Life table

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Life table method is for estimating mortality of a population in time.

Procedure

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.

See also

• 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.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