Age-Standardization & Decomposition

1. Age-Standardization & Decomposition

2. Period Age-Specific Death Rate Death Rate for ages x to x+n during the period spanning 0 to T: M is the death rate D is the number of deaths N is the population

3. Lexis Diagram

4. Components of the Crude Death Rate Dropping the period notation: nCx is the proportion of the population between ages x and x+n

5. 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)

6. 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

7. 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

8. 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 • P1’s age distribution is almost constant, comparatively unloaded on young ages and loaded on old ages • P2’s age distribution is loaded on younger ages and unloaded on older ages

9. Example Mortality Schedules

10. Example Age Distributions

11. Calculation of Standardized CDRs

12. Comparison of CDRs Crude Death Rate

13. 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:

14. 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:

15. An Employment Distribution Effect - Chart

16. An Employment Distribution Effect

17. An Average Income Distribution Effect - Chart

18. An Average Income Distribution Effect

19. A Joint Effect - Chart

20. A Joint Effect

21. 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

22. Components of Difference in Crude Rates

23. Derivation of Decomposition

24. Composition & Rate Contributions to Difference

25. Decomposition Example: CDR

26. Check Decomposition