Signature
P_0 = P / (1 + e * (PR - 1)); P_1 = PR * P_0; n_1 = N * e * P_1
| Inputs | Definition | Unit |
|---|---|---|
P | Proportion of the whole target population that has the condition | proportion |
e | Proportion of the target population that has the exposure | proportion |
PR | Prevalence ratio of the exposed to the unexposed group, taken from a published or survey source | ratio |
N | Number of people in the target population, for example the adults in an area | people |
P_0 | Prevalence of the condition among unexposed people in the target population | proportion |
|---|---|---|
P_1 | Prevalence of the condition among exposed people in the target population | proportion |
n_1 | Number of exposed people in the target population who have the condition | people |
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
Subgroup prevalences and exposed cases in Excel
With named cells OverallPrev, ExposedShare, PrevRatio and Adults, the three formulas return the unexposed prevalence, the exposed prevalence and the number of exposed people with the condition.
=OverallPrev/(1+ExposedShare*(PrevRatio-1)); =PrevRatio*OverallPrev/(1+ExposedShare*(PrevRatio-1)); =Adults*ExposedShare*PrevRatio*OverallPrev/(1+ExposedShare*(PrevRatio-1))
Assumptions
Prevalence ratio transportable to the target population
The PR measured in the source population is assumed to hold in the target population. Where age, deprivation or case-finding differ, the transported ratio belongs in the sensitivity analysis.
Overall prevalence and exposed share from one population and period
P and e describe the same population at the same time and use the case definition behind the PR, so the recovered subgroup prevalences reproduce the overall prevalence when recombined.
Worked examples
Subgroup prevalences in the article's neighbouring area
An area of 200,000 adults has an overall prevalence of 21.75% and 45% exposed. With the survey PR of 2.00 the unexposed prevalence is 0.15 and the exposed prevalence 0.30, so 27,000 exposed adults have the condition, 62% of the area's 43,500 prevalent cases.
P = 0.2175; e = 0.45; PR = 2.00; N = 200000; P_0 = 0.15; P_1 = 0.30; n_1 = 27000
Subgroup prevalences when the whole population is exposed
When everyone is exposed the overall prevalence is the exposed prevalence, so an overall prevalence of 0.30 with a PR of 2.00 returns 0.30 for the exposed and 0.15 for the unexposed, and all 60,000 prevalent cases are exposed.
P = 0.30; e = 1; PR = 2.00; N = 200000; P_0 = 0.15; P_1 = 0.30; n_1 = 60000
Subgroup prevalences when no one is exposed
When no one is exposed the overall prevalence is the unexposed prevalence and the count of exposed cases is zero, a limiting case that checks the implementation.
P = 0.15; e = 0; PR = 2.00; N = 200000; P_0 = 0.15; P_1 = 0.30; n_1 = 0
Common errors
Multiplying the overall prevalence by the prevalence ratio
Treating the overall prevalence as the unexposed baseline overstates the exposed prevalence. In the article's neighbouring area it gives 0.435 instead of 0.30 and an illustrative 39,150 eligible exposed cases instead of 27,000.
Sources
ISPOR good practice report on eligible population size in budget impact
Sullivan SD, Mauskopf JA, Augustovski F, Jaime Caro J, Lee KM, Minchin M, et al. Budget impact analysis-principles of good practice: report of the ISPOR 2012 Budget Impact Analysis Good Practice II Task Force. Value in Health. 2014;17(1):5-14. Abstract: estimating the size of the eligible population is a key element, using data that reflect the decision maker's population.
Canonical Identity
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