1. Adjusted Rates - Direct Standardization

2. Population A 50,000 people 4,000 cancer deaths in a year crude rate = 800 per 10,000 Population B 52,000 people 5,080 cancer deaths in a year crude rate = 977 per 10,000 Population B has a higher crude rate. Does this mean that the risk of cancer death is greater in “B”? Are there greater environmental risks in “B”? Population B has a higher crude rate. Does this mean that the risk of cancer death is greater in “B”? Are there greater environmental risks in “B”? Overall rates, e.g., obtained by dividing total cancer deaths by total population. Crude Rates

3. Age DeathsPop. Rate /10,000DeathsPop. Rate /10,000 30-39 40010,000 400802,000 400 40-49 60010,000 6003005,000 600 50-59 80010,000 800 10,000 800 60-691,00010,0001,0001,50015,0001,000 70-791,20010,0001,2002,40020,0001,200 Totals4,00050,000800 (crude) 5,08052,000 977 (crude) Population “A”Population “B” Is it riskier to live in population “B”? Why are the overall (crude) death rates different? / / Age-Specific Rates

4. Pop. B Pop. A Age Age is an additional factor that is affecting the comparison. (confounding)

5. (Wgt.) Rate (Wgt.) Rate AgePop.% Deaths /10k Pop. % Deaths/10k 30-3910,00020% 400 400 2,000 3.85% 80 400 40-4910,00020% 600 600 5,000 9.62% 300 600 50-5910,00020% 800 80010,00019.23% 800 800 60-6910,00020%1,0001,00015,00028.85% 1,5001,000 70-7910,00020%1,2001,20020,00038.46% 2,4001,200 50,0004,00052,000 5,080 Crude rate - 4,000/50,000 = 800/10,000 Crude rate = 5,080/52,000 = 977/100,000 A Crude Rate Is a Weighted Average of Age-Specific Rates Young Old

6. (Wgt.) Rate (Wgt.) Rate AgePop.% Deaths /10k Pop. % Deaths/10k 30-3910,00020% 400 400 2,000 3.85% 80 400 40-4910,00020% 600 600 5,000 9.62% 300 600 50-5910,00020% 800 80010,00019.23% 800 800 60-6910,00020%1,0001,00015,00028.85% 1,5001,000 70-7910,00020%1,2001,20020,00038.46% 2,4001,200 50,0004,00052,000 5,080 Crude rate - 4,000/50,000 = 800/10,000Crude rate = 5,080/52,000 = 977/100,000.20 x 400 = 80.0385 x 400 = 15.40.20 x 600 = 120.0962 x 600 = 57.72.20 x 800 = 160.1923 x 800 = 153.84.20 x 1,000 = 200.2885 x 1,000 = 288.50.20 x 1,200 = 240.3846 x 1,200 = 461.52 SUM 800 SUM 977 The crude rate is weighted by the age distribution. A Crude Rate Is a Weighted Average of Age-Specific Rates

7. How would the overall cancer mortality rates compare if the age distributions were the same? What if two populations have different age distributions and age affects the cancer rate …? The Real Question

8. If populations being compared have different distributions with respect to age, or other factors, …one can calculate adjusted rates that take into account differences in the structure of the populations being compared. The adjusted rates artificially make the two populations have identical distributions of the confounder (age, race, gender, etc.). Basically, we ask the question, “What if the population distributions were (weighted) the same with respect to the confounder? Then, how would the rates compare? Adjustment (Standardization)

9. “I don’t know about this Florida thing. All I know is that I had two perfectly healthy 65 year old parents. They move down to Florida and then, bang, thirty years later they’re dead. I don’t know … do you think it’s something in the air or the water down there?” Comedian Robert Klein:

10. FloridaAlaska Number of deaths 131,902 2,116 Total population 12,340,000 530,000 Crude mortality rate \(per 100,000) 1,069 399 The crude rates are clearly different. Does this mean that it is riskier to live in Florida? If you are about to retire, would it be better to move to Alaska? Death Rates In Florida & Alaska

11. Florida % of totalRate per Alaska % of totalRate per AgePop. (Weight)100,000 Pop. (Weight) 100,000 <5 850,000 7% 284 60,000 11% 274 5-19 2,280,000 18% 57 130,000 25% 65 20-44 4,410,000 36% 198 240,000 45% 188 45-64 2,600,000 21% 815 80,000 15% 629 >65 2,200,000 18%4,425 20,000 4%4,350 Totals12,340,000 100% 530,000 100% FloridaAlaska Crude mortality rates (per 100,000) 1,069 399 The crude rates are very different, but crude rates are weighted averages of the age-specific rates, and Florida’s population is weighted more heavily with older people. The comparison is confounded by age differences. This contributes 18% to the overall rate. Note: The Age-Specific Rates are Similar

12. The Solution: use each population’s actual age-specific rates, but calculate a summary rate using a single (standard) age distribution (i.e. artificially weight them the same with respect to age distribution.) This is adjustment by Direct standardization. The “adjusted” rates are artificial, but they provide summary rates that can be compared without confounding by age differences. This is adjustment by Direct standardization. The “adjusted” rates are artificial, but they provide summary rates that can be compared without confounding by age differences. Direct Standardization

13. .07 x 284 = 19.88.07 x 274 = 19.18.18 x 57 = 10.26.18 x 65 = 11.70.36 x 198 = 71.28.36 x 188 = 67.68.21 x 815 = 171.15.21 x 629 = 132.09.18 x 4,425 = 796.50.18 x 4,350 = 783.00 SUM 1,069/ 100,000 pop. SUM 1,014/ 100,000 pop. Florida % of totalRate per Alaska % of totalRate per AgePop. (Weight)100,000 Pop. (Weight) 100,000 <5 850,000 7% 284 60,000 11% 274 5-19 2,280,000 18% 57 130,000 25% 65 20-44 4,410,000 36% 198 240,000 45% 188 45-64 2,600,000 21% 815 80,000 15% 629 >65 2,200,000 18%4,425 20,000 4%4,350 Totals 12,340,000 100% 530,000 100% Florida As The Standard: (Age-adjusted) Adjusted Mortality Rates (#1)

14. Average of Florida & Alaska Distributions as the Standard: Florida Alaska Age % Pop. % Pop. Average <5 7% 11% (9.0%) 5-19 18% 25% (21.5%) 20-44 36% 45%(40.5%) 45-64 21% 15% (18.0%) >65 18% 4%(11.0%) 100%100%100% Weight Rate.090 x 284 = 25.56.090 x 274 = 24.66.215 x 57 = 12.26.215 x 65 = 13.98.405 x 198 = 80.19.405 x 188 = 76.14.180 x 815 = 146.70.180 x 629 = 113.22.110 x 4,425 = 486.75.110 x 4,350 = 478.50 SUM 751/ 100,000 pop. SUM 707/ 100,000 pop. Age-adjusted Adjusted Mortality Rates (#2)

15. 1988 U.S. Population as the Standard: Florida Alaska Age % Pop. % Pop. 1988 U.S. <5 7% 11% (7%) 5-19 18% 25% (22%) 20-44 36% 45%(40%) 45-64 21% 15% (19%) >65 18% 4%(12%) 100%100%100% Weight Rate.07 x 284 = 19.88.07 x 274 = 19.18.22 x 57 = 12.54.22 x 65 = 14.30.40 x 198 = 79.20.40 x 188 = 75.20.19 x 815 = 154.85.19 x 629 = 119.51.12 x 4,425 = 531.00.12 x 4,350 = 522.00 SUM 797/ 100,000 pop.SUM 750/ 100,000 pop. Adjusted Mortality Rates (#3)

16. Provides summary rates (all ages) that remove the unwanted effects of differences in the distributions of confounders in the populations. However, the adjusted rates are not real. (Only good for comparison.) Standardization doesn’t always make the two rates more similar (can be more different or no difference). It just allows a fairer comparison after ironing out some of the “other” differences that might be exaggerating or masking differences between the populations. Direct standardization may involve more than 2 groups. Adjustment By Direct Standardization

17. Death Rates in Weymouth Versus Woburn Look at the crude rates. Look at the adjusted rates. How is the comparison affected by adjusting for a factor, such as age? Are the apparent differences greater or smaller? –Did age differences exaggerate differences between the two groups? –Did age differences mask differences between the groups? Was there confounding by age?

18. Crude Adjusted Weymouth Woburn Crude: 250/10,000 vs. 750/10,000 Age Adjusted: 376/10,000 vs. 383/10,000 What is your interpretation? Did age differences have a confounding effect? Were the populations different after adjusting for age? Compare The Crude & Adjusted Rates #1

19. Crude Adjusted Weymouth Woburn Crude: 250/10,000 vs. 750/10,000 Adjusted: 376/10,000 vs. 512/10,000 #2 What is your interpretation? Did age differences have a confounding effect? Were the populations different after adjusting for age? Compare The Crude & Adjusted Rates

20. Weymouth Woburn Crude Adjusted Crude: 250/10,000 vs. 750/10,000 Adjusted: 306/10,000 vs. 813/10,000 Crude Adjusted #3 What is your interpretation? Did age differences have a confounding effect? Were the populations different after adjusting for age? Compare The Crude & Adjusted Rates

21. Crude: 250/10,000 vs. 266/10,000 Adjusted: 276/10,000 vs. 450/10,000 Weymouth Woburn Crude Adjusted #4 What is your interpretation? Did age differences have a confounding effect? Were the populations different after adjusting for age? Compare The Crude & Adjusted Rates

22. Age-adjusted to the 2000 U.S. standard population Age-adjusted mortality rates, by race & ethnicity, MA 2001 1,050 813 617 452 Black non- Hispanic White non- Hispanic Asian/PI 0 200 400 600 800 1,000 1,200 Age-adjusted rate/100,000

24. 1980 1985 1990 1992 It’s The Same Population, But At Multiple Times (It’s Like Comparing Multiple Populations)