Attributable risk
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Population attributable fraction (PAF) of an exposure agent is the fraction of disease that would disappear if the exposure to that agent would disappear.
Contents
Question
How to calculate population attributable fraction?
Answer
Rationale
Based on WHO [1] PAF is
Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): PAF = \frac{\Sigma_{i=1}^n P_i RR_i - \Sigma_{i=1}^n P'_i RR_i}{\Sigma_{i=1}^n P_i RR_i}
where i is a certain exposure level, P is the fraction of population in that exposure level, RR is the relative risk at that exposure level, and P' is the fraction of population in a counterfactual ideal situation (where the exposure is typically lower).
Based on this, we can limit our examination to a situation where there are only two population groups, one exposed to background level (with relative risk 1) and the other exposed to a higher level (with relative risk RR). Thus, we get
Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): PAF = \frac{(P RR + (1-P)*1) - (0*RR + 1*1)}{P RR + (1-P)*1}<math> <math>PAF = \frac{P RR - P}{P RR + 1 - P}
Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): PAF = \frac{P(RR - 1)}{P(RR -1) + 1}
This equation is used in e.g. Health impact assessment.
