# Life-tables and their demographic applications

One important method of assessing the health of a population is to ask how long people can expect to live.  Life expectancy, usually reported at birth although it can be applied to other ages as well, is a commonly used summary measure which can also be used to compare against countries.  Life expectancy is calculated using life tables.

Life tables

A life 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 is:

• the probability of surviving any particular year of age
• the 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.

Life tables are also used in biology.

Construction of life tables

Age specific mortality rates are applied to a notional population, typically of 100,000.  Starting at birth, the probability of dying in each period is applied to the number of people surviving to the beginning of the period, so that the initial figure slowly reduces to zero. The different elements required for a life table include (using standard notations):

 Ix Number of survivors at age x nqx Probability of dying between age x and x+n nDx Number of deaths between age x and x+n nLx Number of person years lived between age x and x+n Tx Total number of person years lived after age x ex Life expectancy at age x

This sort of life table is based on current age-specific death rates for each age or age band used and are called period life tables and are the most frequently used type.  In contrast, actual life expectancy of a particular birth cohort can only be calculated when everyone in this cohort is dead.  This approach uses a cohort life table and requires data over many years to prepare just a single complete cohort life table.

Example

An example of how a life table can be constructed and the mathematics involved can be downloaded from the simple interactive statistical analysis website http://www.quantitativeskills.com/downloads/#Lifetable [accessed 07/01/2016].

Strength

Summary measure of mortality providing an overall picture of mortality, allowing countries and regions to be compared.

Weaknesses

Hypothetical measure that has the potential to be misunderstood by general public/media.

It does not say much about who is still alive, and their quality of life; for example, how many years are lived with disability before dying.  This has led to attempts to bring together morbidity and mortality, with measures such as Health Adjusted Life Expectancy and Disability Adjusted Life Years.

This is calculated by subtracting from the life expectancy a figure which is the number of years lived with disability multiplied by a weighting to represent the effect of the disability.

If       A = years lived healthily

B = years lived with disability

A+B = life expectancy

A+fB = healthy life expectancy, where f is a weighting to reflect
disability level.

N.B. This raises all sorts of moral questions on who defines and measures disability level and how they do it.

Conversely, DALYs combine death and years lived with disability to estimate the burden of disease on populations, and DALYs were used in the Global Burden of Disease study to enable mortality and morbidity comparisons across countries.  Weightings were applied to conditions by using the time trade off approach, in which people were asked to consider living more years in imperfect health compared with fewer years in perfect health.  The study also placed more weight on the life of a young adult compared with a new born.

http://www.who.int/healthinfo/bodproject/en/index.html [accessed 07/01/2016].

Potential Years of Life Lost (PYLL)

A measure related to HALE and DALY, this measure attempts to quantify the potential years of life lost by looking at average age of death from conditions compared to average life expectancy. PYLL can be expressed absolutely or as a rate relative to the population at risk.

Other applications

Other characteristics can also be used to distinguish different risk factors for life expectancy, such as smoking-status, occupation, socio-economic class, and others.  More complex analyses for assessing cancer survival, that involves comparisons between two populations or a population in two points in time can also be undertaken.

In addition to public health domains, life tables are also used by insurance companies and actuary departments.

When used in biology, age specific fertility rates are also included in the calculations.

When data have not been available, such as in low income countries, life tables have been modelled using what data are available, usually childhood mortality data.

© M Goodyear & N Malhotra, 2007, M Goodyear 2016 and S Seager 2018