Signature
PAF = e * (PR - 1) / (1 + e * (PR - 1))
| Inputs | Definition | Unit |
|---|---|---|
e | Proportion of the population whose costs are attributed that has the exposure | proportion |
PR | Crude prevalence ratio of the exposed to the unexposed group | ratio |
PAF | Share of prevalent cases in the population, and of their annual costs, attributed to the exposure | proportion |
|---|
Function
Prevalence ratio function for cross-sectional comparisons and attributable cost inputs
Maps the prevalence of a condition among exposed people and among unexposed people, measured at the same time, to their ratio, and carries that ratio into the prevalence odds ratio, a population attributable fraction of prevalent cases and subgroup prevalences for cost-of-illness and budget impact work. Applying the attributable fraction to aggregate annual costs is the top-down attributable burden HE-FM-COI-002, and the attack rate ratio HE-FM-ATR-003 has the same ratio form for new cases in an outbreak. Survey-weighted prevalence and the link between prevalence, incidence and duration are HE-FM-XSD-001 and HE-FM-XSD-002. Notation follows the Prevalence Ratio article.
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Implementations
Excel
Attributable fraction from a prevalence ratio in Excel
With the exposed share in a cell named ExposedShare and the PR in PrevRatio, Excel returns the attributable fraction of prevalent cases.
=ExposedShare*(PrevRatio-1)/(1+ExposedShare*(PrevRatio-1))
Assumptions
Unconfounded prevalence ratio in the attributable fraction
The PR is read as the causal effect of the exposure on prevalence. Jo notes that the formula holds only where other factors do not affect the association, and that uncontrolled confounding usually biases the ratio, and so the attributable fraction, upwards.
Exposure share and prevalence ratio from the costed population
The exposed share e describes the population whose costs are attributed, and the PR is assumed to hold in that population. The fraction applies to the annual costs of prevalent cases over the same period, in line with a prevalence-based cost-of-illness study.
Worked examples
Attributable fraction for a local population with 40% exposed
In the article's local health economy 40% of 500,000 adults are exposed and the PR is 2.00, so the PAF is about 0.2857. Of 105,000 prevalent cases, 30,000 are attributable, the same as the excess among the exposed, and at an illustrative GBP 1,200 per case the attributable annual cost through HE-FM-COI-002 is GBP 36.0 million.
e = 0.40; PR = 2.00; PAF = 0.2857
Attributable fraction when the whole population is exposed
When everyone is exposed, the PAF reduces to (PR minus 1) / PR, so a PR of 2.00 attributes half of prevalent cases to the exposure, a limiting case that checks the implementation.
e = 1; PR = 2.00; PAF = 0.5000
Attributable fraction at a prevalence ratio of 1
A PR of 1 attributes no prevalent cases to the exposure whatever the exposed share.
e = 0.40; PR = 1; PAF = 0
Common errors
Entering the prevalence odds ratio in a prevalence attributable fraction
With 40% exposed, the POR of 2.4286 (214,200 / 88,200, used unrounded) gives a PAF of about 0.3636 instead of 0.2857. Applied to the article's 105,000 prevalent cases at GBP 1,200 each, attributable cases rise from 30,000 to about 38,182 and the annual cost from GBP 36.0 million to GBP 45.8 million, 27% more.
Treating a prevalence-based attributable cost as avoidable
Removing the exposure would lower prevalence only as existing cases resolve or die, and only to the extent that the association is causal. The attributable annual cost is therefore not the saving expected in the year after the exposure is removed.
Sources
Jo on the attributable-risk formula for top-down cost-of-illness estimates
Jo C. Cost-of-illness studies: concepts, scopes, and methods. Clinical and Molecular Hepatology. 2014;20(4):327-337. Section on top-down, bottom-up and econometric approaches: the PAF from the prevalence of condition A and the unadjusted relative risk of condition B, its use with aggregate costs, the confounding caveat, and the prevalence-based approach over a specific period, usually a year.
Canonical Identity
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