Relative attributal risk
Reading File
Searching the Web
relative attributable risk epidemiology formula interpretation
Finding Sources
Reading File
Reading File
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
This is a shared conversation. Sign in to Orris to start your own chat.