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Attributable Risk and Population Attributable Risk (PAR) Measures

1. Core Knowledge:

These are a set of statistics that estimate the impact of a causal factor.


1. The Attributable Risk indicates the number of cases of a disease among exposed individuals that can be attributed to that exposure:

    Incidence(exposed) – Incidence(unexposed)        (This shows how much extra disease has been caused by this exposure)

1.1 This can also be expressed as a fraction of all exposed:

      [ Incidence(exposed) – Incidence(unexposed) ]  ÷   Incidence(exposed).

2. The Population Attributable Risk (or Population Attributable Fraction) indicates the number (or proportion) of cases that would not occur in a population if the factor were eliminated (e.g. how many lives would be saved if people no longer smoked?)  
(But be careful, for there are several synonyms and related concepts that can easily be confused with each other:  "Population attributable risk";  "population attributable risk proportion";   "etiologic fraction";  "excess fraction")
The attributable risk in a population depends on the prevalence of the risk factor and the strength of its association (relative risk) with the disease. The formula is 

      PAR = Pe (RRe-1)  /  [1 + Pe (RRe-1)],

where  Pe is the prevalence of the exposure (e.g., proportion who are overweight) and RRe is the relative risk of disease due to that exposure.

3. The Population Prevented Fraction refers to situations where exposure to a factor is protective. 
The prevented fraction is the proportion of the hypothetical total load of disease that has been prevented by exposure to the protective factor.  The formula is 

      Pe (1-RR)

4. The Attributable Number refers to the number of cases attributable to an exposure. The formula is 

       AN = Ne (Ie - Iu),

where Ne is the number exposed, Ieis the incidence among those exposed, and Iu is the incidence among those unexposed to that factor.

Link: Number Needed to Treat
    Further details:
B. Rockhill et al. Use and misuse of population attributable fractions"Am J Public Health 1998;38:15-19.