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# Life Expectancy Index

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### Life Expectancy Index

Life expectancy is the expected (in the statistical sense) number of years of life remaining at a given age.[1] It is denoted by $e_x$,[a] which means the average number of subsequent years of life for someone now aged $x$, according to a particular mortality experience. Because life expectancy is an average, a particular person may well die many years before or many years after their "expected" survival. The term "maximum life span" has a quite different meaning. The "median life span" is also a different concept although fairly similar to life expectancy numerically in most developed countries.

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.

## Interpretation of life expectancy

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 and deaths in young adulthood from accidents, epidemics, plagues, 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 years of age or after 55.

In countries with high infant mortality rates, 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.[4] For example, in a hypothetical stationary population in which half the population dies before the age of five, but everybody else dies at exactly 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 another 64 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

Human beings are expected to live on average 49.42 years in Swaziland[5] 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.[6] An analysis published in 2011 in The Lancet attributes Japanese life expectancy to equal opportunities and public health as well as diet.[7][8]

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.[9]

### Life expectancy variation over time

The following information is derived from Encyclopædia Britannica, 1961. and other sources, some with a questionable accuracy. Unless otherwise stated, it 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)
Life Expectancy at Older Age
Upper Paleolithic 33 Based on data from recent hunter-gatherer populations, it is estimated that at age 15, life expectancy was an additional 39 years (total age 54).[10]
Neolithic[11] 20
Bronze Age and Iron Age[12] 26
Classical Greece[13] 28
Classical Rome[14] 20–30 At age 10, life expectancy an additional 35 to 37 years (total age 45 to 47)
Pre-Columbian North America[15] 25–30
Medieval Islamic Caliphate[16] 35+
Medieval Britain[17][18] 30 At age 21, life expectancy additional 43 years (total age 64).[19]
Early Modern Britain[12] 25–40
Early 20th Century[20][21] 31
2010 world average[22] 67.2

Life expectancy increases 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:[19]

• 1200–1300 A.D.: 43 years (to age 64)
• 1300–1400 A.D.: 34 years (to age 55) (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.[23][24] This increased longevity is attributed by some writers to cultural adaptations rather than genetic evolution,[25] although some research indicates that during the Neolithic Revolution natural selection favored increased longevity.[11] Nevertheless, all researchers acknowledge the effect of cultural adaptations upon life expectancy.[24]

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.[26] The average life expectancy in Colonial America was under 25 years in the Virginia colony,[27] and in New England about 40% of children failed to reach adulthood.[28] During the Industrial Revolution, the life expectancy of children increased dramatically.[29] 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.[30][31]

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.[32]

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

There are great variations in life expectancy between different parts of the world, mostly caused by differences in public health, medical care, and diet. The impact of AIDS is particularly notable on life expectancy in many African countries. According to predictions made by the United Nations (UN) in 2002,[34] the life expectancy at birth for 2010–2015 (if HIV/AIDS did not exist) would have been:

The UN's predictions were too pessimistic. Actual life expectancy in Botswana declined from 65 in 1990 to 49 in 2000 before increasing to 66 in 2011. In South Africa, life expectancy was 63 in 1990, 57 in 2000, and 58 in 2011. And in Zimbabwe, life expectancy was 60 in 1990, 43 in 2000, and 54 in 2011.[35]

Countries in Africa over the last 200 years have generally not had the same improvements in mortality rates that have been enjoyed by countries in Asia, Latin America, and Europe.

In the United States, African people have shorter life expectancies than their European counterparts. For example, white Americans born in 2010 are expected to live until age 78.9 but African Americans only until age 75.1. This 3.8-year gap, however, is the lowest it has been since at least 1975. The greatest difference was 7.1 years in 1993.[36] In contrast, Asian-American women live the longest of all ethnic groups in the United States, with a life expectancy of 85.8 years.[37] The life expectancy of Hispanic Americans is 81.2 years.[36]

### Economic circumstances

Economic circumstances 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.[38] 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.[39][40]

A 2013 study found a pronounced relationship between economic inequality and life expectancy.[41] 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.[42] 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. 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.

### Gender differences

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).[45] 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.[46]

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.[47] Men are also more likely to die from injuries, whether unintentional (such as occupational or war or car accidents) or intentional (suicide).[47] 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.[9] 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 (size) individuals (within a species) tend on average to have shorter lives.[48][49] This biological difference occurs because women have more resistance to infections and degenerative diseases.[9]

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 people is due to both biological/genetic and environmental/behavioral risk and protective factors.[50]

There is a recent suggestion that mitochondrial mutations that shorten lifespan continue to be expressed in males (but less so in females) because mitochondria are inherited only through the mother. By contrast natural selection weeds out mitochondria that reduce female survival as such mitochondria are less likely to be passed on to the next generation. Therefore it is suggested human females and female animals tend to live longer than males. The authors claim this is a partial explanation.[51][52]

### 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.[53] 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.[54]

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).[55]

## 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.[56] The finding was supported in a classic study of opossums by Austad,[57] however the opposite relationship was found in an equally prominent study of guppies by Reznick.[58][59]

One prominent and very popular theory attributes aging to a tight budget for food energy called caloric restriction.[60] 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.[61][62][63] This is the key to why animals like Giant Tortoises can live so long.[64] Studies of humans with 100+ year life spans have shown a link to decreased thyroid activity, resulting in their lowered metabolic rate.

In a broad survey of zoo animals, no relationship was found between the fertility of the animal and its life span.[65]

## Calculating life expectancies

The starting point for calculating life expectancies is the age-specific death rates of the population members. In the past, a very simple model of age-specific mortality used the Gompertz function, although these days more sophisticated methods are used.[66]

In cases where the amount of data is relatively small, the most common methods are to fit a mathematical formula, such as an extension of the Gompertz function, to the data, 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.[67] 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 expected future lifetime of a life age $x$ in whole years (the curtate expected lifetime of (x)) is denoted by the symbol $\,e_x\!$.[a] It is the conditional expected future lifetime (in whole years), assuming survival to age $x$. If $K\left(x\right)$ denotes the curtate future lifetime at $x$, then

$e_x = E\left[K\left(x\right)\right] = \sum_\left\{k=0\right\}^\infty k\, Pr\left(K\left(x\right)=k\right) = \sum_\left\{k=0\right\}^\left\{\infty\right\}k\, \,_kp_x \,\, q_\left\{x+k\right\}.$

Substituting $\left\{\right\}_kp_x \, q_\left\{x+k\right\} = \left\{\right\}_k p_x - \left\{\right\}_\left\{k+1\right\}p_x$ in the sum and simplifying, we get the equivalent formula[68]

$e_x = \sum_\left\{k=1\right\}^\infty \left\{\right\}_k p_x.$

If we make the assumption that on average people live a half year in the year of death, then the complete expectation of future lifetime at age $x$ is $e_x + 1/2$.

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[69]).

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.[9]

## 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 EViews, R, SAS, Stata, Matlab, or SPSS.
• Forecasting age specific 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.[71]

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

Disparities in life expectancy are often cited as demonstrating the need for better medical care or increased social support.

Life expectancies are also used when determining the value of a life settlement, a life insurance policy sold for a cash asset.

## 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.[72] 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 individuals who reached old age 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.Life Expectancy by Age, 1850–2004 similarly show a dramatic increase in life expectancy once adulthood was reached.

## Notes

a. ^ ^ In standard actuarial notation, ex refers to the expected future lifetime of (x) in whole years, while ex with a circle above the e denotes the complete expected future lifetime of (x), including the fraction.