# Life expectancy

Life expectancy

Life expectancy is the expected (in the statistical sense) number of years of life remaining at a given age.[1] It is denoted by ex, which means the average number of subsequent years of life for someone now aged x, according to a particular mortality experience. (In technical literature, this symbol means the average number of complete years of life remaining, excluding fractions of a year. The corresponding statistic including fractions of a year, the normal meaning of life expectancy, has a symbol with a small circle over the e.) In modern times, life expectancy has substantially changed on a yearly basis and cannot be used accurately for long-term predictions.[citation needed]

The term that is known as life expectancy is most often used in the context of human populations, but is also used in plant or animal ecology;[2] it is calculated by the analysis of life tables (also known as actuarial tables). The term life expectancy may also be used in the context of manufactured objects[3] although the related term shelf life is used for consumer products and the terms "mean time to breakdown" (MTTB) and "mean time before failures" (MTBF) are used in engineering literature.

## Interpretation of life expectancy

General explanation: It is important to note that life expectancy is an average. In many cultures, particularly before modern medicine was widely available, the combination of high infant mortality, deaths in young adults from accidents, wars, and childbirth, significantly lowers the overall life expectancy. But for someone who survived past these early hazards, living into their sixties or seventies would not be uncommon. For example, a society with a life expectancy of 40 may have very few people dying at age 40, most will die before 30 or after 55.

In countries with high infant mortality rates, the life expectancy at birth is highly sensitive to the rate of death in the first few years of life. Because of this sensitivity to infant mortality, simple life expectancy at age zero can be subject to gross misinterpretation, leading one to believe that a population with a low overall life expectancy will necessarily have a small proportion of older people. For example, in a hypothetical stationary population in which half the population dies before the age of five, but everybody else dies exactly at 70 years old, the life expectancy at age zero will be about 37 years, while about 25% of the population will be between the ages of 50 and 70. Another measure such as life expectancy at age 5 (e5) can be used to exclude the effect of infant mortality to provide a simple measure of overall mortality rates other than in early childhood—in the hypothetical population above, life expectancy at age 5 would be 65 years. Aggregate population measures such as the proportion of the population in various age classes should also be used alongside individual-based measures like formal life expectancy when analyzing population structure and dynamics.

## Human life expectancy patterns

Humans live on average 31.88 years in Swaziland and 82.6 years in Japan, although Japan's recorded life expectancy may have been very slightly increased by counting many infant deaths as stillborn.[4] An analysis published in 2011 in The Lancet attributes Japanese life expectancy to equal opportunities and public health as well as diet.[5][6]

The oldest confirmed recorded age for any human is 122 years (see Jeanne Calment). This is referred to as the "maximum life span", which is the upper boundary of life, the maximum number of years any human is known to have lived.[7]

### Life expectancy variation over time

The following information is derived from Encyclopaedia Britannica, 1961 and other sources, and unless otherwise stated represents estimates of the life expectancies of the population as a whole. In many instances life expectancy varied considerably according to class and gender.

Life expectancy at birth takes account of infant mortality but not pre-natal mortality.

Era Life Expectancy at Birth
(years)
Comment
Upper Paleolithic 33 At age 15, life expectancy an additional 39 years (total age 54).[8][9]
Neolithic[10] 20
Bronze Age and Iron Age[11] 26
Classical Greece[12] 28
Classical Rome[12] 28 At age 15, life expectancy an additional 37 years (total age 52).
Pre-Columbian North America[13] 25-30
Medieval Islamic Caliphate[14] 35+
Medieval Britain[15][16] 30 At age 21, life expectancy an additional 43 years (total age 64).[17]
Early Modern Britain[11][18] 25-40
Early 20th Century[19][20] 31
Current world average[21] 67.2 2010 est.

In some cases life expectancy may increase with age as the individual survives the higher mortality rates associated with childhood. For instance, the table above listed life expectancy at birth in Medieval Britain at 30. A male member of the English aristocracy at the same period could expect to live, having survived until the age of 21[17]:

• 1200-1300 A.D.: 43 years (to age 64)
• 1300-1400 A.D.: 24 years (to age 45) (due to the impact of the Black Death)
• 1400-1500 A.D.: 48 years (to age 69)
• 1500-1550 A.D.: 50 years (to age 71).

In general, the available data indicate that longer lifespans became more common recently in human evolution.[9][22] This increased longevity is attributed by some writers to cultural adaptations rather than genetic evolution,[23] although some research indicates that during the Neolithic Revolution natural selection favored increased longevity.[10] Nevertheless, all researchers acknowledge the effect of cultural adaptations upon life expectancy.[22]

During the early 1600s in England, life expectancy was only about 35 years, largely because two-thirds of all children died before the age of four.[24] The average life expectancy in Colonial America was under 25 years in the Virginia colony,[25] and in New England about 40% of children failed to reach adulthood.[26] During the Industrial Revolution, the life expectancy of children increased dramatically.[27] The percentage of children born in London who died before the age of five decreased from 74.5% in 1730-1749 to 31.8% in 1810-1829.[28][29]

Public health measures are credited with much of the recent increase in life expectancy. During the 20th century, the average lifespan in the United States increased by more than 30 years, of which 25 years can be attributed to advances in public health.[30]

In order to assess the quality of these additional years of life, 'healthy life expectancies' have been calculated for the last 30 years. Since 2001, the World Health Organization publishes statistics called Healthy life expectancy (HALE), defined as the average number of years that a person can expect to live in "full health", excluding the years lived in less than full health due to disease and/or injury. Since 2004, Eurostat publishes annual statistics called Healthy Life Years (HLY) based on reported activity limitations. The United States of America uses similar indicators in the framework of their nationwide health promotion and disease prevention plan "Healthy People 2010". An increasing number of countries are using health expectancy indicators to monitor the health of their population.

### Regional variations

CIA World Factbook 2011 Estimates for Life Expectancy at birth (years).
 over 80   77.5–80   75–77.5   72.5–75   70–72.5 67.5–70   65–67.5   60–65   55–60   50–55 45–50   40–45   under 40   not available
Plot of life expectancy vs. GDP per capita in 2009.
Graphs of life expectancy at birth for some sub-Saharan countries showing the fall in the 1990s primarily due to the AIDS pandemic.[31]

There are great variations in life expectancy between different parts of the world, mostly caused by differences in public health, medical care and diet. Much of the excess mortality (higher death rates) in poorer nations is due to war, starvation, and diseases (AIDS, Malaria, etc.). The impact of AIDS is particularly notable on life expectancy in many African countries. According to the UN[32] the life expectancy at birth for 2010–2015 would have been:

As a result, over the past 200 years, countries with African populations have generally not had the same improvements in mortality rates that have been enjoyed by populations of Asian, Latin American or European origin. Notably, even in countries with a majority of European people, such as the United States, Britain, or Ireland, African people still tend to have shorter life expectancies than their European counterparts. For example, in the United States, Euro-Americans are expected to live until age 78.2, but African Americans only until age 73.6.[33]

In contrast, Asian-Americans live the longest of all ethnic groups in the United States, with a life expectancy of 87 years, almost ten years longer than Euro-Americans.,[34] which falls in line with the longer life expectancy among East Asian countries globally compared to European, Latin American or African countries. Surprisingly, Latino-Americans are second place among ethnic groups on life expectancy, living on average two years longer than Euro-Americans and seven years longer than African-Americans, with a life expectancy of 80.6 years.,[35] in contrast to the on average lower life expectancy of most Latin American countries. These variations among ethnic groups may be ascribed to differing economic circumstances of the groups, and in the United States, notably differing access to health care. It may also be ascribed to different cultural patterns of eating or diet that may cross international lines and explain the variation within ethnic groups in a multiethnic society such as the United States.

Climate may also have an effect, and the way data is collected may also influence the figures.

Economic circumstances may also affect life expectancy. For example, in the United Kingdom, life expectancy in the wealthiest areas is several years longer than in the poorest areas. This may reflect factors such as diet and lifestyle as well as access to medical care. It may also reflect a selective effect: people with chronic life-threatening illnesses are less likely to become wealthy or to reside in affluent areas.[36] In Glasgow the disparity is among the highest in the world with life expectancy for males in the heavily deprived Calton standing at 54 – 28 years less than in the affluent area of Lenzie, which is only eight kilometres away.[37][38]

The relationship between economic circumstance and life expectancy is not clear-cut, however. A study by José A. Tapia Granados and Ana Diez Roux at the University of Michigan found that life expectancy actually increased during the Great Depression, and during recessions and depressions in general.[39] The authors suggest that when people are working extra hard during good economic times, they undergo more stress, exposure to pollution, and likelihood of injury among other longevity-limiting factors.

Life expectancy is also likely to be affected by exposure to high levels of highway air pollution or industrial air pollution.[citation needed] This is one way that occupation can have a major effect on life expectancy. Coal miners (and in prior generations, asbestos cutters) often have shorter than average life expectancies. Other factors affecting an individual's life expectancy are genetic disorders, obesity, access to health care, diet, exercise, tobacco smoking, drug use and excessive alcohol use.

### Sex differences

Comparison of male and female life expectancy at birth for countries and territories as defined in the 2011 CIA Factbook, with selected bubbles labelled. The dotted line corresponds to equal female and male life expectancy. The apparent 3D volumes of the bubbles are linearly proportional to their population.[40][41]

Women tend to have a lower mortality rate at every age. In the womb, male fetuses have a higher mortality rate (babies are conceived in a ratio estimated to be from 107 to 170 males to 100 females, but the ratio at birth in the United States is only 105 males to 100 females).[42] Among the smallest premature babies (those under 2 pounds or 900 g) females again have a higher survival rate. At the other extreme, about 90% of individuals aged 110 are female. The difference in life expectancy between men and women in the United States dropped from 7.8 years in 1979 to 5.3 years in 2005, with women expected to live to age 80.1 in 2005.[43]

In the past, mortality rates for females in child-bearing age groups were higher than for males at the same age. This is no longer the case, and female human life expectancy is considerably higher than that of men. The reasons for this are not entirely certain. Traditional arguments tend to favor socio-environmental factors: historically, men have generally consumed more tobacco, alcohol and drugs than females in most societies, and are more likely to die from many associated diseases such as lung cancer, tuberculosis and cirrhosis of the liver.[44] Men are also more likely to die from injuries, whether unintentional (such as car accidents) or intentional (suicide, violence, war).[44] A 2005 study found that the level of patriarchy predicts men's mortality rates. High levels of patriarchy were associated with high levels of male mortality; low levels of patriarchy were correlated with low mortality levels. The researchers argue that while patriarchy grants men certain privileges over women, it also promotes gender stereotypes which harm men.[45] Men are also more likely to die from most of the leading causes of death (some already stated above) than women. Some of these in the United States include: cancer of the respiratory system, motor vehicle accidents, suicide, cirrhosis of the liver, emphysema, and coronary heart disease.[7] These far outweigh the female mortality rate from breast cancer and cervical cancer etc.

Some argue that shorter male life expectancy is merely another manifestation of the general rule, seen in all mammal species, that larger individuals tend on average to have shorter lives.[46][47] This biological difference occurs because women have more resistance to infections and degenerative diseases.[7]

In her extensive review of the existing literature, Kalben concluded that the fact that women live longer than men was observed at least as far back as 1750 and that, with relatively equal treatment, today males in all parts of the world experience greater mortality than females. Of 72 selected causes of death, only 6 yielded greater female than male age-adjusted death rates in 1998 in the United States. With the exception of birds, for almost all of the animal species studied, the males have higher mortality than the females. Evidence suggests that the sex mortality differential in humans is due to both biological/genetic and environmental/behavioral risk and protective factors.[48]

### Centenarians

In developed countries, the number of centenarians is increasing at approximately 5.5% per year, which means doubling the centenarian population every 13 years, pushing it from some 455,000 in 2009 to 4.1 million in 2050.[49] Japan is the country with the highest ratio of centenarians (347 for every 1 million inhabitants in September 2010). Shimane prefecture had an estimated 743 centenarians per million inhabitants.[50]

In the United States, the number of centenarians grew from 32,194 in 1980 to 71,944 in November 2010 (232 centenarians per million inhabitants).[51]

### Mentally ill

Adults with serious mental illness (SMI) die about 25 years earlier, on average at age 51 versus 76 for Americans generally, primarily due to cardiovascular disease.[52][53]

## Evolution and aging rate

Various species of plants and animals, including humans, have different lifespans. There is an evolutionary theory of aging, and general consensus in the academic community of evolutionary theorists; however the theory doesn't work well in practice, and there are many unexplained exceptions. Evolutionary theory states that organisms that, by virtue of their defenses or lifestyle, live for long periods whilst avoiding accidents, disease, predation, etc., are likely to have genes that code for slow aging - which often translates to good cellular repair. This is theorized to be true because if predation or accidental deaths prevent most individuals from living to an old age, then there will be less natural selection to increase intrinsic life span.[54] The finding was supported in a classic study of opossums by Austad,[55] however the opposite relationship was found in an equally-prominent study of guppies by Reznick.[56][57]

One prominent and very popular theory attributes aging to a tight budget for food energy called caloric restriction.[58] Caloric restriction observed in many animals (most notably mice and rats), shows a near doubling of life span due to a very limited calorific intake. Support for this theory has been bolstered by several new studies linking lower basal metabolic rate to increased life expectancy. [59][60][61] This is the key to why animals like Giant Tortoises can live so long. [62] Studies of humans with 100+ year life spans have shown a link to decreased thyroid activity, resulting in their lowered metabolic rate.[63]

In theory, reproduction is costly and takes energy away from the repair processes that extend life spans. However, in actuality females of many species invest much more energy in reproduction than do their male counterparts, and live longer nevertheless. In a broad survey of zoo animals, no relationship was found between the fertility of the animal and its life span.[64]

## Calculating life expectancies

The starting point for calculating life expectancies is the age-specific death rates of the population members. A very simple model of age-specific mortality uses the Gompertz function, although these days more sophisticated methods can be used.[65]

In cases where the amount of data is relatively small, the most common methods are to fit the data to a mathematical formula, such as an extension of the Gompertz function, or to look at an established mortality table previously derived for a larger population and make a simple adjustment to it (e.g. multiply by a constant factor) to fit the data.

With a large amount of data, one looks at the mortality rates actually experienced at each age, and applies smoothing (e.g. by cubic splines) to iron out any apparently random statistical fluctuations from one year of age to the next.

While the data required are easily identified in the case of humans, the computation of life expectancy of industrial products and wild animals involves more indirect techniques. The life expectancy and demography of wild animals are often estimated by capturing, marking and recapturing them.[66] The life of a product, more often termed shelf life is also computed using similar methods. In the case of long-lived components such as those used in critical applications, such as in aircraft methods such as accelerated aging are used to model the life expectancy of a component.[3]

The age-specific death rates are calculated separately for separate groups of data which are believed to have different mortality rates (e.g. males and females, and perhaps smokers and non-smokers if data is available separately for those groups) and are then used to calculate a life table, from which one can calculate the probability of surviving to each age. In actuarial notation the probability of surviving from age x to age x+n is denoted $\,_np_x\!$ and the probability of dying during age x (i.e. between ages x and x+1) is denoted $q_x\!$. For example, if 10% of a group of people alive at their 90th birthday die before their 91st birthday, then the age-specific death probability at age 90 would be 10%. Note that this is a probability rather than a mortality rate.

The life expectancy at age x, denoted $\,e_x\!$, is then calculated by adding up the probabilities to survive to every age. This is the expected number of complete years lived (one may think of it as the number of birthdays they celebrate).

$e_x =\sum_{t=1}^{\infty}\,_tp_x = \sum_{t=0}^{\infty}t \,_tp_x q_{x+t}$

Because age is rounded down to the last birthday, on average people live half a year beyond their final birthday, so half a year is added to the life expectancy to calculate the full life expectancy. (This is denoted by $\,e_x\!$ with a circle over the "e".)

Life expectancy is by definition an arithmetic mean. It can also be calculated by integrating the survival curve from ages 0 to positive infinity (or equivalently to the maximum lifespan, sometimes called 'omega'). For an extinct or completed cohort (all people born in year 1850, for example), of course, it can simply be calculated by averaging the ages at death. For cohorts with some survivors, it is estimated by using mortality experience in recent years. These estimates are called period cohort life expectancies.

It is important to note that this statistic is usually based on past mortality experience, and assumes that the same age-specific mortality rates will continue into the future. Thus such life expectancy figures need to be adjusted for temporal trends before calculating how long a currently living individual of a particular age is expected to live. Period life expectancy remains a commonly used statistic to summarize the current health status of a population.

However for some purposes, such as pensions calculations, it is usual to adjust the life table used, thus assuming that age-specific death rates will continue to decrease over the years, as they have done in the past. This is often done by simply extrapolating past trends; however some models do exist to account for the evolution of mortality (e.g., the Lee-Carter model[67]).

As discussed above, on an individual basis, there are a number of factors that have been shown to correlate with a longer life. Factors that are associated with variations in life expectancy include family history, marital status, economic status, physique, exercise, diet, drug use including smoking and alcohol consumption, disposition, education, environment, sleep, climate, and health care.[7]

## Life expectancy forecasting

Forecasting life expectancy and mortality forms an important subdivision of demography. Future trends in life expectancy have huge implications for old-age support programs like U.S. Social Security and pension systems, because the cash flow in these systems depends on the number of recipients still living (along with the rate of return on the investments or the tax rate in PAYGO systems). With longer life expectancies, these systems see increased cash outflow; if these systems underestimate increases in life-expectancies, they won't be prepared for the large payments that will inevitably occur as humans live longer and longer.

Life expectancy forecasting usually is based on two different approaches:

• Forecasting the life expectancy directly, generally using ARIMA or other time series extrapolation procedures: This approach has the advantage of simplicity, but it cannot account for changes in mortality at specific ages, and the forecasted number cannot be used to derive other life table results. Analyses and forecasts using this approach can be done with any common statistical/ mathematical software package, like R, SAS, Matlab, or SPSS.
• Forecasting age specific death rates and computing the life expectancy from the results with life table methods: This approach is usually more complex than simply forecasting life expectancy because the analyst must deal with correlated age specific mortality rates, but it seems to be more robust than simple one dimensional time series approaches. This approach also yields a set of age specific rates that may be used to derive other measures, like survival curves or life expectancies at different ages. The most important approach within this group is the Lee-Carter model,[68] which uses the singular value decomposition on a set of transformed age-specific mortality rates to reduce their dimensionality to a single time series, forecasts that time series, and then recovers a full set of age-specific mortality rates from that forecasted value. Software for this approach include Professor Rob J. Hyndman's R package and UC Berkeley's LCFIT system.

## Policy uses of life expectancy

Life expectancy is one of the factors in measuring the Human Development Index (HDI) of each nation, along with adult literacy, education, and standard of living.[69]

Life expectancy is also used in describing the physical quality of life of an area.

## Life expectancy vs. life span

Life expectancy is often confused with life span to the point that they are nearly synonyms; when people hear 'life expectancy was 35 years' they often interpret this as meaning that people of that time or place had short life spans.[70] One such example can be seen in the In Search of... episode "The Man Who Would Not Die" (About Count of St. Germain) where it is stated "Evidence recently discovered in the British Museum indicates that St. Germain may have well been the long lost third son of Rákóczi born in Transylvania in 1694. If he died in Germany in 1784, he lived 90 years. The average life expectancy in the 18th century was 35 years. Fifty was a ripe old age. Ninety... was forever."

This ignores the fact that the life expectancy generally quoted is the at birth number which is an average that includes all the babies that die before their first year of life as well as people that die from disease and war. The genetics of humans and rate of aging were no different in preindustrial societies than today, but people frequently died young because of untreatable diseases, accidents, and malnutrition. Many women did not survive childbirth, and when a person did reach old age they were likely to succumb quickly to health problems.

It can be argued that it is better to compare life expectancies of the period after adulthood to get a better handle on life span.[71] Even during childhood life expectancy can take a huge jump as seen in the Roman Life Expectancy table at the University of Texas where at birth the life expectancy was 25 but at the age of 5 it jumped to 48. Studies like Plymouth Plantation; "Dead at Forty" and Life Expectancy by Age, 1850–2004 similarly show a dramatic increase in life expectancy once adulthood was reached.

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