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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