Life table: Difference between revisions

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{{method}}
[[Category:Health effects]]
[[Category:Health effects]]
{{progression class|progression=Full draft|curator=THL|date=2016-04-09}}
{{method|moderator=Virpi Kollanus}}
'''Life table''' method is for estimating mortality of a population in time.  
'''Life table''' method is for estimating mortality of a population in time.  


==Scope==
== Question ==


==Definition==
How should the life expectancy be measured for an individual or a population?


==Procedure==
== Answer ==
 
The life expectancy Y is
 
<math> Y = \sum_i (S_i t_i + (S_{i-1} - S_i)(t_i/2)),</math>
 
where S<sub>i</sub> 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 [[exposure-response relationship]]s are estimated from log-linear models:
Often the [[exposure-response relationship]]s are estimated from log-linear models:
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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<sub>0</sub> (survival in the beginning) equals 1.
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<sub>0</sub> (survival in the beginning) equals 1.


As we previously showed, the mortality rate can be expressed as k = exp(&alpha; + &beta; x), and thus the survival over time period i with constant rate is
As we previously showed, the mortality rate can be expressed as k = exp(&alpha; + &beta; x), and thus the survival over one time period with a constant mortality rate is


  S<sub>i</sub> = S<sub>0</sub> exp( -exp(&alpha;<sub>i</sub> + &beta; x) t<sub>i</sub>),
  S = S<sub>0</sub> exp( -exp(&alpha; + &beta; x) t),


and the survival over several consequent time periods is (assuming that changes in exposure are reflected in mortality with only a small delay).
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 = &Pi;<sub>i</sub> (exp( -exp(&alpha;<sub>i</sub> + &beta; x<sub>i</sub>) t<sub>i</sub>)).
  S = &Pi;<sub>i</sub> (exp( -exp(&alpha;<sub>i</sub> + &beta; x<sub>i</sub>) t<sub>i</sub>)).


The life years lived is  
The life years lived Y is  


  Y = &Sigma;<sub>i</sub> (S<sub>i</sub>t<sub>i</sub> + (1-S<sub>i</sub>)(1/2 t<sub>i</sub>)),
  Y = &Sigma;<sub>i</sub> (S<sub>i</sub>t<sub>i</sub> + (S<sub>i-1</sub> - S<sub>i</sub>)(1/2 t<sub>i</sub>)),


assuming that those who died, lived half of the period on average.
assuming that those who died, lived half of the period on average.


===Management===
You can use this model: [[:Image:Impact calculation tool.ANA|Impact calculation tool.ANA]].


==See also==
==See also==
{{defend|1 |[[Life tables]] should be merged with this page.|--[[User:Jouni|Jouni]] 09:14, 19 May 2010 (UTC)}}


* http://www.who.int/whosis/database/life_tables/life_tables_process.cfm?path=whosis,life_tables&language=english
* 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/healthinfo/nationalburdenofdiseasemanual.pdf
* http://www.who.int/whosis/database/core/core_select_process.cfm
* http://www.who.int/whosis/database/core/core_select_process.cfm
* http://www.iom-world.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

Latest revision as of 08:37, 9 April 2016

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The quality was last checked: 2016-04-09.


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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Y = \sum_i (S_i t_i + (S_{i-1} - S_i)(t_i/2)),}

where Si 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 exposure-response relationships are estimated from log-linear 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 exposure-response function (ERF). ERF is assumed to be exponential.

Relative risk (RR) between two exposure levels x0 and x is 

RR = p(x)/p(x0).

Therefore, 

ln(RR) = α + β x - (α + β x0) <=> β = ln(RR)/(x - x0)

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 = S0 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, S0 (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 = S0 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 = Πi (exp( -exp(αi + β xi) ti)).

The life years lived Y is 

Y = Σi (Siti + (Si-1 - Si)(1/2 ti)),

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)

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