Difference between revisions of "Attributable risk"
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[[Category:Health impact]] | [[Category:Health impact]] | ||
{{method|moderator=Jouni}} | {{method|moderator=Jouni}} | ||
| − | '''Population attributable fraction (PAF) of an exposure agent is the fraction of disease that would disappear if the exposure to that agent would disappear. | + | '''Population attributable fraction (PAF)''' of an exposure agent is the fraction of disease that would disappear if the exposure to that agent would disappear. |
==Question== | ==Question== | ||
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==Rationale== | ==Rationale== | ||
| − | + | === WHO approach === | |
| + | |||
<ref>WHO: Health statistics and health information systems. [http://www.who.int/healthinfo/global_burden_disease/metrics_paf/en/index.html]. Accessed 16 Nov 2013.</ref> | <ref>WHO: Health statistics and health information systems. [http://www.who.int/healthinfo/global_burden_disease/metrics_paf/en/index.html]. Accessed 16 Nov 2013.</ref> | ||
PAF is | PAF is | ||
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This equation is used in e.g. [[Health impact assessment]]. | This equation is used in e.g. [[Health impact assessment]]. | ||
| + | |||
| + | === Rothman approach === | ||
| + | |||
| + | Modern Epidemiology | ||
| + | <ref>Kenneth J. Rothman, Sander Greenland, Timothy L. Lash: Modern Epidemiology. Lippincott Williams & Wilkins, 2008. 758 pages.</ref> | ||
| + | is the authoritative source of epidemiology. They first define ''attributable fraction AF'' for a cohort of people (pages 295-297). It is the fraction of cases among the exposed that would not have occurred if the exposure would not have taken place: | ||
| + | |||
| + | <math>AF = \frac{RR - 1}{RR},</math> | ||
| + | |||
| + | where RR is the causal risk ratio. | ||
| + | |||
| + | The ''population attributable fraction AF<sub>p</sub>'' is that fraction among the whole cohort: | ||
| + | |||
| + | <math>AF_p = \frac{N_1 (R_1 - R_0)}{N_1 R_1 + N_0 R_0} = \frac{N_1 (R_1 - R_0)/R_0}{N_1 R_1/R_0 + N_0 R_0/R_0} | ||
| + | |||
| + | = \frac{N_1 (RR - 1)}{N_1 RR + N_0}</math> | ||
| + | |||
| + | <math>= \frac{ \frac{N_1 (RR - 1)}{N_1 + N_0} }{ \frac{N_1 RR + N_0}{N_1 + N_0}} | ||
| + | |||
| + | = \frac{ p (RR - 1) }{ \frac{N_1 RR - N_1 + (N_1 + N_0)}{N_1 + N_0}} | ||
| + | |||
| + | = \frac{p (RR - 1)}{p RR - p + 1} = \frac{p (RR - 1)}{p (RR - 1) + 1},</math> | ||
| + | |||
| + | where | ||
| + | * N<sub>1</sub> and N<sub>0</sub> are the numbers of exposed and unexposed people, respectively, | ||
| + | * R<sub>1</sub> and R<sub>0</sub> are the risks of disease in the exposed and unexposed group, respectively, and RR = R<sub>1</sub> / R<sub>0</sub>, | ||
| + | * p is the fraction of exposed people among the whole cohort. | ||
| + | |||
| + | Note that there is a typo in the Modern Epidemiology book: the denominator should be p(RR-1)+1, not p(RR-1)-1. | ||
| + | |||
| + | Population attributable fraction can be calculated as a weighted average based on subgroup data: | ||
| + | |||
| + | <math>AF_p = \Sigma_i p_i AF_{pi},</math> | ||
| + | |||
| + | where | ||
| + | * p<sub>i</sub> is the proportion of '''cases''' falling in stratum (subgroup) i, | ||
| + | * AF<sub>pi</sub> is the population attributable fraction calculated for the subgroup. | ||
| + | |||
| + | Specifically, we can divide the cohort into subgroups based on exposure (in the simplest case exposed and unexposed), so we get | ||
| + | |||
| + | <math>AF_p = p_c \frac{1(RR - 1)}{1(RR - 1) + 1} + (1 - p_c) \frac{0(RR - 1)}{0(RR - 1) +1} | ||
| + | |||
| + | = p_c \frac{RR - 1}{RR},</math> | ||
| + | |||
| + | where p<sub>c</sub> is the proportion of cases in the exposed group among all cases; this is the same as exposure prevalence among cases. | ||
==References== | ==References== | ||
<references/> | <references/> | ||
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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.
Question
How to calculate population attributable fraction?
Answer
Rationale
WHO approach
[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). In the counterfactual situation nobody is exposed. 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}
Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): 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}
See also Attributable risk, although it is a stub.
This equation is used in e.g. Health impact assessment.
Rothman approach
Modern Epidemiology [2] is the authoritative source of epidemiology. They first define attributable fraction AF for a cohort of people (pages 295-297). It is the fraction of cases among the exposed that would not have occurred if the exposure would not have taken place:
Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): AF = \frac{RR - 1}{RR},
where RR is the causal risk ratio.
The population attributable fraction AFp is that fraction among the whole cohort:
Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): AF_p = \frac{N_1 (R_1 - R_0)}{N_1 R_1 + N_0 R_0} = \frac{N_1 (R_1 - R_0)/R_0}{N_1 R_1/R_0 + N_0 R_0/R_0} = \frac{N_1 (RR - 1)}{N_1 RR + N_0}
Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): = \frac{ \frac{N_1 (RR - 1)}{N_1 + N_0} }{ \frac{N_1 RR + N_0}{N_1 + N_0}} = \frac{ p (RR - 1) }{ \frac{N_1 RR - N_1 + (N_1 + N_0)}{N_1 + N_0}} = \frac{p (RR - 1)}{p RR - p + 1} = \frac{p (RR - 1)}{p (RR - 1) + 1},
where
- N1 and N0 are the numbers of exposed and unexposed people, respectively,
- R1 and R0 are the risks of disease in the exposed and unexposed group, respectively, and RR = R1 / R0,
- p is the fraction of exposed people among the whole cohort.
Note that there is a typo in the Modern Epidemiology book: the denominator should be p(RR-1)+1, not p(RR-1)-1.
Population attributable fraction can be calculated as a weighted average based on subgroup data:
Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): AF_p = \Sigma_i p_i AF_{pi},
where
- pi is the proportion of cases falling in stratum (subgroup) i,
- AFpi is the population attributable fraction calculated for the subgroup.
Specifically, we can divide the cohort into subgroups based on exposure (in the simplest case exposed and unexposed), so we get
Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): AF_p = p_c \frac{1(RR - 1)}{1(RR - 1) + 1} + (1 - p_c) \frac{0(RR - 1)}{0(RR - 1) +1} = p_c \frac{RR - 1}{RR},
where pc is the proportion of cases in the exposed group among all cases; this is the same as exposure prevalence among cases.
