AgeStandardization

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Age-Standardization Decomposition
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Period Age-Specific Death Rate

• Death Rate for ages x to xn during the period
  spanning 0 to T

M is the death rate D is the number of deaths N
is the population
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Lexis Diagram
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Components of the Crude Death Rate

• Dropping the period notation

nCx is the proportion of the population between
ages x and xn
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Standardization

• CDR is a function of the mortality schedule AND
  the age distribution
• Changes in either or both affect the level of the
  CDR
• When comparing CDRs, it is important to isolate
  the source of the differences
• Differences in age-specific mortality rates?
• Differences in age distributions?
• Age standardization holds the age structure
  constant so that the only source of difference is
  the mortality schedule
• Same applies to any division of the population
  that produces differing rates (or proportions)

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Age-Standardized CDR ASCDR

• Replacing the n,x notation with i

The Age-Standardized Crude Death Rate is
Where Cs is a standard age distribution
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Selection of a Standard

• There is no correct way to choose a standard
• As the covariance between the standard and the
  schedule increases, so will the value of the
  standardized rate
• The average of the proportionate distributions
  being compared is a good choice in general

Where there are N distributions indexed over x
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Age Standardization CDR

• We want to compare the crude death rate from two
  populations
• P1 has lower child and higher old-age mortality
• P2 has higher child and lower old-age mortality
• P1s age distribution is almost constant,
  comparatively unloaded on young ages and loaded
  on old ages
• P2s age distribution is loaded on younger ages
  and unloaded on older ages

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Example Mortality Schedules
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Example Age Distributions
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Calculation of Standardized CDRs
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Comparison of CDRs
Crude Death Rate
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Standardization Income

• We want to compare male and female average income
  distributions for the working population
• The proportionate measure is the job
  category-specific average income, AIj, for the
  period 0 to T

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Job Category Standardized Average Income

• As with the CDR, AIj can be written as the
  product of two components the job
  category-specific average income and the
  proportion of the population holding jobs of each
  category

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An Employment Distribution Effect - Chart
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An Employment Distribution Effect
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An Average Income Distribution Effect - Chart
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An Average Income Distribution Effect
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A Joint Effect - Chart
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A Joint Effect
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Decomposition

• Decomposition refers to a technique that
  identifies the proportion of the difference
  between two crude death rates that results from
  the differences in the mortality schedules and
  the differences in the age distributions
• As with the standardization technique described
  earlier, this is a general technique that can be
  used with any crude proportion formed as the sum
  of proportionate distribution and a proportional
  measure

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Components of Difference in Crude Rates
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Derivation of Decomposition
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Composition Rate Contributions to Difference
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Decomposition Example CDR
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Check Decomposition