Signature
YLL_a = N_a * e_a
| Inputs | Definition | Unit |
|---|---|---|
N_a | Number of deaths from the cause in age group a in the reference year | deaths |
e_a | Remaining life expectancy for age group a in the standard life table, for example 83.63 years at ages 1 to 4 in the GBD 2010 standard | years per death |
YLL_a | Years of life lost from the cause's 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.
Computational function
Computational function: total years of life lost for a cause from deaths by age group and a named standard life table
Takes the deaths from one cause by age group and the name of a standard life table, looks up the standard remaining life expectancy for each age group in that table, and returns the cause's total YLLs and each age group's share of the total. The inputs differ from the formula's symbols: the deaths arrive as a set of age-group counts and the standard values are looked up rather than entered, so one set of deaths can be run under GBD 2010 and WHO GHE 2021 and the results compared.
Inputs and outputs:
deaths: Deaths from the cause in each of WHO's 20 age groups (neonatal, postneonatal, 1 to 4, five-year groups to 80 to 84, and 85 and over); required, zero or above. Unit: deaths.;standard: Name of the standard life table, for example GBD 2010 or WHO GHE 2021, whose column of Table 2.1 in WHO's 2024 methods paper supplies the values; required. Unit: none.;yll_total: Years of life lost from the cause. Unit: years.;share: Each age group's share of yll_total. Unit: proportion from 0 to 1.Assumption: Every death in an age group counts the tabulated value for that group, the standard applies to both sexes, and no discounting or age weighting is applied, as in HE-FM-YLL-001.
Worked example (Three age groups under the GBD 2010 standard): The article's illustrative 20 deaths at ages 1 to 4, 50 at ages 40 to 44 and 100 at ages 75 to 79 give 5,169.1 YLLs. The older deaths are 59 per cent of deaths but 24.9 per cent of YLLs.
deaths_1to4 = 20; deaths_40to44 = 50; deaths_75to79 = 100; e_1to4 = 83.63; e_40to44 = 44.23; e_75to79 = 12.85; yll_total = 5169.1; share_75to79 = 0.2486Worked example (Same deaths under the WHO GHE 2021 standard): With 89.74, 50.43 and 17.19 years the total is 6,035.3, 16.8 per cent higher, as in the article, and the share of the older deaths rises to 28.5 per cent (computed here for illustration).
deaths_1to4 = 20; deaths_40to44 = 50; deaths_75to79 = 100; e_1to4 = 89.74; e_40to44 = 50.43; e_75to79 = 17.19; yll_total = 6035.3; share_75to79 = 0.2848Excel:
=SUMPRODUCT(Deaths,INDEX(StdTable,0,MATCH(StdName,StdNames,0)))With deaths for the 20 age groups in a column named Deaths, the Table 2.1 values in a 20-row range named StdTable with one column per standard, the names of the standards in a header row named StdNames and the chosen name in StdName, the formula returns the total. Each group's YLLs divided by the total give the shares.R:
yll_cause <- function(deaths, std) { yll <- deaths * std[names(deaths)]; list(total = sum(yll), share = yll / sum(yll)) }Takes a named vector of deaths and a named vector holding one column of Table 2.1, for examplec(a1to4 = 83.63, a40to44 = 44.23, a75to79 = 12.85)for GBD 2010, and matches them by age group.Python:
def yll_cause(deaths, std): yll = {a: n * std[a] for a, n in deaths.items()}; total = sum(yll.values()); return total, {a: v / total for a, v in yll.items()}Takes dictionaries of deaths and standard values keyed by age group and returns the total and the shares.Test (WHO GHE 2021 total at least the GBD 2010 total): Every WHO GHE 2021 value in Table 2.1 exceeds the GBD 2010 value for the same age group, so for the same deaths the WHO total is the larger. Expected result: TRUE. Excel check:
=SUMPRODUCT(Deaths,INDEX(StdTable,0,MATCH("WHO GHE 2021",StdNames,0)))>=SUMPRODUCT(Deaths,INDEX(StdTable,0,MATCH("GBD 2010",StdNames,0)))Test (Mean years lost per death within the range of the standard): With the chosen standard's column in StdCol, the total divided by all deaths lies between the standard's lowest and highest values, 5.05 and 86.01 years for GBD 2010; the first example gives about 30.4 years per death. Expected result: TRUE. Excel check:
=AND(SUMPRODUCT(Deaths,StdCol)/SUM(Deaths)>=MIN(StdCol),SUMPRODUCT(Deaths,StdCol)/SUM(Deaths)<=MAX(StdCol))Common error (Matching deaths to the wrong age-group rows): The deaths and the standard column must be in the same age-group order. Shifting the 100 deaths at ages 75 to 79 one row down, to the 80 to 84 value of 9.34, cuts their YLLs from 1,285 to 934 under GBD 2010 (computed here for illustration).
Source: 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 (YLL formula with a standard loss function) and Table 2.1 (standard loss functions by age group for GBD 1990, GBD 2010 and WHO GHE).
yll_total = deaths_1to4 * e_1to4 + deaths_40to44 * e_40to44 + deaths_75to79 * e_75to79; share_75to79 = deaths_75to79 * e_75to79 / yll_total
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Implementations
Excel
Years of life lost for one age group from named cells
With the deaths in a cell named Deaths and the standard value for the age group in StdLE, the formula returns the YLLs for the group, held in YLLGroup.
=Deaths*StdLE
Assumptions
One normative standard for every population and both sexes
The years lost for a death depend only on the age at death, not on where the death happened or on local life expectancy. GBD from 2010 onwards and WHO use one standard for both sexes; the GBD 1990 standard had separate tables for males and females.
Standard value applied to every death in the age group
Each death in an age group counts the tabulated value for that group, so the result depends on the age grouping of the death data. WHO tabulates the standards for neonatal and postneonatal deaths, ages 1 to 4, five-year groups to 80 to 84, and 85 and over.
Years of life lost counted without discounting or age weighting
Each standard year counts in full, as in GBD from 2010 onwards and in WHO estimates since its 2012 consultations. The discounted form of the original DALY is HE-FM-YLL-003.
Worked examples
Twenty child deaths at ages 1 to 4 under the GBD 2010 standard
In the article's illustrative example 20 deaths at ages 1 to 4, at 83.63 standard years each, give 1,672.6 YLLs.
N_a = 20; e_a = 83.63; YLL_a = 1672.6
Fifty deaths at ages 40 to 44 under the GBD 2010 standard
In the same example 50 deaths at ages 40 to 44, at 44.23 standard years each, give 2,211.5 YLLs.
N_a = 50; e_a = 44.23; YLL_a = 2211.5
One hundred deaths at ages 75 to 79 under the GBD 2010 standard
The 100 deaths at ages 75 to 79, at 12.85 standard years each, give 1,285 YLLs. They are 59 per cent of the example's 170 deaths but 25 per cent of its 5,169.1 YLLs, as in the article.
N_a = 100; e_a = 12.85; YLL_a = 1285
One hundred deaths at ages 75 to 79 under the WHO GHE 2021 standard
Under the WHO GHE 2021 standard the same 100 deaths count 17.19 years each and give 1,719 YLLs, 33.8 per cent more than under GBD 2010, as in the article.
N_a = 100; e_a = 17.19; YLL_a = 1719
Common errors
Subtracting age at death from the standard life expectancy at birth
The standard value is the remaining life expectancy of a person who has already reached the age of death. In the GBD 2010 standard a death at ages 80 to 84 counts 9.34 years, whereas 86.0 years minus age would give between 2 and 6 years, and a death after age 86 would count nothing.
Comparing YLL totals computed with different standard life tables
The same 100 deaths at ages 75 to 79 give 1,285 YLLs under GBD 2010 and 1,719 under WHO GHE 2021, 33.8 per cent more, against 7.3 per cent more for the article's child deaths. A total should name its standard, and WHO states that its estimates for 2000 to 2021 are not directly comparable with its earlier DALY estimates.
Using local life expectancy in place of a standard life table without saying so
Larson's worked example takes the local age-specific life expectancy of the person who died. With local values a death at a given age counts less in a high-mortality country than in a low-mortality one, which the LSHTM teaching module published by the IUSSP calls inequitable, so a study of YLLs or DALYs averted should state which life expectancy it uses.
Sources
GBD 2021 calculation of years of life lost from deaths and standard life expectancy
GBD 2021 Diseases and Injuries Collaborators. Global incidence, prevalence, years lived with disability (YLDs), disability-adjusted life-years (DALYs), and healthy life expectancy (HALE) for 371 diseases and injuries in 204 countries and territories and 811 subnational locations, 1990-2021: a systematic analysis for the Global Burden of Disease Study 2021. The Lancet. 2024;403(10440):2133-2161 (full text read). Summary, Methods: YLLs were calculated by multiplying cause, age, sex, location and year specific deaths by the standard life expectancy at the age that death occurred; DALYs are the sum of YLDs and YLLs.
WHO formula and standard loss functions for 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: YLL(c,s,a,t) = N(c,s,a,t) x L(s,a), where L(s,a) is a standard loss function specifying years of life lost for a death at age a. Section 2.2 and Table 2.1: the GBD 2010 standard, with life expectancy at birth of 86.0 years, and the WHO GHE standard, with 92.7 years, give 83.63 and 89.74 years at ages 1 to 4, 44.23 and 50.43 at 40 to 44, 12.85 and 17.19 at 75 to 79 (the last printed 17,19) and 9.34 and 13.08 at 80 to 84. Section 1.4: the estimates for 2000 to 2021 are not directly comparable with previous WHO estimates of DALYs.
GBD 2010 years of life lost without age weighting or discounting
Murray CJL, Vos T, Lozano R, Naghavi M, Flaxman AD, Michaud C, et al. Disability-adjusted life years (DALYs) for 291 diseases and injuries in 21 regions, 1990-2010: a systematic analysis for the Global Burden of Disease Study 2010. The Lancet. 2012;380(9859):2197-2223 (abstract read). Abstract: neither YLLs nor YLDs were age-weighted or discounted.
LSHTM teaching module on local life expectancy as an inequitable loss function for years of life lost
London School of Hygiene and Tropical Medicine. Measuring the burden of disease (PAPP104, session 5). In: Population Analysis for Policies and Programmes. Paris: International Union for the Scientific Study of Population; undated, accessed 2 October 2026 (full text read). Page "Years of life lost": with local life expectancy the death of someone in a high-mortality country contributes less to the global burden of disease than a death at the same age in a low-mortality country, which the module calls inequitable.
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