"Life Expectancy" – What does this actually mean?
How is life expectancy calculated and what does it mean? What’s the difference between period and cohort life expectancy?
Life expectancy has doubled in all world regions. What does this mean exactly?
Despite its importance and prominence in research and policy, it is surprisingly difficult to find a simple yet detailed description of what “life expectancy” actually means. In this section, we try to fill this gap.
The term "life expectancy" refers to the number of years a person can expect to live. By definition, life expectancy is based on an estimate of the average age that members of a particular population group will be when they die.
In practice, however, things are often more complicated:
One important distinction and clarification is the difference between cohort and period life expectancy.
The cohort life expectancy is the average life length of a particular cohort – a group of individuals born in a given year. When we can track a group of people born in a particular year, many decades ago, and observe the exact date in which each one of them died then we can calculate this cohort's life expectancy by simply calculating the average of the ages of all members when they died.
You can think of life expectancy in a particular year as the age a person born in that year would expect to live if the average age of death did not change over their lifetime.
It is of course not possible to know this metric before all members of the cohort have died. Because of that, statisticians commonly track members of a particular cohort and predict the average age-at-death for them using a combination of observed mortality rates for past years and projections about mortality rates for future years.
An alternative approach consists in estimating the average length of life for a hypothetical cohort assumed to be exposed, from birth through death, to the mortality rates observed at one particular period – commonly a year. This approach leads to what is known as 'period life expectancy' and it is the much more commonly used life expectancy metric. It is the definition used by most international organizations, including the UN and the World Bank, when reporting 'life expectancy' figures. Period life expectancy estimates do not take into account how mortality rates are changing over time and instead only reflects the mortality pattern at one point in time. Because of this, period life expectancy figures are usually different to cohort life expectancy figures.
An example to illustrate the measurement of life expectancy
Since period life expectancy estimates are ubiquitous in research and public debate, it is helpful to use an example to flesh out the concept. Let's consider the map showing life expectancy—specifically period life expectancy—at birth in 2005. You can hover the mouse over a country to display the corresponding estimate.
For Japan, we can see that life expectancy in 2005 was 82.3 years. This means that a hypothetical cohort of infants living through the age-specific mortality of Japan in 2005 could expect to live 82.3 years, under the assumption that mortality patterns observed in 2005 remain constant throughout their lifetime. But if life expectancies are increasing the reality for a cohort born then is that the cohort life expectancy is higher than that period life expectancy. We see this in the data: if you move the slider below the map forward, you'll see that in 2019 the period life expectancy in Japan was 84.6 years, which means that mortality patterns in Japan did improve in the period 2005-2019.
In general, the commonly-used period life expectancies tend to be lower than the cohort life expectancies, because mortality rates were falling over the course of modern development.
Life expectancy is an average
An important point to bear in mind when interpreting life expectancy estimates is that very few people will die at precisely the age indicated by life expectancy, even if mortality patterns stay constant.
For example, very few of the infants born in South Africa in 2009 will die at 52.2 years of age, as per the figures in the map above. Most will die much earlier or much later, since the risk of death is not uniform across the lifetime. Life expectancy is the average.
In societies with high infant mortality rates many people die in the first few years of life; but once they survive childhood, people often live much longer. Indeed, this is a common source of confusion in the interpretation of life expectancy figures: It is perfectly possible that a given population has a low life expectancy at birth, and yet has a large proportion of old people.
Commonly we study life expectancy at birth, but life expectancy at higher ages are also relevant
Given that life expectancy at birth is highly sensitive to the rate of death in the first few years of life, it is common to report life expectancy figures at different ages, both under the period and cohort approaches. For example, the UN estimates that the (period) global life expectancy at age 15 in 2005 was 73.6 years. This means that the group of 15-year-old children alive around the world in 2005 could expect to live another 58.6 years (i.e. until the age of 73.6), provided that mortality patterns observed in 2005 remained constant throughout their lifetime.
Finally, another point to bear in mind is that period and cohort life expectancy estimates are statistical measures, and they do not take into account any person-specific factors such as lifestyle choices. Clearly, the length of life for an average person is not very informative about the predicted length of life for a person living a particularly unhealthy lifestyle.
How is life expectancy calculated?
In practical terms, estimating life expectancy entails predicting the probability of surviving successive years of life, based on observed age-specific mortality rates. How is this actually done?
Age-specific mortality rates are usually estimated by counting (or projecting) the number of age-specific deaths in a time interval (e.g. the number of people aged 10-15 who died in the year 2005), and dividing by the total observed (or projected) population alive at a given point within that interval (e.g. the number of people aged 10-15 alive on 1 July 2015).
To ensure that the resulting estimates of the probabilities of death within each age interval are smooth across the lifetime, it is common to use mathematical formulas, to model how the force of mortality changes within and across age intervals. Specifically, it is often assumed that the proportion of people dying in an age interval starting in year x and ending in year n+x corresponds to:
where m(n,x) is the age-specific mortality rate as measured in the middle of that interval (a term often referred to as the 'central death rate' for the age interval).1
Once we have estimates of the fraction of people dying across age intervals, it is simple to calculate a 'life table' showing the evolving probabilities of survival and the corresponding life expectancies by age. Here is an example of a life table from the US, and this tutorial from MEASURE Evaluation explains how life tables are constructed, step by step (see Section 3.2 'The Fergany Method').
Period life expectancy figures can be obtained from 'period life tables' (i.e. life tables that rely on age-specific mortality rates observed from deaths among individuals of different age groups at a fixed point in time). And similarly, cohort life expectancy figures can be obtained from 'cohort life tables' (i.e. life tables that rely on age-specific mortality rates observed from tracking and forecasting the death and survival of a group of people as they become older).
For some countries and for some time intervals, it is only possible to reconstruct life tables from either period or cohort mortality data. As a consequence, in some instances—for example in obtaining historical estimates of life expectancy across world regions—it is necessary to combine period and cohort data. In these cases, the resulting life expectancy estimates cannot be simply classified into the 'period' or 'cohort' categories.
What else can we learn from 'life tables'?
Life tables are not just instrumental to the production of life expectancy figures (as noted above), they also provide many other perspectives on the mortality of a population. For example, they allow for the production of 'population survival curves', which show the share of people who are expected to survive various successive ages. This chart provides an example, plotting survival curves for individuals born at different points in time, using cohort life tables from England and Wales.
At any age level in the horizontal axis, the curves in this visualization mark the estimated proportion of individuals who are expected to survive that age. As we can see, less than half of the people born in 1851 in England and Wales made it past their 50th birthday. In contrast, more than 95% of the people born in England and Wales today can expect to live longer than 50 years.
Since life expectancy estimates only describe averages, these indicators are complementary, and help us understand how health is distributed across time and space. In our entry on Life Expectancy you can read more about related complementary indicators, such as the median age of a population.
Endnotes
The underlying assumption is that the force of mortality is constant within each age interval. The seminal reference introducing this method is Fergany (1971) "On the Human Survivorship Function and Life Table Construction," Demography8(3):331-334).
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Esteban Ortiz-Ospina (2017) - “"Life Expectancy" – What does this actually mean?” Published online at OurWorldinData.org. Retrieved from: 'https://ourworldindata.org/life-expectancy-how-is-it-calculated-and-how-should-it-be-interpreted' [Online Resource]BibTeX citation
@article{owid-life-expectancy-how-is-it-calculated-and-how-should-it-be-interpreted,
author = {Esteban Ortiz-Ospina},
title = {"Life Expectancy" – What does this actually mean?},
journal = {Our World in Data},
year = {2017},
note = {https://ourworldindata.org/life-expectancy-how-is-it-calculated-and-how-should-it-be-interpreted}
}
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