Relative attributal risk
Relative Attributable Risk (RAR) is an epidemiological measure that quantifies the proportion of disease risk in an exposed group that is attributable to the exposure itself. It is also called the attributable risk percent (AR%) or attributable fraction among the exposed.
Formula:
RAR = (Risk_exposed - Risk_unexposed) / Risk_exposed × 100%
Or equivalently:
RAR = (RR - 1) / RR × 100%
Where RR = Relative Risk.
Interpretation: If RR = 4, then RAR = (4-1)/4 = 75% - meaning 75% of the disease in exposed individuals is due to the exposure, assuming causality.
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Here is a complete explanation of Relative Attributable Risk (also called Attributable Risk %, Attributable Fraction, or Attributable Risk Percent):
Relative Attributable Risk (RAR)
Also called: Attributable Risk (AR%), Attributable Fraction (AF), Attributable Proportion
Definition
Relative Attributable Risk expresses what fraction (or percent) of the disease in the exposed group is due to the exposure itself - i.e., the proportion of disease that would be eliminated if the exposure were removed.
It is derived from the Relative Risk (RR) and answers the question: "Of all the cases occurring in exposed people, what percentage would not have occurred without the exposure?"
Formula
From incidence rates:
AR% = [(Ie - Iu) / Ie] × 100
Where:
- Ie = Incidence rate in the exposed group
- Iu = Incidence rate in the unexposed group
From Relative Risk directly:
AR% = [(RR - 1) / RR] × 100
Worked Example (from Park's Textbook)
Using lung cancer and smoking data:
- Lung cancer rate in smokers: 10 per 1,000
- Lung cancer rate in non-smokers: 1 per 1,000
- RR = 10/1 = 10
AR% = (10 - 1) / 10 × 100 = 90%
Interpretation: 90% of lung cancers in smokers are attributable to smoking. If smoking were eliminated, 90% of lung cancer in smokers could potentially be prevented.
How RR Value Determines AR%
| RR | AR% |
|---|---|
| 1 | 0% (no attributable risk) |
| 2 | 50% |
| 4 | 75% |
| 5 | 80% |
| 10 | 90% |
| 20 | 95% |
As RR increases, AR% approaches 100%.
Relative Risk vs. Attributable Risk - Key Distinction
| Feature | Relative Risk | Attributable Risk % |
|---|---|---|
| Purpose | Measures strength of causal association | Measures public health impact of exposure |
| Use | Aetiological enquiry | Planning prevention programs |
| Limitation | Doesn't tell you how much disease is preventable | Assumes causality |
A classic example from Park's Textbook (Table 20): oral contraceptive use has an equal RR of 2.8 for cardiovascular complications in women aged 30-39 and 40-44. Yet the AR is 3.5 vs. 20.0 per 100,000 respectively - showing the older age group bears a far greater preventable burden. This is why oral contraceptives are not recommended beyond age 35.
Population Attributable Risk (PAR%) - Related Concept
A separate but related measure - the fraction of disease in the entire population attributable to the exposure:
PAR% = [(Ipop - Iu) / Ipop] × 100
Or using Levin's formula:
PAR% = [Px(RR - 1)] / [1 + Px(RR - 1)] × 100
Where Px = prevalence of exposure in the population.
PAR% is useful for public health planning because it accounts for how common the exposure is in the population, not just how strong the association is.
Important Caveats
- AR% is a statistical measure, not proof of causation.
- It assumes the exposure-disease relationship is causal when used for prevention estimates.
- AR% is only valid in prospective (cohort) studies using true incidence rates; in case-control studies, the odds ratio is used as a proxy for RR.
- A high RR does not automatically mean a high AR% in the population - if the exposure is rare, the population impact may still be small.
- Park's Textbook of Preventive and Social Medicine, pp. 90-91
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