Mapping Rates and Proportions

1
Mapping Rates and Proportions
2
Mapping Rates and Proportions

• Incidence rates
• Mortality rates
• Birth rates

• Prevalence
• Proportions
• Percentages

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Sample DataBreast Cancer Incidence in Iowa

• Years 1993-1996
• 7813 Cases (including in-situ)
• For each case Age, county
• Source State Health Registry of Iowa

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Geography and Population

• 99 counties
• Number of women 1,061,096 (ages 20)
• Population available for each county by age
  group.
• Age groups 20-24, 25-29, , 80-84, 85
• Source 1990 census

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The 99 Iowa Counties
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Poisson Data
Numerator Number of events over time, such as
incidence or mortality cancer cases.
Denominator Population years at risk.
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Rates and Relative Risks
c cancer cases in e.g. a county n county
population C cancer cases in e.g. a state N
state population Rate c/n Relative Risk
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Breast Cancer Incidence, Relative Risks
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Bernoulli Data (0/1 data)
Individual people with one of two traits, such as
cancer vs. no cancer, late vs. early disease or
two different treatments. Numerator The trait
of interest. Denominator All individuals. The
denominator may be a complete count or a random
sample.
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Proportions and Relative Risks
c late stage cancer cases in a county n
total number of cases C late stage cancer
cases in state N total cases in state Crude
Rate c/n Crude Relative Risk
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The statistical methods used are slightly
different for Poisson and Bernoulli data, but in
terms of mapping, the principles are the same.
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Age Adjustment

• Indirect vs. Direct Standardization
• Internal vs. External Standard
• Relative Risk vs. Rate

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Age Adjustment
Notation
Area to be mapped (e.g. Johnson county, Iowa) cs
cancer cases in age group s ns population in
age group s Area used as the standard (e.g.
State of Iowa) Cs cancer cases in age group
s Ns population in age group s
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Indirect Standardization
(relative risk)
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Direct Standardization
(relative risk)
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Direct Standardization
(rate)
The crude state rate, if the whole state had the
same age-specific rates as the county.
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Direct Standardization
Indirect Standardization
Relative Risk
Rate
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Indirect vs. Direct Standardization

Population Cases
county state
state Children, 0-19 1 200,000
400 Young Adults, 20-69 19
600,000 2200 Old Adults, 70 80
200,000 2400 Expected cases in county
1.03

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Indirect vs. Direct Standardization

Population Cases
county state
state Children, 0-19 1 200,000
400 Young Adults, 20-69 19
600,000 2200 Old Adults, 70 80
200,000 2400 Expected cases in county
1.03
County Cases
Children, 0-19 0 0
1 Young Adults, 20-69 0 1 0
Old Adults, 70 1 0 0 Direct
Standardization 0.5 6.3 40.0 Indirect
Standardization 1.0 1.0 1.0
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Indirect vs. Direct Standardization

Population Cases
county state
state Children, 0-19 1 200,000
400 Young Adults, 20-69 19
600,000 2200 Old Adults, 70 80
200,000 2400 Expected cases in county
1.03
County Cases
Children, 0-19 0 0 1
0 0 1 Young Adults, 20-69 0
1 0 0 1 0 Old Adults, 70
1 0 0 2 1 1 Direct
Standardization 0.5 6.3 40.0 1.0 6.8
40.5 Indirect Standardization 1.0 1.0 1.0
1.9 1.9 1.9
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Indirect vs. Direct Standardization

Population Cases
county state
state Children, 0-19 1 200,000
400 Young Adults, 20-69 19
600,000 2200 Old Adults, 70 80
200,000 2400 Expected cases in county
1.03
County Cases
Children, 0-19 0 0 1
0 0 1 0 0 1 Young
Adults, 20-69 0 1 0 0 1
0 1 2 1 Old Adults, 70
1 0 0 2 1 1 2 1
1 Direct Standardization 0.5 6.3 40.0
1.0 6.8 40.5 7.3 13.1 46.8 Indirect
Standardization 1.0 1.0 1.0 1.9 1.9 1.9
2.9 2.9 2.9
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Indirect vs. Direct Standardization

Population Cases
county state
state Children, 0-19 20 200,000
400 Young Adults, 20-69 60
600,000 2200 Old Adults, 70 20
200,000 2400 Expected cases in county
0.5
County Cases
Children, 0-19 0 0 1
0 0 1 0 0 1 Young
Adults, 20-69 0 1 0 0 1
0 1 2 1 Old Adults, 70
1 0 0 2 1 1 2 1
1 Direct Standardization 2.0 2.0 2.0
4.0 4.0 4.0 6.0 6.0 6.0 Indirect
Standardization 2.0 2.0 2.0 4.0 4.0 4.0
6.0 6.0 6.0
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Indirect vs. Direct Standardization

Population Cases
county state
state Children, 0-19 1 200,000
2000 Young Adults, 20-69 19
600,000 6000 Old Adults, 70 80
200,000 2000 Expected cases in county
1.0
County Cases
Children, 0-19 0 0 1
0 0 1 0 0 1 Young
Adults, 20-69 0 1 0 0 1
0 1 2 1 Old Adults, 70
1 0 0 2 1 1 2 1
1 Direct Standardization 0.25 3.2 20.0
0.5 3.4 20.2 0.7 6.6 23.4 Indirect
Standardization 1.0 1.0 1.0 2.0 2.0 2.0
3.0 3.0 3.0
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Indirect Standardization

• With indirect standardization, estimates of rates
  and relative risks have lower variance. This is
  especially important for small areas such as
  counties or census tracts.
• Method of choice for maps with estimates of
  multiple areas, showing geographical variation.
• Use internal standard.

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Breast Cancer Incidence, Relative
Risks Age-Adjusted, Indirect Standardization
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Breast Cancer Incidence, Relative Risks Not
Age-Adjusted
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Indirect Standardization
(relative risk)
No need to know age-specific case counts in the
county, only the total.
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Direct Standardization
(rate)
No need to know case counts for the
reference area.
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Direct Standardization

• Very useful to compare rates for areas studied
• at different times, by different people, using
  different data sets.
• Use external standards
• 1970 United States Population Standard
• 2000 United States Population Standard
• European Standard
• World Standard

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U.S 1970 and World Standards
U.S. 1970 World 45-49 5,962
5,000 50-54 5,464 5,000 55-59 4,908
4,000 60-64 4,240 4,000 65-69 3,441
3,000 70-74 2,679 2,000 75-79 1,887
1,000 80-84 1,124 500 85 743
500
U.S. 1970 World 0-4 8,442
12,000 5-9 9,820 10,000 10-14 10,230
9,000 15-19 9,384 9,000 20-24 8,056
8,000 25-29 6,632 8,000 30-34
5,625 6,000 35-39 5,466
6,000 40-44 5,896 6,000
World Standard From Waterhouse et al., Cancer
Incidence in Five Continents, 1976
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Iowa Breast Cancer Incidence Rates
1993-1996
Crude Rate 136.4 / 100,000 women Age-Adjusted,
Direct Standardization U.S. 1970 Standard
Population 106.4 / 100,000 U.S. 2000 Standard
Population 129.3 / 100,000 World Standard
Population 91.0 / 100,000
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Conclusions

• Use indirect standardization, with an internal
  standard, for mapping geographical variation.
• Use direct standardization, with a few different
  standards, to calculate the rate for the map as a
  whole.

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Uncertainty of Rate Estimates
In a regular map, a relative risk of 2 could mean
that there are 2000 cases with 1000 expected in
an urban county, or 2 cases with 1 expected in a
rural county. For the urban county, the
relative risk of 2 is a good estimate of the true
relative risk, but not for the rural county.
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Probability Map
For a particular county, one can test whether the
observed cases are significantly more than
expected, providing a p-value for that county. A
map of these p-values is called a probability
map. Reference Chownowski M. Maps Based on
Probabilities. Journal of the American
Statistical Association, 54385-388, 1959.
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Probability Map
(Poisson Data)
m expected number of cases c observed number
of cases
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Probability Map
plt0.05
0.05ltplt0.10
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County p-values
County Obs Exp RR p
Dubuque 275 235 1.17 0.004 Polk 892 817 1.09 0.
004 Clayton 77 57 1.34 0.006 Mills 51
36 1.43 0.006 Scott 411 368 1.12 0.012 Linn 467
429 1.09 0.033 Marion 97 82 1.18 0.048
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Regular vs. Probability Map
plt0.05
0.05ltplt0.10
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Warning
By chance, 5 of the counties will by chance have
a statistically significant p-value at the
0.05 level. Need to adjust for multiple testing.
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Pickle et al United States Mortality Atlas
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Pickle et al United States Mortality Atlas
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Dilemma
- Too little aggregation Unstable rates. - Too
much aggregation Geographical variation in
disease may not follow political
boundaries. Solution Smoothed Maps