Mapping Rates and Proportions
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Transcript of Mapping Rates and Proportions
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Mapping Rates and Proportions
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Mapping Rates and Proportions
• Incidence rates
• Mortality rates
• Birth rates
• Prevalence
• Proportions
• Percentages
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Sample Data:Breast 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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IO W A
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 Risksc = # cancer cases in e.g. a countyn = county populationC = # cancer cases in e.g. a stateN = state population
Rate = c/n
Relative Risk = c n
C N
/
/
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Breast Cancer Incidence, Relative Risks
Not a djuste d<0.750.75-0.850.85-0.950.95-1.051.05-1.15>1.25
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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 Risksc = # late stage cancer cases in a countyn = total number of casesC = # late stage cancer cases in stateN = total cases in state
Crude Rate = c/n
Crude Relative Risk = c n
C N
/
/
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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
Area to be mapped (e.g. Johnson county, Iowa)cs = cancer cases in age group sns = population in age group s
Area used as the standard (e.g. State of Iowa)Cs = cancer cases in age group sNs = population in age group s
Notation
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Indirect Standardization(relative risk)
c
nCN
s
ss
s
o b serv ed in co u n ty
ex p ec ted in co u n ty
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Direct Standardization(relative risk)
Ncn
C
ss
s
s
cases in s ta te if it h ad th e sam e
ag e - sp ec ific ra tes as th e co u n ty
o b serv ed in s ta te
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Direct Standardization
Ncn
N
ss
s
s
The crude state rate, if thewhole state had the sameage-specific rates as thecounty.
(rate)
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IndirectStandardization
c
nCN
s
ss
s
RelativeRisk
Rate
DirectStandardization
C
N
c
nCN
s
s
s
ss
s
Ncn
C
ss
s
s
C
N
Ncn
C
Ncn
Ns
s
ss
s
s
ss
s
s
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Indirect vs. Direct Standardization Population Cases county state stateChildren, 0-19 1 200,000 400Young Adults, 20-69 19 600,000 2200Old Adults, 70+ 80 200,000 2400 Expected cases in county: 1.03
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Indirect vs. Direct Standardization Population Cases county state stateChildren, 0-19 1 200,000 400Young Adults, 20-69 19 600,000 2200Old Adults, 70+ 80 200,000 2400 Expected cases in county: 1.03
County Cases Children, 0-19 0 0 1Young Adults, 20-69 0 1 0 Old Adults, 70+ 1 0 0Direct Standardization 0.5 6.3 40.0Indirect Standardization 1.0 1.0 1.0
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Indirect vs. Direct Standardization Population Cases county state stateChildren, 0-19 1 200,000 400Young Adults, 20-69 19 600,000 2200Old Adults, 70+ 80 200,000 2400 Expected cases in county: 1.03
County Cases Children, 0-19 0 0 1 0 0 1Young Adults, 20-69 0 1 0 0 1 0Old Adults, 70+ 1 0 0 2 1 1 Direct Standardization 0.5 6.3 40.0 1.0 6.8 40.5Indirect 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 stateChildren, 0-19 1 200,000 400Young Adults, 20-69 19 600,000 2200Old 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 1Young Adults, 20-69 0 1 0 0 1 0 1 2 1Old Adults, 70+ 1 0 0 2 1 1 2 1 1Direct Standardization 0.5 6.3 40.0 1.0 6.8 40.5 7.3 13.1 46.8Indirect 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 stateChildren, 0-19 20 200,000 400Young Adults, 20-69 60 600,000 2200Old 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 1Young Adults, 20-69 0 1 0 0 1 0 1 2 1Old Adults, 70+ 1 0 0 2 1 1 2 1 1Direct Standardization 2.0 2.0 2.0 4.0 4.0 4.0 6.0 6.0 6.0Indirect 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 stateChildren, 0-19 1 200,000 2000Young Adults, 20-69 19 600,000 6000Old 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 1Young Adults, 20-69 0 1 0 0 1 0 1 2 1Old Adults, 70+ 1 0 0 2 1 1 2 1 1Direct Standardization 0.25 3.2 20.0 0.5 3.4 20.2 0.7 6.6 23.4Indirect Standardization 1.0 1.0 1.0 2.0 2.0 2.0 3.0 3.0 3.0
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Indirect StandardizationWith 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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Age a djuste d<0.750.75-0.850.85-0.950.95-1.051.05-1.15>1.25
Breast Cancer Incidence, Relative RisksAge-Adjusted, Indirect Standardization
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Breast Cancer Incidence, Relative Risks Not Age-Adjusted
Not a djuste d<0.750.75-0.850.85-0.950.95-1.051.05-1.15>1.25
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Indirect Standardization(relative risk)
c
nCN
s
ss
s
No need to knowage-specific case counts in the county,only the total.
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Direct Standardization(rate)
Ncn
N
ss
s
s
No need to know casecounts for the referencearea.
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Direct StandardizationVery useful to compare rates for areas studiedat 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 World45-49 5,962 5,00050-54 5,464 5,00055-59 4,908 4,00060-64 4,240 4,00065-69 3,441 3,00070-74 2,679 2,00075-79 1,887 1,00080-84 1,124 50085+ 743 500
World Standard From: Waterhouse et al., Cancer Incidence in Five Continents, 1976
U.S. 1970 World0-4 8,442 12,0005-9 9,820 10,00010-14 10,230 9,00015-19 9,384 9,00020-24 8,056 8,00025-29 6,632 8,00030-34 5,625 6,00035-39 5,466 6,00040-44 5,896 6,000
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Iowa Breast Cancer Incidence Rates1993-1996
Crude Rate: 136.4 / 100,000 women
Age-Adjusted, Direct Standardization
U.S. 1970 Standard Population: 106.4 / 100,000U.S. 2000 Standard Population: 129.3 / 100,000World 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, 54:385-388, 1959.
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Probability Map
m = expected number of casesc = observed number of cases
P c H em
im
i
ci
( | )!
# cases
0 0
11
(Poisson Data)
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IO W A
Probability Map
p<0.05 0.05<p<0.10
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County ‘p-values’
County Obs Exp RR p= Dubuque 275 235 1.17 0.004Polk 892 817 1.09 0.004Clayton 77 57 1.34 0.006Mills 51 36 1.43 0.006Scott 411 368 1.12 0.012Linn 467 429 1.09 0.033Marion 97 82 1.18 0.048
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Age a djuste d<0.750.75-0.850.85-0.950.95-1.051.05-1.15>1.25
p<0.05Regular vs. Probability Map
0.05<p<0.10
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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