In
actuarial science and
demography
Demography () is the statistical study of populations, especially human beings.
Demographic analysis examines and measures the dimensions and dynamics of populations; it can cover whole societies or groups defined by criteria such as edu ...
, a life table (also called a mortality table or actuarial table) is a table which shows, for each age, what the probability is that a person of that age will die before their next birthday ("probability of
death
Death is the irreversible cessation of all biological functions that sustain an organism. For organisms with a brain, death can also be defined as the irreversible cessation of functioning of the whole brain, including brainstem, and brain ...
"). In other words, it represents the
survivorship of people from a certain population.
They can also be explained as a long-term mathematical way to measure a population's longevity.
Tables have been created by demographers including Graunt, Reed and Merrell, Keyfitz, and Greville.
There are two types of life tables used in actuarial science. The period life table represents mortality rates during a specific time period of a certain population. A cohort life table, often referred to as a generation life table, is used to represent the overall mortality rates of a certain population's entire lifetime. They must have had to be born during the same specific time interval. A
cohort life table is more frequently used because it is able to make a prediction of any expected changes in mortality rates of a population in the future. This type of table also analyzes patterns in mortality rates that can be observed over time.
Both of these types of life tables are created based on an actual population from the present, as well as an educated prediction of the experience of a population in the near future.
In order to find the true life expectancy average, 100 years would need to pass and by then finding that data would be of no use as healthcare is continually advancing.
Other life tables in historical demography may be based on historical records, although these often undercount infants and understate infant mortality, on comparison with other regions with better records, and on mathematical adjustments for varying mortality levels and life expectancies at birth.
From this starting point, a number of inferences can be derived.
*The
probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speakin ...
of surviving any particular year of age
*The remaining
life expectancy
Life expectancy is a statistical measure of the average time an organism is expected to live, based on the year of its birth, current age, and other demographic factors like sex. The most commonly used measure is life expectancy at birth ...
for people at different ages
Life tables are also used extensively in
biology
Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...
and
epidemiology
Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and determinants of health and disease conditions in a defined population.
It is a cornerstone of public health, and shapes policy decisions and evide ...
. An area that uses this tool is Social Security. It examines the mortality rates of all the people who have Social Security to decide which actions to take.
The concept is also of importance in
product life cycle management
Product life-cycle management (PLM) is the succession of strategies by business management as a product goes through its life-cycle. The conditions in which a product is sold (advertising, saturation) changes over time and must be managed as it ...
.
All mortality tables are specific to environmental and life circumstances, and are used to probabilistically determine expected maximum age within those environmental conditions.
Background
There are two types of life tables:
* ''Period'' or ''static'' life tables show the current probability of death (for people of different ages, in the current year)
* ''Cohort'' life tables show the probability of death of people from a given cohort (especially birth year) over the course of their lifetime.
Static life tables
sample individuals assuming a stationary population with overlapping generations. "Static life tables" and "cohort life tables" will be identical if population is in
equilibrium and environment does not change. If a population were to have a constant number of people each year, it would mean that the probabilities of death from the life table were completely accurate. Also, an exact number of 100,000 people were born each year with no
immigration
Immigration is the international movement of people to a destination country of which they are not natives or where they do not possess citizenship in order to settle as permanent residents or naturalized citizens. Commuters, tourists, a ...
or
emigration
Emigration is the act of leaving a resident country or place of residence with the intent to settle elsewhere (to permanently leave a country). Conversely, immigration describes the movement of people into one country from another (to permanent ...
involved.
"Life table" primarily refers to ''period'' life tables, as cohort life tables can only be constructed using data up to the current point, and distant projections for future mortality.
Life tables can be constructed using projections of future mortality rates, but more often they are a snapshot of age-specific mortality rates in the recent past, and do not necessarily purport to be projections. For these reasons, the older ages represented in a life table may have a greater chance of not being representative of what lives at these ages may experience in future, as it is predicated on current advances in medicine,
public health
Public health is "the science and art of preventing disease, prolonging life and promoting health through the organized efforts and informed choices of society, organizations, public and private, communities and individuals". Analyzing the det ...
, and safety standards that did not exist in the early years of this cohort. A life table is created by mortality rates and census figures from a certain population, ideally under a closed demographic system. This means that immigration and emigration do not exist when analyzing a cohort. A closed demographic system assumes that migration flows are random and not significant, and that immigrants from other populations have the same risk of death as an individual from the new population.
Another benefit from mortality tables is that they can be used to make predictions on demographics or different populations.
However, there are also weaknesses of the information displayed on life tables. One being that they do not state the overall health of the population. There is more than one disease present in the world, and a person can have more than one disease at different stages simultaneously, introducing the term
comorbidity
In medicine, comorbidity - from Latin morbus ("sickness"), co ("together"), -ity (as if - several sicknesses together) - is the presence of one or more additional conditions often co-occurring (that is, concomitant or concurrent) with a primary ...
. Therefore, life tables also do not show the direct correlation of mortality and morbidity.
The life table observes the mortality experience of a single generation, consisting of 100,000 births, at every age number they can live through.
Life tables are usually constructed separately for men and for women because of their substantially different
mortality rate
Mortality rate, or death rate, is a measure of the number of deaths (in general, or due to a specific cause) in a particular population, scaled to the size of that population, per unit of time. Mortality rate is typically expressed in units of d ...
s. Other characteristics can also be used to distinguish different risks, such as
smoking status, occupation, and socioeconomic class.
Life tables can be extended to include other information in addition to mortality, for instance health information to calculate health expectancy. Health expectancies such as
disability-adjusted life year
The disability-adjusted life year (DALY) is a measure of overall disease burden, expressed as the number of years lost due to ill-health, disability or early death. It was developed in the 1990s as a way of comparing the overall health and life ex ...
and
Healthy Life Years are the remaining number of years a person can expect to live in a specific health state, such as free of
disability
Disability is the experience of any condition that makes it more difficult for a person to do certain activities or have equitable access within a given society. Disabilities may be cognitive, developmental, intellectual, mental, physical, ...
. Two types of life tables are used to divide the life expectancy into life spent in various states:
* Multi-state life tables (also known as increment-decrements life tables) are based on transition rates in and out of the different states and to death
* Prevalence-based life tables (also known as the Sullivan method) are based on external information on the proportion in each state. Life tables can also be extended to show life expectancies in different
labor force
The workforce or labour force is a concept referring to the pool of human beings either in employment or in unemployment. It is generally used to describe those working for a single company or industry, but can also apply to a geographic reg ...
states or
marital status
Civil status, or marital status, are the distinct options that describe a person's relationship with a significant other. ''Married'', '' single'', ''divorced'', and ''widowed'' are examples of civil status.
''Civil status'' and ''marital stat ...
states.
Life tables that relate to maternal deaths and infant moralities are important, as they help form family planning programs that work with particular populations. They also help compare a country's average life expectancy with other countries.
Comparing life expectancy globally helps countries understand why one country's life expectancy is rising substantially by looking at each other's healthcare, and adopting ideas to their own systems.
Insurance applications
In order to price
insurance
Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to hedge ...
products, and ensure the solvency of insurance companies through adequate reserves, actuaries must develop projections of future insured events (such as death, sickness, and disability). To do this, actuaries develop mathematical models of the rates and timing of the events. They do this by studying the incidence of these events in the recent past, and sometimes developing expectations of how these past events will change over time (for example, whether the progressive reductions in mortality rates in the past will continue) and deriving expected rates of such events in the future, usually based on the age or other relevant characteristics of the population. An actuary's job is to form a comparison between people at risk of death and people who actually died to come up with a probability of death for a person at each age number, defined as qx in an equation.
When analyzing a population, one of the main sources used to gather the required information is insurance by obtaining individual records that belong to a specific population.
These are called mortality tables if they show death rates, and morbidity tables if they show various types of sickness or disability rates.
The availability of computers and the proliferation of data gathering about individuals has made possible calculations that are more voluminous and intensive than those used in the past (i.e. they crunch more numbers) and it is more common to attempt to provide different tables for different uses, and to factor in a range of non-traditional behaviors (e.g. gambling, debt load) into specialized calculations utilized by some institutions for evaluating risk. This is particularly the case in non-life insurance (e.g. the pricing of motor insurance can allow for a large number of risk factors, which requires a correspondingly complex table of expected claim rates). However the expression "life table" normally refers to human survival rates and is not relevant to non-life insurance.
The mathematics
The basic algebra used in life tables is as follows.
*
: the probability that someone aged exactly
will die before reaching age
.
*
: the probability that someone aged exactly
will survive to age
.
::
*
: the number of people who survive to age
:: note that this is based on a
radix or starting point, of
lives, typically taken as 100,000
::
::
*
: the number of people who die aged
last birthday
::
*
: the probability that someone aged exactly
will survive for
more years, i.e. live up to at least age
years
::
*
: the probability that someone aged exactly
will survive for
more years, then die within the following
years
::
* ''μ''
''x'' : the ''
force of mortality In actuarial science, force of mortality represents the instantaneous rate of mortality at a certain age measured on an annualized basis. It is identical in concept to failure rate, also called hazard function, in reliability theory.
Motivation a ...
'', i.e. the instantaneous mortality rate at age ''x'', i.e. the number of people dying in a short interval starting at age ''x'', divided by ''ℓ''
''x'' and also divided by the length of the interval.
Another common variable is
*
This symbol refers to central rate of mortality. It is approximately equal to the average force of mortality, averaged over the year of age.
Further descriptions:
The variable dx stands for the number of deaths that would occur within two consecutive age numbers. An example of this is the number of deaths in a cohort that were recorded between the age of seven and the age of eight.
The variable ''ℓx'', which stands for the opposite of ''dx'', represents the number of people who lived between two consecutive age numbers. ''ℓ'' of zero is equal to 100,000. The variable ''Tx'' stands for the years lived beyond each age number x by all members in the generation. ''Ėx'' represents the life expectancy for members already at a specific age number.
Ending a mortality table
In practice, it is useful to have an ultimate age associated with a mortality table. Once the ultimate age is reached, the mortality rate is assumed to be 1.000. This age may be the point at which life insurance benefits are paid to a survivor or annuity payments cease.
Four methods can be used to end mortality tables:
*The Forced Method: Select an ultimate age and set the mortality rate at that age equal to 1.000 without any changes to other mortality rates. This creates a discontinuity at the ultimate age compared to the penultimate and prior ages.
*The Blended Method: Select an ultimate age and blend the rates from some earlier age to dovetail smoothly into 1.000 at the ultimate age.
*The Pattern Method: Let the pattern of mortality continue until the rate approaches or hits 1.000 and set that as the ultimate age.
*The Less-Than-One Method: This is a variation on the Forced Method. The ultimate mortality rate is set equal to the expected mortality at a selected ultimate age, rather 1.000 as in the Forced Method. This rate will be less than 1.000.
Epidemiology
In
epidemiology
Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and determinants of health and disease conditions in a defined population.
It is a cornerstone of public health, and shapes policy decisions and evide ...
and public health, both standard life tables (used to calculate life expectancy), as well as the Sullivan and multi-state life tables (used to calculate health expectancy), are the most commonly mathematical used devices. The latter includes information on health in addition to mortality. By watching over the life expectancy of any year(s) being studied, epidemiologists can see if diseases are contributing to the overall increase in mortality rates.
Epidemiologists are able to help demographers understand the sudden decline of life expectancy by linking it to the health problems that are arising in certain populations.
See also
*
Age-adjusted life expectancy
Life expectancy is a statistical measure of the average time an organism is expected to live, based on the year of its birth, current age, and other demographic factors like sex. The most commonly used measure is life expectancy at birth ...
*
Actuarial present value The actuarial present value (APV) is the expected value of the present value of a contingent cash flow stream (i.e. a series of payments which may or may not be made). Actuarial present values are typically calculated for the benefit-payment or seri ...
*
Decrement table Decrement tables, also called life table methods, are used to calculate the probability of certain events.
Birth control
Life table methods are often used to study birth control effectiveness. In this role, they are an alternative to the Pearl Ind ...
*
Gompertz–Makeham law of mortality
The Gompertz–Makeham law states that the human death rate is the sum of an age-dependent component (the Gompertz function, named after Benjamin Gompertz), which increases exponentially with age and an age-independent component (the Makeham ter ...
*
Strategies for engineered negligible senescence
*
Survival analysis
Survival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysi ...
*
Service life
A product's service life is its period of use in service. Several related terms describe more precisely a product's life, from the point of manufacture, storage, and distribution, and eventual use.
Service life has been defined as "a product li ...
Notes
References
*
*
*
Further reading
*
External links
Human Life Table DatabaseHuman Mortality DatabaseCanadian Human Mortality DatabaseAustralian Human Mortality Database(AHMD)
The Japanese Mortality Database(JMD)
United States Mortality Database(USMDB)
Latin American Human Mortality Database(LAHMD)
Latin American Mortality Database(LAMBdA)
UN Model Life Tables for Developing CountriesUN Extended Model Life TablesWHO-Global Health Observatory Life TablesUK Government Actuary Department's Interim Life Tables*
ttps://www.cdc.gov/nchs/products/pubs/pubd/nvsr/nvsr.htm US CDC Vital Statistics Reportsbr>
Ehemu Database
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Actuarial science
Population
Statistical data types
Survival analysis