Adjusted Rates
Direct Standardization
Crude Rates
Overall rates, e.g., obtained by dividing total
cancer deaths by total population.
Population A
Population B
50,000 people
52,000 people
4,000 cancer deaths in a year
5,080 cancer deaths in a year
crude rate = 800 per 10,000
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”?
Age-Specific Rates
Population “A”
Age
Deaths
Pop.
Population “B”
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)
/
/
• Is it riskier to live in population “B”?
• Why are the overall (crude) death rates different?
Age
Pop. A
Age
Pop. B
Age is an additional factor that
is affecting the comparison.
(confounding)
A Crude Rate Is a Weighted Average
of Age-Specific Rates
(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 = 977/100,000
Young
Old
Young
Old
A Crude Rate Is a Weighted Average of Age-Specific Rates
Age
30-39
40-49
50-59
60-69
70-79
(Wgt.)
Pop.
%
10,000 20%
10,000 20%
10,000 20%
10,000 20%
10,000 20%
50,000
Rate
Deaths /10k
400
400
600
600
800
800
1,000 1,000
1,200 1,200
4,000
Crude rate - 4,000/50,000 = 800/10,000
(Wgt.)
Pop. %
Deaths
2,000 3.85%
80
5,000 9.62%
300
10,000 19.23%
800
15,000 28.85% 1,500
20,000 38.46% 2,400
52,000
5,080
Rate
/10k
400
600
800
1,000
1,200
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.
What if two populations have different age
distributions and age affects the cancer rate …?
The Real Question
How would the overall cancer mortality rates
compare if the age distributions were the same?
Adjustment (Standardization)
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?
Comedian Robert Klein:
“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?”
Death Rates In Florida & Alaska
Number of deaths
Total population
Crude mortality rate
\(per 100,000)
Florida
131,902
12,340,000
Alaska
2,116
530,000
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?
Note: The Age-Specific Rates are Similar
Florida
% of total
Age
Pop.
(Weight)
<5
850,000
7%
5-19
2,280,000 18%
20-44
4,410,000 36%
45-64
2,600,000 21%
>65
2,200,000 18%
Totals 12,340,000 100%
This contributes 18%
to the overall rate.
Crude mortality rates
(per 100,000)
Rate per
100,000
284
57
198
815
4,425
Alaska % of total
Pop. (Weight)
60,000 11%
130,000 25%
240,000 45%
80,000 15%
20,000
4%
530,000 100%
Florida
1,069
Rate per
100,000
274
65
188
629
4,350
Alaska
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.
Direct Standardization
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.
Florida As
The Standard:
Florida
% of total
Age
Pop.
(Weight)
<5
850,000
7%
5-19
2,280,000 18%
20-44
4,410,000 36%
45-64
2,600,000 21%
>65
2,200,000 18%
Totals 12,340,000 100%
Adjusted Mortality Rates (#1)
.07 x
284 = 19.88
.18 x
57 = 10.26
.36 x
198 = 71.28
.21 x
815 = 171.15
.18 x 4,425 = 796.50
SUM
Rate per
100,000
284
57
198
815
4,425
Alaska % of total
Pop.
(Weight)
60,000 11%
130,000 25%
240,000 45%
80,000 15%
20,000
4%
530,000 100%
Rate per
100,000
274
65
188
629
4,350
.07 x
274 = 19.18
.18 x
65 = 11.70
.36 x
188 = 67.68
.21 x
629 = 132.09
.18 x 4,350 = 783.00
1,069/ 100,000 pop.
SUM
(Age-adjusted)
1,014/ 100,000 pop.
Adjusted Mortality Rates (#2)
Florida
Age
<5
5-19
20-44
45-64
>65
% Pop.
7%
18%
36%
21%
18%
100%
Average of Florida & Alaska
Distributions as the Standard:
Alaska
% Pop.
11%
25%
45%
15%
4%
100%
Weight Rate
.090 x
284 = 25.56
.215 x
57 = 12.26
.405 x
198 = 80.19
.180 x
815 = 146.70
.110 x 4,425 = 486.75
SUM 751/ 100,000 pop.
Average
(9.0%)
(21.5%)
(40.5%)
(18.0%)
(11.0%)
100%
Weight
Rate
.090 x
274 = 24.66
.215 x
65 = 13.98
.405 x
188 = 76.14
.180 x
629 = 113.22
.110 x 4,350 = 478.50
SUM 707/ 100,000 pop.
Age-adjusted
Adjusted Mortality Rates (#3)
Florida
Age
<5
5-19
20-44
45-64
>65
% Pop.
7%
18%
36%
21%
18%
100%
Alaska
% Pop.
11%
25%
45%
15%
4%
100%
Weight Rate
.07 x
284 = 19.88
.22 x
57 = 12.54
.40 x
198 = 79.20
.19 x
815 = 154.85
.12 x 4,425 = 531.00
SUM
797/ 100,000 pop.
1988 U.S. Population
as the Standard:
1988 U.S.
(7%)
(22%)
(40%)
(19%)
(12%)
100%
Weight
Rate
.07 x
274 = 19.18
.22 x
65 = 14.30
.40 x
188 = 75.20
.19 x
629 = 119.51
.12 x 4,350 = 522.00
SUM
750/ 100,000 pop.
Adjustment By Direct Standardization
•
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.
Death Rates in Weymouth Versus Woburn
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?
#1
Compare The Crude & Adjusted Rates
What is your interpretation?
Did age differences have a confounding effect?
Were the populations different after adjusting for age?
800
600
Crude:
Weymouth
Woburn
250/10,000 vs. 750/10,000
400
200
0
Crude
800
600
Age
Adjusted: 376/10,000 vs. 383/10,000
400
200
0
Adjusted
#2
Compare The Crude & Adjusted Rates
What is your interpretation?
Did age differences have a confounding effect?
Were the populations different after adjusting for age?
800
600
Weymouth
Crude:
Woburn
250/10,000 vs. 750/10,000
400
200
0
Crude
800
600
Adjusted: 376/10,000 vs. 512/10,000
400
200
0
Adjusted
#3
Compare The Crude & Adjusted Rates
What is your interpretation?
Did age differences have a confounding effect?
Were the populations different after adjusting for age?
800
600
Crude:
Weymouth
Woburn
250/10,000 vs. 750/10,000
400
200
0
Crude
800
600
Adjusted: 306/10,000 vs. 813/10,000
400
200
0
Adjusted
#4
Compare The Crude & Adjusted Rates
What is your interpretation?
Did age differences have a confounding effect?
Were the populations different after adjusting for age?
800
600
Weymouth
Crude:
Woburn
250/10,000 vs. 266/10,000
400
200
0
Crude
800
600
Adjusted: 276/10,000 vs. 450/10,000
400
200
0
Adjusted
Age-adjusted mortality rates, by race & ethnicity, MA 2001
Age-adjusted rate/100,000
1,200
1,050
1,000
813
800
617
600
452
400
200
0
Black non- White nonHispanic
Hispanic
Hispanic
Asian/PI
Age-adjusted to the 2000 U.S. standard population
It’s The Same Population,
But At Multiple Times
(It’s Like Comparing
Multiple Populations)
1990
1985
1980
1992