Life table
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Life table method is for estimating mortality of a population in time.
Question
How should the life expectancy be measured for an individual or a population?
Answer
The life expectancy Y is
where S_{i} is survival at the end of time period i (with duration t) assuming that those who died, lived half of the period on average.
Rationale
Often the exposureresponse relationships are estimated from loglinear models:
ln p(x) = α + β x,
where p(x) is the probability of event at exposure level x, exp(α) is the background risk, and β is the slope for the exposureresponse function (ERF). ERF is assumed to be exponential.
Relative risk (RR) between two exposure levels x_{0} and x is
RR = p(x)/p(x_{0}).
Therefore,
ln(RR) = α + β x  (α + β x_{0}) <=> β = ln(RR)/(x  x_{0})
The life table is a table where the a) survival of and b) the years lived by a population are followed over the lifetime of the individuals in the population.
Assuming a constant rate of mortality (k) for a given time period, the survival S is
S = S_{0} exp(kt),
where t is the length of the time period. If we look at the survival conditional that the population is alive in the beginning, S_{0} (survival in the beginning) equals 1.
As we previously showed, the mortality rate can be expressed as k = exp(α + β x), and thus the survival over one time period with a constant mortality rate is
S = S_{0} exp( exp(α + β x) t),
and the survival over several consequent time periods (from the beginning up to time period i) is (assuming that changes in exposure are reflected in mortality with only a small delay).
S = Π_{i} (exp( exp(α_{i} + β x_{i}) t_{i})).
The life years lived Y is
Y = Σ_{i} (S_{i}t_{i} + (S_{i1}  S_{i})(1/2 t_{i})),
assuming that those who died, lived half of the period on average.
Management
You can use this model: Impact calculation tool.ANA.
See also
←1: . Life tables should be merged with this page. Jouni 09:14, 19 May 2010 (UTC) (type: truth; paradigms: science: defence)
 http://www.who.int/whosis/database/life_tables/life_tables_process.cfm?path=whosis,life_tables&language=english
 http://www.who.int/healthinfo/nationalburdenofdiseasemanual.pdf
 http://www.who.int/whosis/database/core/core_select_process.cfm
 http://www.iomworld.org/research/iomlifet.php
 http://www.who.int/healthinfo/global_burden_disease/tools_software/en/index.html
 http://www.who.int/healthinfo/global_burden_disease/tools_national/en/index.html