1. Samuel Clark Department of Sociology, University of Washington Institute of Behavioral Science, University of Colorado at Boulder Agincourt Health and Population Unit, University of the Witwatersrand Age-Standardization & Decomposition

2. 1 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. 2 Lexis Diagram

4. 3 Components of the Crude Death Rate Dropping the period notation: n C x is the proportion of the population between ages x and x+n

5. 4 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. 5 Age-Standardized CDR = ASCDR Replacing the n,x notation with i: The Age-Standardized Crude Death Rate is: Where C s is a standard age distribution

7. 6 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. 7 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. 8 Example Mortality Schedules

10. 9 Example Age Distributions

11. 10 Calculation of Standardized CDRs

12. 11 Comparison of CDRs Crude Death Rate

13. 12 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, AI j, for the period 0 to T:

14. 13 Job Category Standardized Average Income  As with the CDR, AI j 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. 14 An Employment Distribution Effect - Chart

16. 15 An Employment Distribution Effect

17. 16 An Average Income Distribution Effect - Chart

18. 17 An Average Income Distribution Effect

19. 18 A Joint Effect - Chart

20. 19 A Joint Effect

21. 20 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. 21 Components of Difference in Crude Rates

23. 22 Derivation of Decomposition

24. 23 Composition & Rate Contributions to Difference

25. 24 Decomposition Example: CDR

26. 25 Check Decomposition