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Core concept1 exam ›

```

odds = p / (1 - p) p = odds / (1 + odds)

new odds = baseline odds x OR

```

Three steps: risk -> odds, multiply by OR, odds -> risk
OR is not a risk ratio. They converge only when the outcome is rare (<~10%)
- Common outcome -> OR exaggerates the RR, away from 1, in both directions

Worked

Baseline prevalence 30%, OR 2.0
- odds = 0.30/0.70 = 0.429
- new odds = 0.429 x 2 = 0.857
- new p = 0.857/1.857 = ~46%
- RR here is 46/30 = 1.5, not 2.0
Baseline 2%, OR 2.0
- odds 0.0204 -> 0.0408 -> p = 3.9%; RR = 1.96 ~ OR. Rare-disease approximation holds

Direct formula

```

RR = OR / [ (1 - p0) + (p0 x OR) ] p0 = baseline risk

```

Which measure comes from which design

Measure	Design
Odds ratio	Case-control (risk is not estimable), logistic regression, meta-analysis
Risk ratio / relative risk	Cohort, RCT
Hazard ratio	Time-to-event (Cox) - an instantaneous rate ratio, assumes proportional hazards
Rate ratio	Poisson, person-time denominators

ARR = p_control - p_treated; NNT = 1/ARR; NNH = 1/ARI
NNT is meaningless without the time horizon and the baseline risk it was derived from

Genetic and risk-factor associations are almost always reported as ORs - converting to absolute risk is what the patient needs
- An OR of 3 on a 0.1% background risk is still a 0.3% risk
Do not quote an OR as "3 times more likely" when the outcome is common - it overstates the effect
Case-control studies of common outcomes (in-hospital mortality, delirium, readmission) systematically inflate apparent effect
Applying a trial's relative effect to your patient's own baseline risk is the correct way to individualise benefit - relative effects transport across risk strata, absolute effects do not

Hierarchy of evidence; study design and measure of effect
Positive predictive value and pre-test probability (odds/LR arithmetic is identical)
P-value and confidence interval interpretation
Interpreting forest plots (ratio scales are log-transformed)

4 of 4 sections written · drafted 2026-09-04