NationMaster - Encyclopedia: Life table

In actuarial science, a life table (also called a mortality table or actuarial table) is a table which shows, for a person at each age, what the probability is that they die before their next birthday. From this starting point, a number of statistics can be derived and thus also included in the table: Image File history File links Download high resolution version (900x1189, 108 KB) Summary Licensing File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Actuary Actuarial science Life table ... Image File history File links Download high resolution version (900x1189, 108 KB) Summary Licensing File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Actuary Actuarial science Life table ... Actuarial science applies mathematical and statistical methods to finance and insurance, particularly to the assessment of risk. ... A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ...

the probability of surviving any particular year of age
remaining life expectancy for people at different ages
the proportion of the original birth cohort still alive.

Life tables are usually constructed separately for men and for women because of their substantially different mortality rates. Other characteristics can also be used to distinguish different risks, such as smoking-status, occupation, socio-economic class, and others. World map showing Human Life expectancy Life expectancy is the average number of years remaining for a living being (or the average for a class of living beings) of a given age to live. ... Mortality rate (the word mortality comes from mortal, which originates from Latin mors, death) is the number of deaths (from a disease or in general) per 1000 people and typically reported on an annual basis. ...

Life tables are also used in biology, and as an alternative to the Pearl Index in studies of birth control effectiveness. The Pearl Index, also called the Pearl rate, is a technique used in clinical trials for measuring the effectiveness of a birth control method. ...

1 Insurance applications
2 The mathematics of life tables
3 Life tables in biology
4 Life tables as an alternative to the Pearl Index
5 References
6 See also
7 External links

Insurance applications

In order to price insurance products, and ensure the solvency of insurance companies through adequate reserves, actuaries must develop projections of future insured events (such as death, sickness, disability, etc.). To do this, actuaries develop mathematical models of the causes of these events, as well as the amount and timing of the events. They do this by studying the incidence and severity of these events in the recent past, developing expectations about how the drivers of these past events will change over time (for example, whether the increase in life expectancy that has been experienced by most generations over prior generations will continue) and, accordingly, develop an expectation for what the timing and amount of such events will be into the future. These expectations usually take the form of tables of percentages indicating the number of such events that will occur in a population, usually based on the age or other relevant characteristics of the population. More specifically, they may be referred to as mortality tables (if they provide rates of mortality, or death), morbidity tables (if they provide rates of disability and recovery), or by other names if they cover other decrements. Insurance, in law and economics, is a form of risk management primarily used to hedge against the risk of potential financial loss. ... World map showing Human Life expectancy Life expectancy is the average number of years remaining for a living being (or the average for a class of living beings) of a given age to live. ...

The invention of computers and the proliferation of data gathering about individuals has led to fundamental changes in the way actuarial tables are computed for different uses, and a variety of emerging methods factor a range of non-traditional behaviors (e.g. gambling, debt load) into specialized calculations utilized by some institutions for evaluating risk.

The mathematics of life tables

To give an indication of how life tables are used, here are a few sample calculations. These samples may not be obvious to someone who has never studied probability theory, but are intended to introduce new ideas to people who have some understanding of discrete probability theory. Probability theory is the mathematical study of probability. ...

$,q_x$ : the probability that someone aged exactly $,x$ will die before their $,(x+1)$ ^th birthday
$,p_x$ : the probability of surviving from age $,x$ to age $,(x+1)$

$,p_x = 1-q_x$

$,l_x$ : the number of people who survive to age $,x$

note that this is based on a starting point of $,l_0$ lives, typically 100,000

$,l_{x + 1} = l_x cdot (1-q_x) = l_x cdot p_x$

$,{l_{x + 1} over l_x} = p_x$

$,d_x$ : the number of people who die aged $,x$

$,d_x = l_x-l_{x+1}$

$,{}_tp_x$ : the probability that someone aged exactly $,x$ will survive for $,t$ more years, i.e. live up to at least age $,x+t$ years

$,{}_tp_x = {l_{x+t} over l_x}$

Life tables in biology

When biologists use life tables, they will normally also include fertility for each ages. The extra parameter used is

$,m_x$ : expected number of progeny for an individual aged $,x$

Life tables as an alternative to the Pearl Index

When used to study birth control effectiveness, a life table calculates a separate effectiveness rate for each month of the study, as well as for a standard period of time (usually 12 months). Use of life tables eliminates time-related biases (i.e. the most fertile couples getting pregnant and dropping out of the study early, and couples becoming more skilled at using the method as time goes on), and in this way is superior to the more common Pearl Index.

In studies that use life tables, usually two kinds are created. Multiple-decrement life tables report net effectiveness rates which are useful for comparing competing reasons for couples dropping out of a study. Single-decrement life tables report gross effectiveness rates, which can be used to accurately compare one study to another.^[1]

References

^ Kippley, John; Sheila Kippley (1996). The Art of Natural Family Planning, 4th addition, Cincinatti, OH: The Couple to Couple League. ISBN 0926412132, 140-141., which cites:

Trussell J, Hatcher RA, Cates W, et al (1990). "A guide to interpreting contraceptive efficacy studies". Obstetrics and Gynecology 76: 558-567. PMID 2199875.
Potter RG (1966). "Application of life table techniques to measurement of contraceptive effectiveness". Demography 3 (2): 297-304.
Trussell J (1991). "Methodological pitfalls in the analysis of contraceptive failure". Statistics in medicine 10: 201-220. PMID 2052800.
Trussell J, Grummer-Strawn L (1991). "Further analysis of contraceptive failure of the ovulation method". American Journal of Obstetrics and Gynecology 165: 2054-2059. PMID 1755470.
Sheps MC (1966). "Characteristics of a ratio used to estimate failure rates: occurrences per person year of exposure". Biometrics 22: 310-321. PMID 5961447.
Trussell J, Kost K (1987). "Contraceptive failure in the United States: A critical review of the literature". Studies in family planning 18: 237-282. PMID 3318006.
Trussell J, Grummer-Strawn L (1990). "Contraceptive failure of the ovulation method of periodic abstinence". Family Planning Perspectives 22: 65-75. PMID 2189750.
Trussell J, Strickler J, Vaughan B (1993). "Contraceptive efficacy of the diaphragm, the sponge and the cervical cap". Family Planning Perspectives 25: 100-105, 135. PMID 8354373.

External links

Canadian Human Mortality Database
UK Government Actuary Department's Interim Life Tables
US CDC Mortality Reports

Categories: Population | Insurance | Actuarial science

Results from FactBites:

DRL life table (908 words)
	Table 1 is an example of a set of such rates for United States males in 1988 (taken from the Statistical Abstract of the U.S., 1990; you can find similar sets of rates in almost any almanac).
	To construct a life table from such data we first convert the death rates per thousand to rates per capita, by dividing each ASDR by 1000 (move the decimal point three places) as in Table 2.
	Table 4 shows what would happen if the mortality schedule represented by q were applied to a hypothetical group of 100,000 newborns (this hypothetical group is called the "radix").

The Table of Life and Death (481 words)
	Since that time, Zack has given his life to God and is dedicated to bringing the word of hope and the power of God to those still trapped in the big hole.
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	The deceiving thing about this table is that it's the one that your flesh is attracted to because of all it's frills and thrills.

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