5.1 Mortality measures and life tables

Mortality measures and life tables are crucial tools for understanding population health and longevity. They provide insights into death rates, survival probabilities, and life expectancy across different age groups and populations.

These measures help researchers and policymakers identify trends, compare populations, and make informed decisions. From basic rates like crude death rate to complex analyses using life tables, these tools offer a comprehensive view of mortality patterns and their implications for society.

Mortality Measures and Calculations

Fundamental Mortality Rates

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• Crude death rate (CDR) measures overall mortality in a population
  • Calculated by dividing total deaths by total population size
  • Typically expressed per 1,000 individuals
  • Formula: $CDR = \frac{\text{Total deaths}}{\text{Total population}} \times 1,000$
  • Example: If a population of 100,000 experiences 800 deaths in a year, the CDR would be 8 per 1,000
• Age-specific mortality rates (ASMR) analyze mortality patterns across life stages
  • Measure deaths in a specific age group relative to that group's population
  • Allow for more detailed analysis than CDR
  • Formula: $ASMR = \frac{\text{Deaths in age group}}{\text{Population in age group}} \times 1,000$
  • Example: The ASMR for ages 65-69 might be 20 per 1,000, while for ages 20-24 it might be 1 per 1,000
• Infant mortality rate (IMR) serves as a critical indicator of population health
  • Calculated as deaths of children under one year per 1,000 live births in a given year
  • Formula: $IMR = \frac{\text{Deaths under age 1}}{\text{Live births}} \times 1,000$
  • Example: An IMR of 5 means 5 infants die per 1,000 live births

Advanced Mortality Measures

• Standardized mortality ratios (SMR) enable accurate comparisons between populations
  • Adjust for differences in age structure between populations
  • Allow comparisons across different groups or time periods
  • Formula: $SMR = \frac{\text{Observed deaths}}{\text{Expected deaths}} \times 100$
  • Example: An SMR of 120 indicates 20% more deaths than expected based on the standard population
• Maternal mortality ratio (MMR) reflects risk associated with pregnancy and childbirth
  • Measures maternal deaths per 100,000 live births
  • Formula: $MMR = \frac{\text{Maternal deaths}}{\text{Live births}} \times 100,000$
  • Example: An MMR of 10 means 10 maternal deaths occur per 100,000 live births
• Cause-specific mortality rates focus on deaths from particular causes
  • Provide insights into leading causes of death within a population
  • Calculated for specific diseases or external factors (heart disease, cancer)
  • Formula: $\text{Cause-specific rate} = \frac{\text{Deaths from specific cause}}{\text{Total population}} \times 100,000$
  • Example: A lung cancer mortality rate of 50 per 100,000 indicates 50 deaths from lung cancer per 100,000 population

Life Table Structure and Analysis

Life Table Components

• Life tables present comprehensive summaries of population mortality experiences
  • Organized by age intervals (typically 1-year or 5-year groups)
  • Contain columns for age, probability of dying, survivors, deaths, person-years lived, and life expectancy
  • Example: A life table might show survival probabilities from birth to age 100 in 5-year intervals
• Radix represents the hypothetical starting cohort size
  • Usually set at 100,000 individuals
  • Serves as the basis for subsequent calculations in the life table
  • Example: If the radix is 100,000, all calculations will be based on this initial cohort size
• Life table columns provide specific information about mortality patterns
  • Age (x): The age interval
  • Probability of dying (qx): Likelihood of dying before the next age interval
  • Number of survivors (lx): Individuals still alive at the beginning of each age interval
  • Number of deaths (dx): Deaths occurring within each age interval
  • Person-years lived (Lx): Total years lived by the cohort between two consecutive ages
  • Life expectancy (ex): Average additional years of life expected at each age

Life Table Types and Assumptions

• Period life tables represent mortality conditions for a specific time period
  • Based on mortality rates observed in a particular year or set of years
  • Assume these rates remain constant for the hypothetical cohort throughout their lives
  • Example: A 2020 period life table would use mortality rates observed in 2020 for all future years
• Cohort life tables follow the mortality experience of a particular birth cohort
  • Track a group of individuals born in the same year throughout their lifetime
  • Reflect actual mortality experiences as they unfold over time
  • Example: A cohort life table for those born in 1950 would use observed mortality rates for this group from 1950 onward
• Multiple decrement life tables analyze competing risks or causes of death
  • Extend the basic life table concept to provide more detailed understanding
  • Account for various ways individuals can exit the population (death, migration)
  • Example: A multiple decrement table might show probabilities of dying from heart disease, cancer, and other causes separately

Life Table Functions and Interpretation

Probability and Survival Functions

• Probability of dying (qx) represents likelihood of death before next age interval
  • Calculated for each age group in the life table
  • Formula: $q_x = \frac{d_x}{l_x}$
  • Example: A qx of 0.02 for age 60 means a 2% chance of dying before reaching age 61
• Number of survivors (lx) shows individuals alive at beginning of each age interval
  • Reflects cumulative effect of mortality on the initial cohort
  • Decreases with age as deaths occur
  • Example: If lx at age 30 is 95,000, it means 95,000 individuals from the initial 100,000 survived to age 30
• Survival function (Sx) indicates proportion of initial cohort surviving to each age
  • Complement of the cumulative probability of dying
  • Formula: $S_x = \frac{l_x}{l_0}$
  • Example: An Sx of 0.75 at age 65 means 75% of the initial cohort survived to age 65

Life Expectancy and Mortality Rates

• Life expectancy (ex) represents average additional years of life expected at a given age
  • Assumes current mortality conditions persist
  • Formula: $e_x = \frac{T_x}{l_x}$
  • Example: A life expectancy of 40 years at age 20 means individuals aged 20 are expected to live, on average, to age 60
• Person-years lived (Lx) function represents total years lived by cohort between ages
  • Accounts for deaths occurring within the interval
  • Used in calculating life expectancy
  • Example: If Lx for ages 70-75 is 450,000, it means the cohort collectively lived 450,000 years during this 5-year period
• Mortality rate (mx) expresses ratio of deaths to person-years lived within age interval
  • Provides measure of force of mortality
  • Formula: $m_x = \frac{d_x}{L_x}$
  • Example: An mx of 0.05 for ages 80-84 means 5 deaths per 100 person-years lived in this age group

Comparing Mortality Experiences

Analytical Techniques

• Decomposition techniques quantify contributions to life expectancy differences
  • Analyze impact of different age groups or causes of death on overall life expectancy disparities
  • Used to compare populations or time periods
  • Example: Determining how much of the life expectancy gap between two countries is due to differences in infant mortality versus adult mortality
• Model life tables estimate mortality patterns for populations with incomplete data
  • Based on observed relationships in well-documented populations
  • Used when reliable mortality data unavailable
  • Example: Estimating mortality patterns for a developing country with limited vital registration using data from countries with similar characteristics
• Years of potential life lost (YPLL) quantifies premature mortality impact
  • Calculates years of life lost due to death before a specified age
  • Formula: $YPLL = \sum_{i=1}^{n} (L - a_i)$ Where L is the selected age limit, ai is the age at death for individual i
  • Example: If the age limit is 75, a death at age 25 contributes 50 years to YPLL

Advanced Life Table Applications

• Multistate life tables incorporate transitions between different states
  • Extend traditional life table concept
  • Analyze transitions between health conditions, marital statuses, etc
  • Example: A multistate life table might show probabilities of transitioning between healthy, disabled, and deceased states at different ages
• Period and cohort life expectancy comparisons reveal mortality improvements
  • Show how mortality changes affect different generations and age groups
  • Period life expectancy based on current mortality rates
  • Cohort life expectancy incorporates projected future improvements
  • Example: Comparing life expectancy at birth for those born in 1950 versus 2000 using both period and cohort approaches
• Life tables project future mortality patterns and population structures
  • Inform policy decisions and resource allocation
  • Used in areas such as healthcare and social services planning
  • Example: Projecting the number of individuals aged 85+ in 2050 to plan for future eldercare needs