arithmetic.
Relative risk — for cohort studies and RCTs
Relative risk (RR), also called the risk ratio, divides the risk in the exposed by the risk in the unexposed. Because it uses true risks, it can only be calculated where you can measure incidence — namely cohort studies and randomised controlled trials, which follow defined groups forward and observe how many develop the outcome.
Odds ratio — for case-control studies
A case-control study starts from the outcome — it recruits people who already have the disease and a comparison group who do not, then looks back at exposure. That design samples on outcome, so it cannot measure incidence and cannot give a true risk. Instead it uses the odds ratio (OR), the cross-product of the table.
Hazard ratio — for survival analysis
A hazard ratio (HR) compares the rate at which events occur over time between two groups, derived from survival (time-to-event) methods such as Cox regression. It is the natural measure when when the event happens matters as much as whether it happens — for example time to relapse or to death.
Reading any of the three
All three share one interpretation scale:
Worked example — RR and OR from one table
A cohort of 400 people is followed; 200 are exposed to a risk factor and 200 are not. Among the exposed, 40 develop the disease; among the unexposed, 20 do.
| Outcome + | Outcome − | |
|---|---|---|
| Exposed | a = 40 | b = 160 |
| Unexposed | c = 20 | d = 180 |
The exposure roughly doubles the risk. Notice the OR (2.25) sits a little above the RR (2.0): with a fairly common outcome (10–20%), the odds ratio exaggerates the relative risk. Had the outcome been rare — say 1% in each group — the two would have been almost identical.
Try it yourself
Risk measures (RR / OR / ARR)
Use RR for cohort studies and RCTs (you can measure true incidence). Use the OR for case-control studies (you can’t). The OR exaggerates the RR as the outcome becomes common.
High-yield summary
- RR = risk in exposed ÷ risk in unexposed — cohort studies and RCTs
- OR = (a × d) ÷ (b × c) — case-control studies
- HR = ratio of event rates over time — survival / Cox analysis
- 1 = no effect; >1 = increased risk/harm; <1 = protective
- OR ≈ RR when the outcome is rare; OR exaggerates RR for common outcomes
- Match the measure to the design: case-control → OR, cohort/RCT → RR, survival → HR
Check your understanding
Check your understanding
3 questionsQ1.A team recruits 150 patients with bladder cancer and 150 matched controls, then compares their past occupational exposure to a dye. Which measure of association is appropriate?
Q2.In a cohort study, the risk of the outcome is 15% in the exposed group and 10% in the unexposed group. What is the relative risk?
Q3.A case-control study of a common outcome reports an odds ratio of 3.0. Compared with the true relative risk for that outcome, the odds ratio is most likely to be: