A life table is a statistical tool used in demography, epidemiology, and actuarial science to summarize the mortality and survival experience of a population. It presents, for a hypothetical cohort of births, the probability of dying or surviving at each age (or age group).
Life tables are useful for calculating life expectancy, mortality risks, survival rates, and for making health, insurance, and population policy decisions.
Techniques in Preparing a Life Table
A life table is prepared in several systematic steps. The basic functions (columns) of a complete life table are:
- Age interval (x to x+n): Specific age or age group.
- lxl_xlx: Number surviving to exact age x – number of persons alive at the start of the age interval (from a hypothetical cohort, usually starting with 100,000 births).
- dxd_xdx: Number dying in age interval x to x+n – difference between survivors at beginning and end of interval.
- qxq_xqx: Probability of dying in the interval x to x+n – chance that a person aged x will die before reaching
- pxp_xpx: Probability of surviving – complement of
- LxL_xLx: Person-years lived in interval – total years lived by the cohort between ages x and x+n.
- TxT_xTx: Total person-years lived above age x – cumulative total of person-years from age x to last age.
- exe_xex: Expectation of life at age x – average number of years a person aged x is expected to live.
Techniques of Life Table Construction
There are two main techniques:
1. Complete Life Table
- Uses single-year age intervals (0, 1, 2, 3, … up to 85+).
- Provides detailed mortality and survival data for each exact age.
- Common in developed countries with reliable mortality statistics.
2. Abridged Life Table
- Uses wider age groups (e.g., 0, 1–4, 5–9, 10–14 … 70–74, 75+).
- Mortality probabilities are calculated for each age group instead of each year.
- Easier to prepare when data are limited or sample sizes are small.
- Widely used in developing countries where age-reporting is not precise.
Preparation of an Abridged Life Table
Steps:
- Start with observed mortality rates (mxm_xmx) for each age group.
- Convert to probability of dying (qxq_xqx) using formulas or standard approximations.
- For large age groups:
- Assume a radix (e.g., l0=100,000l_0 = 100,000l0=100,000) for the starting cohort.
- Calculate survivors (lxl_xlx) and deaths (dxd_xdx) across age groups.
- Compute person-years lived (Lx), total person-years (Tx), and life expectancy (ex).
Example (Simplified Abridged Life Table for Illustration Only)
| Age Group (x to x+n) | lx (survivors) | dx (deaths) | qx (prob. of dying) | Lx (person-years) | Tx (total yrs left) | ex (life expectancy) |
|---|---|---|---|---|---|---|
| 0 | 100,000 | 6,000 | 0.06 | 97,000 | 6,500,000 | 65.0 yrs |
| 1–4 | 94,000 | 2,000 | 0.021 | 372,000 | 6,403,000 | 68.1 yrs |
| 5–9 | 92,000 | 500 | 0.005 | 455,000 | 6,031,000 | 65.5 yrs |
| … | … | … | … | … | … | … |
(Table truncated for brevity — real abridged life tables extend until 80+ or 100+ years.)
Conclusion
- Life tables are fundamental tools in demography to measure mortality, survival, and life expectancy.
- Complete life tables use single-year intervals for precision.
- Abridged life tables use grouped ages, making them simpler and practical where detailed data is lacking.
- Both are essential in public health planning, actuarial science (insurance), and population studies.
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