# Life expectancy

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Life expectancy is a statistical measure defined as the expected (mean) survival of human beings based upon a number of criteria such as gender and geographic location. Popularly, it is most often construed to mean the life expectancy at birth for a given human population, which is the same as the expected age at death. However, technically life expectancy means the expected number of years remaining to live, and it can be calculated for any age.

Life expectancy is heavily dependent on the criteria used to select the group. 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. In these cases, another measure such as life expectancy at age 5 (e5) can be used to exclude the effects of infant mortality to reveal the effects of other causes of death. Typically, life expectancy at birth (e0) is specified. If the data on infant mortality rates are suspect for some reason, such as the underreporting of births or of infant deaths, then life expectancy at age 1 (e1) or age 2 (e2) might also be used.

In the developed world there has been a considerable increas in life expecancy since the turn of the last century. For example in the UK in 1901 life expectancy for men was 45 and by 2008 it was 82 and for women it has gone up from 49 to 85 . So improved health care, reduction in war, good nutrition etc has lead to a doubling of life expectancy in that period.

## Variations in life expectancy in the world todayEdit

There are great variations in life expectancy worldwide, mostly caused by differences in public health, medicine and nutrition from country to country.

There are also variations between groups within single countries. For example, in the United States during the early 20th century there were large differences in life expectancy between people of different ethnicity, which have since lessened. Significant differences still remain in life expectancy between men and women in the US and other developed countries, with women outliving men. These gender differences have been lessening in recent years, with men's life expectancy improving at a faster rate than women's. Poverty has a very substantial effect on life expectancy. In the United Kingdom life expectancy in the wealthiest areas is ten years longer than the poorest areas and the gap appears to be increasing as life expectancy for the prosperous continues to increase while in more deprived communities there is little increase.[1]

Life expectancy may also be reduced for people exposed to high levels of highway air pollution[How to reference and link to summary or text] or industrial air pollution. Occupation may also have a major effect on life expectancy. Well-educated professionals working in offices have a high life expectancy, while coal miners (and in prior generations, asbestos cutters) do not. Other factors affecting an individual's life expectancy are genetic disorders, obesity, access to health care, diet, exercise, tobacco smoking, and excessive drug and alcohol use.

As pointed out above, AIDS has recently had a negative effect on life expectancy in Sub-Saharan Africa.

## Evolution and aging rate Edit

The different lifespans of different plants and animals, including humans raises the question of why such lifespans are found.

The evolutionary theory is that organisms that are able by virtue of their defenses or lifestyle to live for long periods whilst avoiding accidents, disease, predation etc. are likely to have genes that code for slow aging- good repair.

This is so because if a change to the organism (for example a bird might evolve stronger wings) may mean that it is exceptionally capable of escaping from predation, then it will live longer, and typically die of old age. It will also be more likely to survive to reproduce, so these genes will spread through the gene pool. Thus, a member of the population with the better wings who by chance also has genes that code for better repair will spend a longer time as its contemporaries in the best reproductive years and have more successors. Its genes will tend to dominate more and more of the gene pool and genes for slower aging and by a similar argument a slower reproduction rate, will dominate.

Conversely a change to the environment that means that organisms die younger from a common disease or a new threat from a predator will mean that organisms that have genes that code for putting more energy into reproduction than repair will do better.

The support for this theory includes the fact that better defended animals, for example small birds that can fly away from danger live for a decade or more whereas mice which cannot, die of old age in a year or two. Tortoises and turtles are very well defended indeed and can live for over a hundred years.

## Calculating life expectancyEdit

The starting point for calculating life expectancies is the age-specific death rates of the population members. For example, if 10% of a group of people alive at their 90th birthday die before their 91st birthday, then the age-specific death rate at age 90 would be 10%.

These values 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 $q_x\!$.

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.

Life expectancy is by definition an arithmetic mean. It can be calculated also by integrating the survival curve from ages 0 to infinite (the ultimate age, sometimes called 'omega'). For an extinct cohort (all people born in year 1850, for example), of course, it can simply be calculated by averaging the ages at death.

Note that no allowance has been made in this calculation for expected changes in life expectancy in the future. Usually when life expectancy figures are quoted, they have been calculated like this with no allowance for expected future changes. This means that quoted life expectancy figures are not generally appropriate for calculating how long any given individual of a particular age is expected to live, as they effectively assume that current death rates will be "frozen" and not change in the future. Instead, life expectancy figures can be thought of as a useful statistic to summarize the current health status of a population. Some models do exist to account for the evolution of mortality (e.g., the Lee-Carter model[2]).

## Interpreting life expectancyEdit

Useful information can be gleaned from life expectancy at ages other than 0 as medical technology changes over time. For example, in the United States the life expectancy at birth over the past 100 years has increased by over 50%. However, the life expectancy for 60 year old persons has only increased 10%. This means that the improvements in medical technology have done much to decrease mortality among the young, but relatively little to help the elderly. In other words, although the odds of living to old age have increased, the maximum probable lifespan has not changed dramatically.

The age-adjusted statistics help to show the limits of health technology as well. It has been suggested that there is a maximum human life span of around 125 years -- not even by chance has anyone been documented to live longer than that. In other words, even if a person never dies of disease, accident or violence, we can expect them to die of "old age" by that time.

Typically, the expected age at death (i.e. age x + life expectancy at age x) of an individual of age X is greater than the life expectancy at birth for the population as a whole. For example, in a population with a life expectancy of 75 years, a 20-year-old might be expected to live to her or his mid-80s. But it is theoretically possible that there could be an inversion of life-expectancy between the old and the young if there were sufficiently dramatic medical advances. For example, some diseases such as shingles occur during old age, but are caused at a young age. If shingles were a leading cause of death, we could imagine that the chicken pox vaccine would so much increase their life expectancy, that they would likely out-live their elders. Another example would be where in some places like southern Africa the incidence of HIV is so high among the adult population, that a new, effective and widely-distributed vaccine might increase life expectancy of a Lesotho 11-year old (who would benefit from the vaccine and never get HIV disease) to be higher than the life expectancy of a Lesotho 21-year old (who might have a 50% chance of dying soon of AIDS and cannot be helped by the vaccine)..

## ReferencesEdit

1. Department of Health -Tackling health inequalities: Status report on the Programme for Action
2. Ronald D. Lee and Lawrence Carter. 1992. "Modeling and Forecasting the Time Series of U.S. Mortality," Journal of the American Statistical Association 87 (September): 659-671.