🪵Intro to Demographic Methods Unit 7 – Life Tables & Survival Analysis in Demography
Life tables and survival analysis are fundamental tools in demography, providing insights into mortality patterns and longevity. These methods summarize population mortality experiences, track survival rates, and examine factors influencing lifespans. They're crucial for understanding demographic trends and informing policy decisions.
From historical roots in 17th-century mortality observations to modern applications in public health and insurance, life tables have evolved significantly. Today, demographers use various types of life tables and survival analysis techniques to study mortality, project population changes, and analyze the impacts of health interventions and social factors on lifespan.
Life tables summarize mortality experiences of a population over a specified period
Survival analysis examines the time until an event occurs (death, marriage, divorce)
Cohort life tables track the mortality experience of a specific group of individuals born during the same time period
Period life tables represent the mortality experience of a population during a specific time period, often a calendar year
Abridged life tables contain data for age intervals of 5 or 10 years, while complete life tables have single-year age intervals
Life expectancy at birth (e0) represents the average number of years a newborn is expected to live given the mortality rates of a specific period
Survival curves graphically represent the proportion of individuals surviving to each age, with the area under the curve equal to life expectancy
Historical Context
John Graunt's 1662 book "Natural and Political Observations Made Upon the Bills of Mortality" laid the foundation for modern life tables and demographic analysis
Early life tables were constructed using data from specific cities or regions (London, Breslau)
Edmond Halley developed the first modern life table in 1693 using data from Breslau, Germany
19th-century improvements in data collection and mathematical techniques led to the development of national life tables
Life tables played a crucial role in the development of actuarial science and the insurance industry
Advances in public health and medical technology during the 20th century led to significant increases in life expectancy and changes in the shape of survival curves
Types of Life Tables
Period life tables represent the mortality experience of a population during a specific time period, often a calendar year
Assume that age-specific mortality rates remain constant throughout the lifetime of a hypothetical cohort
Useful for comparing mortality patterns across populations or over time
Cohort life tables track the mortality experience of a specific group of individuals born during the same time period
Require data on the actual mortality experience of the cohort over their entire lifetime
Provide a more accurate representation of the cohort's mortality but are less timely than period life tables
Multiple decrement life tables analyze the impact of competing risks (causes of death) on mortality
Cause-deleted life tables estimate the impact of eliminating a specific cause of death on life expectancy
Multistate life tables model transitions between different states (marital status, health status) over the life course
Data Sources and Collection
Vital registration systems provide data on births, deaths, and causes of death
Coverage and quality of vital registration data vary across countries and time periods
Incomplete or inaccurate reporting of deaths can lead to biases in life table estimates
Census data provide information on population size and structure by age and sex
Used to estimate the population at risk of dying in each age group
Undercount or age misreporting can affect the accuracy of life table estimates
Sample surveys (demographic and health surveys) collect data on mortality and health in populations lacking reliable vital registration systems
Indirect estimation techniques (Brass methods, model life tables) are used when direct data on mortality are unavailable or incomplete
Constructing Life Tables
Begin with age-specific mortality rates (nMx) calculated from death counts and population estimates for each age group
Convert mortality rates to probabilities of dying (nqx) using assumptions about the distribution of deaths within age intervals
Calculate the number of survivors to each age (lx) starting with a hypothetical cohort of 100,000 live births (l0)
lx+n=lx∗(1−nqx)
Compute the number of person-years lived in each age interval (nLx) using assumptions about the distribution of deaths
nLx=n∗(lx+lx+n)/2 for most age groups
Special formulas used for the first and last age intervals
Calculate the total number of person-years lived above each age (Tx) by summing nLx values from the oldest to the youngest age
Compute life expectancy at each age (ex) by dividing Tx by lx
Survival Analysis Techniques
Kaplan-Meier estimator is a non-parametric method for estimating survival curves from censored data
Calculates the probability of surviving to each event time, conditional on surviving to the previous event time
Useful when the underlying distribution of survival times is unknown or does not follow a specific parametric model
Cox proportional hazards model is a semi-parametric regression method for analyzing the effect of covariates on survival times
Assumes that the hazard ratios between groups are constant over time
Estimates the baseline hazard function non-parametrically and the effects of covariates parametrically
Parametric survival models (exponential, Weibull, log-normal) assume that survival times follow a specific probability distribution
Allows for the estimation of survival curves and hazard functions based on the chosen distribution
More efficient than non-parametric methods when the distributional assumption is valid
Interpreting Results
Life expectancy at birth (e0) is a summary measure of mortality representing the average number of years a newborn is expected to live
Higher values indicate lower overall mortality
Comparisons across populations or over time should consider differences in the age structure and mortality patterns
Age-specific mortality rates (nMx) and probabilities of dying (nqx) provide insights into the age pattern of mortality
Typically high in infancy, low in childhood and early adulthood, and increasing exponentially at older ages
Deviations from this pattern can indicate unusual mortality risks or data quality issues
Survival curves depict the proportion of individuals surviving to each age
Steeper curves indicate higher mortality and shorter life expectancy
Shifts in the curve over time or differences between populations reflect changes in mortality patterns
Hazard ratios from Cox models quantify the relative risk of an event between groups with different covariate values
Ratios greater than 1 indicate increased risk, while ratios less than 1 suggest decreased risk
Statistical significance and confidence intervals should be considered when interpreting hazard ratios
Real-World Applications
Life insurance and annuity pricing rely on accurate life tables to determine premiums and benefits
Pension and social security systems use life tables to project future costs and adjust eligibility ages based on changes in life expectancy
Public health researchers use life tables to monitor population health, identify disparities, and evaluate the impact of interventions
Epidemiologists employ survival analysis to study the incidence and progression of diseases and the efficacy of treatments
Demographers use life tables and survival analysis to project population size and structure, estimate healthy life expectancy, and analyze the determinants of longevity
Actuaries apply life table and survival analysis techniques to assess and manage risks in various industries (insurance, finance, healthcare)
Government agencies and policymakers rely on life table indicators to inform resource allocation, set public health priorities, and develop social policies