Relative and attributable risk PSM
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Relative Risk and Attributable Risk - PSM (Park's Textbook)
Estimation of Risk in Cohort Studies
After calculating incidence rates in exposed and non-exposed groups, risk is expressed using two indices:
- Relative Risk (RR)
- Attributable Risk (AR)
The classic example used is smoking and lung cancer (hypothetical data):
- Incidence among smokers = 10 per 1,000
- Incidence among non-smokers = 1 per 1,000
1. Relative Risk (RR)
Definition: The ratio of incidence of disease among exposed to incidence among non-exposed. Also called "risk ratio."
$$RR = \frac{\text{Incidence among exposed}}{\text{Incidence among non-exposed}}$$
Example:
$$RR = \frac{10}{1} = 10$$
Smokers are 10 times more likely to develop lung cancer than non-smokers.
Interpretation of RR:
| RR Value | Meaning |
|---|---|
| RR = 1 | No association |
| RR > 1 | Positive association (exposure increases risk) |
| RR = 2 | Incidence 2x higher in exposed; 100% increase in risk |
| RR = 0.25 | 75% reduction in incidence (protective exposure) |
| RR < 1 | Negative/protective association |
Key use: RR is the best index for aetiological enquiries - the larger the RR, the stronger the association between cause and effect.
The 95% confidence interval of RR is important - it indicates the range of likely and maximum levels of risk.
2. Attributable Risk (AR)
Definition: The difference in incidence rates between exposed and non-exposed groups. Also called "risk difference."
$$AR% = \frac{\text{Incidence (exposed)} - \text{Incidence (non-exposed)}}{\text{Incidence (exposed)}} \times 100$$
Example:
$$AR = \frac{10 - 1}{10} \times 100 = 90%$$
This means 90% of lung cancer among smokers is attributable to smoking - this is the amount of disease that could be eliminated if the factor were controlled.
Key use: AR indicates the public health importance of an exposure - how much disease could be prevented by eliminating the factor.
3. Population Attributable Risk (PAR)
Definition: Incidence in the total population minus incidence in the unexposed group.
$$PAR = \frac{\text{Incidence (total population)} - \text{Incidence (non-exposed)}}{\text{Incidence (total population)}} \times 100$$
Example (UK physicians study - Table 19):
| Group | Deaths per 100,000 person-years |
|---|---|
| Heavy smokers (a) | 224 |
| Non-smokers (b) | 10 |
| Total population (c) | 74 |
| Individual RR | a/b = 224/10 = 22.4 |
| Population AR | (c-b)/c = 86% |
So 86% of lung cancer deaths in the population could be prevented by eliminating smoking.
4. Relative Risk vs. Attributable Risk - The Key Distinction
| Feature | Relative Risk | Attributable Risk |
|---|---|---|
| Type | Ratio | Difference |
| Best for | Identifying aetiology / causal strength | Measuring public health impact |
| Reflects background risk? | No | Yes |
| Used for | Research/causation | Prevention planning |
Classic illustrative examples:
Example 1 - Oral Contraceptives & Cardiovascular Complications (Table 20):
| Age group | RR | AR (per 100,000 patient-years) |
|---|---|---|
| 30-39 years | 2.8 | 3.5 |
| 40-44 years | 2.8 | 20.0 |
- The RR is the same (2.8) across both age groups
- But the AR is 5 times higher in older women (20.0 vs 3.5)
- This is why OCs are not recommended for women ≥35 years - the absolute burden of risk is much higher even though the relative increase is the same
Example 2 - Smoking and disease:
| Disease | RR | AR% |
|---|---|---|
| Lung cancer | High | 92% |
| CHD | Moderate | 13.3% |
- Smoking causes 92% of lung cancers (both RR and AR are high - strong causal role)
- For CHD, even though RR and AR are not very high, CHD is so common that the population-level burden from smoking and CHD is actually greater in absolute numbers
Summary Mnemonics
- RR = Ratio - used for Research (aetiology, causation)
- AR = Absolute difference - used for Action (prevention programmes, public health impact)
- When RR is same but AR differs across groups → background risk drives the difference → the group with higher background risk has higher AR
Source: Park's Textbook of Preventive and Social Medicine, pp. 90-91
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