Signature
PYLL_a = N_a * max(C - m_a, 0)
| Inputs | Definition | Unit |
|---|---|---|
N_a | Number of deaths in age group a | deaths |
C | Conventional cut-off age, usually 65 in CDC reporting; 70 and 85 are also used | years of age |
m_a | Midpoint of age group a, for example 42.5 for ages 40 to 44 and 3 for ages 1 to 4 | years of age |
PYLL_a | Potential years of life lost before the cut-off from deaths in age group a | years |
|---|
Function
Years of life lost from deaths weighted by a loss function of age at death
Converts deaths from a cause into years of life lost by multiplying the deaths at each age by the years that a loss function assigns to a death at that age, then summing over ages. In the Global Burden of Disease (GBD) study from 2010 onwards and in WHO's Global Health Estimates (GHE) the loss function is the remaining life expectancy at the age of death in a normative standard life table (HE-FM-YLL-001). Potential years of life lost replace it with the years from the age at death to a fixed cut-off age (HE-FM-YLL-002), and the original DALY discounted the standard years (HE-FM-YLL-003). YLLs added to years lived with disability (HE-FN-YLD-001, HE-FM-DWT-001) give DALYs. Notation follows the Years of Life Lost article.
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Implementations
Excel
Potential years of life lost for one age group from named cells
With the deaths in Deaths, the cut-off age in CutOff and the midpoint of the age group in AgeMid, the formula returns the potential years of life lost for the group, held in PYLLGroup.
=Deaths*MAX(CutOff-AgeMid,0)
Assumptions
All deaths in an age group placed at its midpoint
Each death counts as if it occurred at the midpoint of its age group, as in the CDC method, so the result depends on the age grouping of the death data.
No potential years counted at or above the cut-off age
Deaths at or above the cut-off count zero whatever the remaining life expectancy at that age, so the total reflects early deaths only.
Worked examples
Twenty child deaths before a cut-off age of 70
Twenty deaths at ages 1 to 4, placed at a midpoint of 3, give 1,340 potential years of life lost before age 70, as in the article.
N_a = 20; C = 70; m_a = 3; PYLL_a = 1340
Fifty deaths at ages 40 to 44 before a cut-off age of 70
Fifty deaths at ages 40 to 44, placed at 42.5, give 1,375 potential years of life lost before age 70, as in the article.
N_a = 50; C = 70; m_a = 42.5; PYLL_a = 1375
One hundred deaths at ages 75 to 79 above a cut-off age of 70
Deaths placed at 77.5 are above the cut-off and count nothing, so the article's three age groups give 2,715 potential years of life lost against 5,169.1 YLLs under the GBD 2010 standard.
N_a = 100; C = 70; m_a = 77.5; PYLL_a = 0
One hundred deaths at ages 75 to 79 before a cut-off age of 85
With the cut-off of 85 that the CDC's 1992 report also used, the same 100 deaths count 750 potential years of life lost (computed here for illustration).
N_a = 100; C = 85; m_a = 77.5; PYLL_a = 750
Common errors
Comparing potential years of life lost computed with different cut-off ages
The same 100 deaths at ages 75 to 79 count nothing with a cut-off of 70 and 750 years with 85, so totals and rankings change with the cut-off. WHO records that GBD 1990 chose not to use an arbitrary cut-off such as 70 years.
Using the lower bound of the age group in place of its midpoint
Placing the 20 deaths at ages 1 to 4 at age 1 in place of 3 gives 1,380 potential years before 70 in place of 1,340 (computed here for illustration), and the bias grows with wider age groups.
Reading potential years of life lost as years of life lost
In the article's example potential years of life lost before 70 total 2,715 against 5,169.1 YLLs under GBD 2010, because the cut-off drops the older deaths and no life table is used. The two measures answer different questions, and only YLLs enter the DALY.
Sources
CDC method for years of potential life lost before a cut-off age
Centers for Disease Control. Years of potential life lost before ages 65 and 85: United States, 1989-1990. Morbidity and Mortality Weekly Report. 1992;41(18):313-315 (full text read). The measure reflects deaths before a conventional cut-off, usually 65 years, and is calculated by multiplying the deaths in an age category by the difference between the cut-off age and the mid-year of the age category, then adding the products.
WHO on the DALY as an extension of potential years of life lost
World Health Organization. WHO methods and data sources for global burden of disease estimates 2000-2021. Global Health Estimates Technical Paper WHO/DDI/DNA/GHE/2024.3. Geneva: WHO; 2024 (full text read). Section 2: the DALY extends the Potential Years of Life Lost measure to include lost good health, and the GBD 1990 study chose not to use an arbitrary age cut-off such as 70 years for the loss function used for YLLs.
Canonical Identity
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