Core concept
- Case-control studies sample on outcome, so true incidence/risk cannot be calculated -- odds ratio (OR) is the only valid measure of association
- 2x2 table: rows = exposure (yes/no), columns = outcome (case/control)
```
Cases Controls
Exposed a b
Unexposed c d
```
- OR = (a x d) / (b x c) -- the cross-product ratio -- not a/(a+b) vs c/(c+d) (that would need incidence, which case-control data cannot give)
Key detail
- OR = 1 -> no association; OR >1 -> exposure associated with increased odds of the outcome; OR <1 -> associated with decreased odds
- She will be given a table and asked to compute it -- state the formula, plug in a/b/c/d exactly as labelled in the question, do not assume which cell is "a"
- OR approximates relative risk (RR) only when the outcome is rare (<~10%) -- this is why case-control studies are specifically used for rare diseases, where the approximation holds; for common outcomes OR overstates the RR
Clinical relevance
- Trap: interpreting an OR as if it were a relative risk when the outcome is common -- state "odds", not "risk", when describing a case-control finding
- Always check which group is the reference (unexposed/control) row before computing -- swapping rows inverts the OR (gives its reciprocal)
- Confidence interval crossing 1 -> not statistically significant, regardless of how far the point estimate itself sits from 1
Correlations
- Cohort studies calculate relative risk directly (incidence in exposed / incidence in unexposed) -- the design, not preference, dictates which statistic is valid (see study design note)
- Logistic regression output is reported as adjusted OR -- same interpretation principles apply, adjusted for confounders
- Converting an OR to an estimated absolute risk requires a known baseline/control-group risk (see separate note on OR-to-risk conversion)
4 of 4 sections written · drafted 2026-09-13