15.2: Life Tables

A life table is a statistical tool that summarizes the mortality and survival patterns of a population, providing detailed insights into the likelihood of survival or death across different age intervals within a cohort. By organizing data on survival probabilities and mortality rates, life tables offer a clear snapshot of population dynamics over time. They are extensively used in demography, public health, actuarial science, and ecology to analyze life expectancy, design health interventions, estimate insurance risks, and study species survival patterns in various ecosystems. In general, a typical life table is divided into several key columns:

1. Age Interval: Represents specific age ranges. This column breaks the population into distinct intervals, such as 0-5 years, 5-10 years, etc.
2. Number Alive: Indicates the number of individuals surviving to the start of each age interval. Starting from a hypothetical cohort (often 100,000), this column shows how many are still alive at each age interval.
3. Number of Deaths: This shows the number of individuals who die within each interval. It is calculated by subtracting the number alive at the end of an interval from the number alive at the start.
4. Mortality Rate: Represents the probability of dying during the age interval for those alive at the beginning of the interval. It provides an age-specific likelihood of death.
5. Survival Probability: This represents the probability of surviving the age interval. It is the complement of the mortality rate.
6. Life Expectancy: Indicates the average remaining years an individual of age (x) is expected to live. This is computed by summing the person-years lived by those alive in each subsequent age group and dividing by the number alive at age (x).

Life tables can be categorized into cohort life tables, which track a group of individuals born during the same period over their lifetimes, and period life tables, which offer a snapshot of mortality rates for a population at a specific point in time.These tables are invaluable for understanding population health, forecasting future lifespans, calculating life insurance premiums, and comparing survival patterns across populations or groups. For example, they can highlight differences in life expectancy between countries or assess the impact of specific interventions on survival rates.

A life table or a mortality table represents the survival patterns of a population.

It comprises multiple columns, each serving a practical purpose, starting with time intervals in the first column.

The second column lists the number of individuals, patients, or subjects at the start of the study, and the third column lists those who died during the interval.

The fourth column indicates the number of people missing follow-ups, and the fifth column shows the number of people who withdrew alive during the interval.

The sixth column presents the effective number of participants exposed to the risk under study.

The count is considered effective because it adjusts for the participants who were either withdrawn alive or lost to follow-up, assuming that withdrawals happen uniformly throughout the interval.

It is typically estimated that withdrawals occur midway through the interval, leading to a reduction by half in the denominator for calculating risks.

The following two columns are conditional probabilities of death and survival. They are typically calculated as follows.

Finally, the last column measures cumulative survival rates across all intervals.