Adjusted Rates -

Direct Standardization

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

AgeDeaths Pop.

Rate/10,000 Deaths Pop.

Rate/10,000

30-39 400 10,000 400 80 2,000 400

40-49 600 10,000 600 300 5,000 600

50-59 800 10,000 800 800 10,000 800

60-69 1,000 10,000 1,000 1,500 15,000 1,000

70-79 1,200 10,000 1,200 2,400 20,000 1,200

Totals 4,000 50,000 800

(crude)

5,080 52,000 977 (crude)

Population “A” Population “B”

• Is it riskier to live in population “B”?• Why are the overall (crude) death rates different?

/ /

Age-Specific RatesAge-Specific Rates

Pop. B

Pop. A

Age

Age

Age is an additional factor that is affecting the comparison.

(confounding)

(Wgt.) Rate (Wgt.) RateAge Pop. % Deaths /10k Pop. % Deaths /10k30-39 10,000 20% 400 400 2,000 3.85% 80 40040-49 10,000 20% 600 600 5,000 9.62% 300 60050-59 10,000 20% 800 800 10,000 19.23% 800 80060-69 10,000 20% 1,000 1,000 15,000 28.85% 1,500 1,00070-79 10,000 20% 1,200 1,200 20,000 38.46% 2,400 1,200

50,000 4,000 52,000 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

A Crude Rate Is a Weighted Average of Age-Specific Rates

Young Old Young Old

(Wgt.) Rate (Wgt.) RateAge Pop. % Deaths /10k Pop. % Deaths /10k30-39 10,000 20% 400 400 2,000 3.85% 80 40040-49 10,000 20% 600 600 5,000 9.62% 300 60050-59 10,000 20% 800 800 10,000 19.23% 800 80060-69 10,000 20% 1,000 1,000 15,000 28.85% 1,500 1,00070-79 10,000 20% 1,200 1,200 20,000 38.46% 2,400 1,200

50,000 4,000 52,000 5,080

Crude rate - 4,000/50,000 = 800/10,000 Crude 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

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

If populations being compared have different distributionswith 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)

“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:

Florida AlaskaNumber of deaths 131,902 2,116Total 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 & AlaskaDeath Rates In Florida & Alaska

Florida % of total Rate per Alaska % of total Rate perAge Pop. (Weight) 100,000 Pop. (Weight) 100,000<5 850,000 7% 284 60,000 11% 2745-19 2,280,000 18% 57 130,000 25% 6520-44 4,410,000 36% 198 240,000 45% 18845-64 2,600,000 21% 815 80,000 15% 629>65 2,200,000 18% 4,425 20,000 4% 4,350Totals 12,340,000 100% 530,000 100%

Florida AlaskaCrude 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 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

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.

Direct Standardization

.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 total Rate per Alaska % of total Rate perAge Pop. (Weight) 100,000 Pop. (Weight) 100,000<5 850,000 7% 284 60,000 11% 2745-19 2,280,000 18% 57 130,000 25% 6520-44 4,410,000 36% 198 240,000 45% 18845-64 2,600,000 21% 815 80,000 15% 629>65 2,200,000 18% 4,425 20,000 4% 4,350Totals 12,340,000 100% 530,000 100%

Florida As The Standard:

(Age-adjusted)

Adjusted Mortality Rates (#1)

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 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)

1988 U.S. Populationas 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 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)

• 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

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?

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800

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Crude

Adjusted

Weymouth Woburn Crude: 250/10,000 vs. 750/10,000

AgeAdjusted: 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

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Crude

Adjusted

Weymouth Woburn

Crude: 250/10,000 vs. 750/10,000

Adjusted: 376/10,000 vs. 512/10,000

#2What is your interpretation? Did age differences have a confounding effect?Were the populations different after adjusting for age?

Compare The Crude & Adjusted Rates

Weymouth Woburn

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800

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Crude

Adjusted

Crude: 250/10,000 vs. 750/10,000

Adjusted: 306/10,000 vs. 813/10,000

Crude

Adjusted

#3What is your interpretation? Did age differences have a confounding effect?Were the populations different after adjusting for age?

Compare The Crude & Adjusted Rates

Crude: 250/10,000 vs. 266/10,000

Adjusted: 276/10,000 vs. 450/10,000

Weymouth Woburn

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Crude

Adjusted

#4What is your interpretation? Did age differences have a confounding effect?Were the populations different after adjusting for age?

Compare The Crude & Adjusted Rates

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

Hispanic Asian/PI0

200

400

600

800

1,000

1,200A

ge-

ad

just

ed

rat

e/1

00

,00

0

19801985

19901992

It’s The Same Population, But At Multiple Times (It’s Like Comparing Multiple Populations)

It’s The Same Population, But At Multiple Times (It’s Like Comparing Multiple Populations)