Years of Life Lost

Years of Life Lost, Premature Mortality and the Fatal Component of the DALY

Years of life lost (YLLs) turn a count of deaths into a count of life cut short, so that a death in childhood and a death in old age no longer carry the same weight in burden of disease tables. Every YLL estimate rests on a choice that the short formula hides, namely the standard life table that fixes how many years a death at each age is taken to remove. The Global Burden of Disease (GBD) study and the World Health Organization (WHO) each tabulate such a standard, a normative benchmark used instead of local life expectancy. GBD dropped discounting in GBD 2010, and GBD 2021 reports the leading causes of YLLs. YLLs are a different count from potential years of life lost (PYLL) and from the life-years gained used in economic evaluation.

Deaths multiplied by a standard remaining life expectancy

YLLs are the fatal component of the disability-adjusted life year (DALY), added to years lived with disability (YLDs), which record non-fatal health loss. GBD 2021 calculated them by multiplying deaths for each cause, age, sex, location and year by the standard life expectancy at the age of death. For one cause in one population and year, the calculation is as follows.

$$YLL_{c} = \sum_{a} N_{c,a} \times e^{*}_{a}$$

where $YLL_{c}$ is the years of life lost from cause $c$, $N_{c,a}$ is the number of deaths from cause $c$ at age $a$, and $e^{*}_{a}$ is the remaining life expectancy at age $a$ in the standard life table. WHO describes $e^{*}_{a}$ as a loss function, giving the years lost for a death at each age.

The standard value at age $a$ is the remaining life expectancy of a person who has already reached that age, not life expectancy at birth minus age. The two part company at older ages, because people who have survived to old age have, on average, more years left than the gap between their age and the expectation at birth. In the GBD 2010 standard a death at ages 80 to 84 counts 9.34 years, whereas subtracting age from the 86.0 years expected at birth would give between 2 and 6 years, and a death after 86 would count nothing at all.

The GBD and WHO standard life tables

Each change of standard alters every YLL total, so the history matters when estimates are compared. For GBD 1990, WHO's methods paper records life expectancy at birth fixed at 82.5 years for females, close to the highest then observed (Japanese women), and 80.0 years for males, reflecting an assumed biologically determined minimum gap between the sexes. Murray's 1994 technical paper describes the standard as based on model life table West Level 26. GBD 2010 replaced it with one standard for both sexes, built from the lowest observed death rate in each age group in countries with more than 5 million people, giving life expectancy at birth of 86.0 years.

Later GBD rounds kept that construction with newer data. GBD 2016 reported a standard life expectancy at birth of 86.6 years. The reference life table released for GBD 2019, called the theoretical minimum risk life table, uses the lowest observed age-specific mortality rates across all estimation years in locations with more than 5 million people in 2016. GBD 2021 describes its standard as calculated from the lowest age-specific mortality rate between countries.

WHO's Global Health Estimates (GHE) take a different route. Some experts consulted by WHO argued that even the lowest observed death rates include preventable deaths, and Japanese women had reached life expectancy at birth of 87.1 years in 2013, above the GBD 2010 standard. WHO therefore bases its standard on the frontier national life expectancy implied by the lowest projected age-specific mortality rates for 2050 in the United Nations World Population Prospects, meant to represent the maximum life span of a person in good health. For GHE 2019 this gave life expectancy at birth of 90 years; the methods paper for GHE 2021, published in 2024, uses the 2024 projections and gives 92.7 years (the paper's own summary in section 1.4 still states 90 years).

The table shows the standard remaining life expectancy, in years, at selected ages as tabulated by WHO. The GBD 1990 columns are the versions without age weights or discounting.

The gap between standards is proportionally largest at older ages. The WHO GHE 2021 standard gives a death at 80 to 84 about 40% more years than GBD 2010 (13.08 against 9.34), but a neonatal death only about 8% more (92.65 against 86.01).

Why the standard is normative rather than local

Using each population's own life expectancy might look more realistic, but it would make the burden of a death depend on where it happened. A London School of Hygiene and Tropical Medicine teaching module, published by the International Union for the Scientific Study of Population (IUSSP), notes that, with local life expectancy, a death at a given age in a high-mortality country adds less to the global burden than the same death in a low-mortality country, and calls this inequitable. With one standard, a death at a given age counts the same everywhere, and measured burden becomes, as WHO puts it, the gap between a population's health and that of a normative reference population.

The single standard for both sexes from GBD 2010 rests on the same reasoning. The module notes that it is unclear whether any of the sex gap in life expectancy is biological, and that society should at least aspire to bring men's mortality down to women's level. The cost of a normative standard is that YLLs are not forecasts, since they do not say how long the people who died would have lived in their own setting, and where mortality is high the standard sits well above local life expectancy at every age.

Discounting and age weighting before GBD 2010

The standard DALYs of the original GBD study and later WHO updates added two value choices to the YLL. Future years were discounted at 3% a year, and age weighting gave less weight to years lost at young and older ages. With continuous discounting and no age weighting, one death counts for the number of years given below.

$$YLL_{disc} = \frac{1 - e^{-rL}}{r}$$

where $YLL_{disc}$ is the discounted years of life lost for one death, $L$ is the standard number of years remaining for the age at death and $r$ is the annual discount rate. At 3%, a death that removes 80 standard years counts as about 30.3 years, so discounting compresses the difference between deaths at different ages.

GBD 2010 calculated neither YLLs nor YLDs with age weighting or discounting, and WHO adopted a 0% discount rate and no age weighting after consultations in 2012. Discounting remains an open choice when YLLs averted are used as an outcome in economic evaluation.

Worked example with one cause, three age groups and four counting rules

The figures are illustrative. In one year a cause kills 20 children aged 1 to 4, 50 adults aged 40 to 44 and 100 adults aged 75 to 79. The GBD 2010 standard, as tabulated by WHO, gives 83.63, 44.23 and 12.85 remaining years for these age groups.

1. YLLs under the GBD 2010 standard. Deaths in each group are multiplied by the standard value and summed.

$$YLL = 20 \times 83.63 + 50 \times 44.23 + 100 \times 12.85 = 1{,}672.6 + 2{,}211.5 + 1{,}285 = 5{,}169.1$$

where the three products are the YLLs from each age group. The 100 deaths at ages 75 to 79 are 59% of deaths but 25% of YLLs (1,285 of 5,169.1).

2. PYLL with a cut-off at age 70. Following the method described by the US Centers for Disease Control (CDC), each death counts the years between the midpoint of its age group (3, 42.5 and 77.5) and the cut-off, and deaths above the cut-off count zero.

$$PYLL_{70} = 20 \times (70 - 3) + 50 \times (70 - 42.5) + 100 \times 0 = 1{,}340 + 1{,}375 + 0 = 2{,}715$$

where $PYLL_{70}$ is potential years of life lost before age 70. The older deaths disappear from the total.

3. YLLs under the WHO GHE 2021 standard. The same deaths with WHO's values of 89.74, 50.43 and 17.19 years give the following total.

$$YLL_{WHO} = 20 \times 89.74 + 50 \times 50.43 + 100 \times 17.19 = 1{,}794.8 + 2{,}521.5 + 1{,}719 = 6{,}035.3$$

where $YLL_{WHO}$ is the total under the WHO standard. The total is 16.8% higher, but the rise is 7.3% for the child deaths and 33.8% for the deaths at ages 75 to 79.

4. Discounting at 3%. Using the continuous formula above with the GBD 2010 values, each death counts $(1 - 0.0814)/0.03 = 30.62$ years at ages 1 to 4, $(1 - 0.2653)/0.03 = 24.49$ at ages 40 to 44 and $(1 - 0.6801)/0.03 = 10.66$ at ages 75 to 79, where 0.0814, 0.2653 and 0.6801 are $e^{-rL}$ for each age group. The discounted total is shown below.

$$YLL_{disc} = 20 \times 30.62 + 50 \times 24.49 + 100 \times 10.66 = 612.4 + 1{,}224.5 + 1{,}066 = 2{,}902.9$$

where $YLL_{disc}$ is the discounted total for the cause.

5. What the numbers show. Discounting cuts the YLLs from the child deaths by 63% but those from the older deaths by only 17%, so the older deaths rise from 25% to 37% of the total. Undiscounted, a child death counts 6.5 times an older death; discounted, 2.9 times. PYLL removes the older deaths altogether, while the WHO standard gives them more weight than GBD 2010 does. A cause that kills mainly older people can therefore move up or down a ranking with no change in deaths, which is why a burden estimate should name its standard, any cut-off and any discount rate.

YLLs compared with PYLL and with life-years in evaluation

Several measures count years lost or gained through death, and they answer different questions. The table at the end of this section sets them side by side.

The CDC describes years of potential life lost as reflecting deaths before a conventional cut-off age, usually 65, calculated from the difference between the cut-off and the midpoint of each age group; its 1992 report also used a cut-off of 85. WHO describes the DALY as a generalisation of PYLL to include lost good health, and records that GBD 1990 chose not to use an arbitrary cut-off such as 70 years. PYLL is simple and transparent, but deaths beyond the cut-off count as nothing and the result depends on the cut-off chosen.

An economic evaluation models the extra survival an intervention gives, usually combines it with quality of life in quality-adjusted life years (QALYs) and discounts it. NICE's manual (PMG36) asks for health effects in QALYs, discounted at 3.5% a year in the reference case, and for life years gained among the key results of a cost-utility analysis. When a cost-effectiveness analysis uses DALYs averted, the life expectancy behind each death averted is a further choice. Larson's worked example takes the local age-specific life expectancy of the person who died, not a standard table, so studies should state which they use.

Leading causes of YLLs in GBD 2021 and priority setting

Burden tables usually report YLLs both as counts and as age-standardised rates, and the two can rank causes differently. Counts show where premature death is concentrated, while age-standardised rates remove the effects of population size and age structure.

GBD 2021 estimated 1.98 billion YLLs worldwide in 2021, 68.7% of all DALYs. YLLs rose from 1.89 billion in 2010, a non-significant increase of 4.6%, while the age-standardised YLL rate fell by 12.0%, from 28,595.8 to 25,175.4 per 100,000. By count, the leading causes in 2021 were COVID-19 (198 million YLLs), ischaemic heart disease (184 million) and neonatal disorders (165 million). By age-standardised rate, neonatal disorders ranked first, COVID-19 second and ischaemic heart disease third.

The leading causes of death look different. Ranked by age-standardised death rate in 2021, the first four were ischaemic heart disease, COVID-19, stroke and chronic obstructive pulmonary disease, with no place for neonatal disorders, which reach the top of the age-standardised YLL ranking because each neonatal death carries the whole of the standard life expectancy from birth.

The GBD 2021 authors present their cause of death and YLL estimates as information for policy makers setting health priorities. A YLL ranking shows where deaths cut most life short but not whether effective and affordable interventions exist, so choosing among them needs a cost-effectiveness analysis, for example of cost per DALY averted.

Limits and misreadings of YLL estimates

Most errors with YLLs come from reading them as more than they are. The points below concern the fatal component; wider DALY errors are covered on the DALY page.

• Subtracting age from life expectancy at birth. The standard uses the life expectancy remaining for the age at death, which gives older deaths more years and never falls to zero.
• Mixing standards or rounds. GBD and WHO standards differ, and WHO states that its estimates for 2000 to 2021 are not directly comparable with its earlier DALY estimates.
• Ignoring cause attribution. YLLs inherit the quality of cause of death data, including GBD's reassignment of deaths coded to non-specific or implausible causes, which it calls garbage codes.
• Treating the age gradient as an added weight. Even without age weighting a young death counts far more than an old one, because that is what the standard measures.

Sources

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