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”?

Overall rates, e.g., obtained by dividing total

cancer deaths by total population.

Crude Rates

Age Deaths

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 Rates

Pop. B

Pop. A

Age

Age

Age is an additional factor that

is affecting the comparison.

Confounding Effect of Age

(Wgt.) Rate (Wgt.) Rate

Age Pop. % Deaths /10k Pop. % Deaths /10k

30-39 10,000 20% 400 400 2,000 3.85% 80 400

40-49 10,000 20% 600 600 5,000 9.62% 300 600

50-59 10,000 20% 800 800 10,000 19.23% 800 800

60-69 10,000 20% 1,000 1,000 15,000 28.85% 1,500 1,000

70-79 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 = 977/10,000

A Crude Rate Is a Weighted Average

of Age-Specific Rates

Young Old Young Old

(Wgt.) Rate (Wgt.) Rate

Age Pop. % Deaths /10k Pop. % Deaths /10k

30-39 10,000 20% 400 400 2,000 3.85% 80 400

40-49 10,000 20% 600 600 5,000 9.62% 300 600

50-59 10,000 20% 800 800 10,000 19.23% 800 800

60-69 10,000 20% 1,000 1,000 15,000 28.85% 1,500 1,000

70-79 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 = 977/10,000

.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.

Crude Rate: 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 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)

“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 Alaska

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

Florida % of total Rate per Alaska % of total Rate per

Age Pop. (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 Alaska

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

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 per

Age Pop. (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)

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. 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 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

Was there confounding by age?

• 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?

Death Rates in Weymouth vs. Woburn

0

200

400

600

800

0

200

400

600

800

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?

#1 Compare The Crude & Adjusted Rates

0

200

400

600

800

0

200

400

600

800

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

Weymouth Woburn

0

200

400

600

800

0

200

400

600

800

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

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

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

Weymouth Woburn

0

200

400

600

800

0

200

400

600

800

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

Age-adjusted to the 2000 U.S. standard population

1,050

813

617

452

Black non- Hispanic

White non- Hispanic

Hispanic Asian/PI

0

200

400

600

800

1,000

1,200 A

ge-a

dju

ste

d r

ate

/100,0

00

Age-adjusted Mortality Rates

by Race & Ethnicity, MA 2001

Heart Disease Death Rates

by Race & Gender, MA

Rates are age-adjusted (direct method using the 1940 US population.

1980 1985

1990 1992

It’s The Same Population,

But At Multiple Times

(It’s Like Comparing

Multiple Populations)