Chapter analogy
Diabetic vs non-diabetic CKD · CV events · 40/100 vs 20/100
Study details
Group 1 (exposed)
Group 2 (reference)
OR → RR converter (Zhang-Yu formula)
If a paper reports only an OR, use this to estimate the approximate RR — as long as you know the event rate in the reference group.
RR = OR ÷ ((1 − p₀) + (p₀ × OR))
p₀ = event rate in the reference (unexposed/control) group
The 10% rule — how OR diverges from RR as outcome rate increases
Assuming a fixed true RR = 2.0 and varying outcome rates in the reference group.
| Outcome rate | True RR | OR (same data) | OR overstates RR by |
|---|---|---|---|
| 5% | 2.0 | 2.11 | +5% ✓ |
| 10% | 2.0 | 2.25 | +13% ⚠️ |
| 20% | 2.0 | 2.56 | +28% ⚠️ |
| 30% | 2.0 | 2.91 | +46% ⚠️ |
| 40% | 2.0 | 3.29 | +65% ⚠️ |
| 50% | 2.0 | 4.00 | +100% ⚠️ |
Before you trust an adjusted OR — read the footnote
Every adjusted OR comes with a footnote that specifies what was adjusted for. That footnote is the most important part of the result. An OR of 1.4 adjusted for age, sex, BP, HbA1c, BMI, and eGFR is a different number from an OR of 1.4 adjusted for age and sex alone. Both are labelled "adjusted OR." Neither label tells you how complete the adjustment is.
Check the baseline characteristics table. Ask: what important predictor of this outcome is not in this table? Whatever is missing from the baseline table is almost certainly missing from the adjustment.