Mapping Rates and Proportions Mapping Rates and Proportions

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Mapping Rates and Proportions

Mapping Rates and Proportions

Mapping Rates and Proportions • Incidence rates • Mortality rates • Birth rates •

Mapping Rates and Proportions • Incidence rates • Mortality rates • Birth rates • Prevalence • Proportions • Percentages

Sample Data: Breast Cancer Incidence in Iowa • • Years: 1993 -1996 7813 Cases

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

Geography and Population • 99 counties • Number of women: 1, 061, 096 (ages

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

The 99 Iowa Counties

The 99 Iowa Counties

Poisson Data Numerator: Number of events over time, such as incidence or mortality cancer

Poisson Data Numerator: Number of events over time, such as incidence or mortality cancer cases. Denominator: Population years at risk.

Rates and Relative Risks c = # cancer cases in e. g. a county

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 =

Breast Cancer Incidence, Relative Risks

Breast Cancer Incidence, Relative Risks

Bernoulli Data (0/1 data) Individual people with one of two traits, such as cancer

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.

Proportions and Relative Risks c = # late stage cancer cases in a county

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 =

The statistical methods used are slightly different for Poisson and Bernoulli data, but in

The statistical methods used are slightly different for Poisson and Bernoulli data, but in terms of mapping, the principles are the same.

Age Adjustment • Indirect vs. Direct Standardization • Internal vs. External Standard • Relative

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

Age Adjustment Notation Area to be mapped (e. g. Johnson county, Iowa) cs =

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

Indirect Standardization (relative risk)

Indirect Standardization (relative risk)

Direct Standardization (relative risk)

Direct Standardization (relative risk)

Direct Standardization (rate) The crude state rate, if the whole state had the same

Direct Standardization (rate) The crude state rate, if the whole state had the same age-specific rates as the county.

Indirect Standardization Relative Risk Rate Direct Standardization

Indirect Standardization Relative Risk Rate Direct Standardization

Indirect vs. Direct Standardization Population county state Children, 0 -19 1 200, 000 Young

Indirect vs. Direct Standardization Population county state Children, 0 -19 1 200, 000 Young Adults, 20 -69 19 600, 000 Old Adults, 70+ 80 200, 000 Expected cases in county: 1. 03 Cases state 400 2200 2400

Indirect vs. Direct Standardization Population county state Children, 0 -19 1 200, 000 Young

Indirect vs. Direct Standardization Population county state Children, 0 -19 1 200, 000 Young Adults, 20 -69 19 600, 000 Old Adults, 70+ 80 200, 000 Expected cases in county: 1. 03 Cases state 400 2200 2400 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

Indirect vs. Direct Standardization Population county state Children, 0 -19 1 200, 000 Young

Indirect vs. Direct Standardization Population county state Children, 0 -19 1 200, 000 Young Adults, 20 -69 19 600, 000 Old Adults, 70+ 80 200, 000 Expected cases in county: 1. 03 Children, 0 -19 0 0 Young Adults, 20 -69 0 1 Old Adults, 70+ 1 0 Direct Standardization 0. 5 6. 3 Indirect Standardization 1. 0 Cases state 400 2200 2400 County Cases 1 0 0 2 1 1 40. 0 1. 0 6. 8 40. 5 1. 0 1. 9

Indirect vs. Direct Standardization Population county state Children, 0 -19 1 200, 000 Young

Indirect vs. Direct Standardization Population county state Children, 0 -19 1 200, 000 Young Adults, 20 -69 19 600, 000 Old Adults, 70+ 80 200, 000 Expected cases in county: 1. 03 Children, 0 -19 0 0 Young Adults, 20 -69 0 1 Old Adults, 70+ 1 0 Direct Standardization 0. 5 6. 3 Indirect Standardization 1. 0 Cases state 400 2200 2400 County Cases 1 0 0 2 1 1 40. 0 1. 0 6. 8 40. 5 1. 0 1. 9 0 1 2 7. 3 2. 9 0 1 2 1 13. 1 46. 8 2. 9

Indirect vs. Direct Standardization Population county state Children, 0 -19 20 200, 000 Young

Indirect vs. Direct Standardization Population county state Children, 0 -19 20 200, 000 Young Adults, 20 -69 60 600, 000 Old Adults, 70+ 20 200, 000 Expected cases in county: 0. 5 Cases state 400 2200 2400 County Cases Children, 0 -19 0 0 1 Young Adults, 20 -69 0 1 0 Old Adults, 70+ 1 0 0 2 1 1 Direct Standardization 2. 0 4. 0 Indirect Standardization 2. 0 4. 0 0 1 2 6. 0 0 2 1 6. 0 1 1 1 6. 0

Indirect vs. Direct Standardization Population county state Children, 0 -19 1 200, 000 Young

Indirect vs. Direct Standardization Population county state Children, 0 -19 1 200, 000 Young Adults, 20 -69 19 600, 000 Old Adults, 70+ 80 200, 000 Expected cases in county: 1. 0 Children, 0 -19 0 Young Adults, 20 -69 0 Old Adults, 70+ 1 Direct Standardization 0. 25 Indirect Standardization 1. 0 0 1 0 3. 2 1. 0 Cases state 2000 6000 2000 County Cases 1 0 0 2 1 1 20. 0 0. 5 3. 4 20. 2 1. 0 2. 0 0 1 2 0. 7 3. 0 0 1 2 1 1 1 6. 6 23. 4 3. 0

Indirect Standardization With indirect standardization, estimates of rates and relative risks have lower variance.

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.

Breast Cancer Incidence, Relative Risks Age-Adjusted, Indirect Standardization

Breast Cancer Incidence, Relative Risks Age-Adjusted, Indirect Standardization

Breast Cancer Incidence, Relative Risks Not Age-Adjusted

Breast Cancer Incidence, Relative Risks Not Age-Adjusted

Indirect Standardization (relative risk) No need to know age-specific case counts in the county,

Indirect Standardization (relative risk) No need to know age-specific case counts in the county, only the total.

Direct Standardization (rate) No need to know case counts for the reference area.

Direct Standardization (rate) No need to know case counts for the reference area.

Direct Standardization Very useful to compare rates for areas studied at different times, by

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

U. S 1970 and World Standards U. S. 1970 World 0 -4 8, 442

U. S 1970 and World Standards 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 U. S. 1970 45 -49 5, 962 50 -54 5, 464 55 -59 4, 908 60 -64 4, 240 65 -69 3, 441 70 -74 2, 679 75 -79 1, 887 80 -84 1, 124 85+ 743 World 5, 000 4, 000 3, 000 2, 000 1, 000 500 World Standard From: Waterhouse et al. , Cancer Incidence in Five Continents, 1976

Iowa Breast Cancer Incidence Rates 1993 -1996 Crude Rate: 136. 4 / 100, 000

Iowa Breast Cancer Incidence Rates 1993 -1996 Crude Rate: 136. 4 / 100, 000 women Age-Adjusted, Direct Standardization U. S. 1970 Standard Population: U. S. 2000 Standard Population: World Standard Population: 106. 4 / 100, 000 129. 3 / 100, 000 91. 0 / 100, 000

Conclusions • Use indirect standardization, with an internal standard, for mapping geographical variation. •

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.

Uncertainty of Rate Estimates In a regular map, a relative risk of 2 could

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.

Probability Map For a particular county, one can test whether the observed cases are

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.

Probability Map (Poisson Data) m = expected number of cases c = observed number

Probability Map (Poisson Data) m = expected number of cases c = observed number of cases

Probability Map p<0. 05<p<0. 10

Probability Map p<0. 05<p<0. 10

County ‘p-values’ County Dubuque Polk Clayton Mills Scott Linn Marion Obs 275 892 77

County ‘p-values’ County Dubuque Polk Clayton Mills Scott Linn Marion Obs 275 892 77 51 411 467 97 Exp 235 817 57 36 368 429 82 RR 1. 17 1. 09 1. 34 1. 43 1. 12 1. 09 1. 18 p= 0. 004 0. 006 0. 012 0. 033 0. 048

Regular vs. Probability Map p<0. 05<p<0. 10

Regular vs. Probability Map p<0. 05<p<0. 10

Warning By chance, 5% of the counties will by chance have a ‘statistically significant’

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.

Pickle et al: United States Mortality Atlas

Pickle et al: United States Mortality Atlas

Pickle et al: United States Mortality Atlas

Pickle et al: United States Mortality Atlas

Dilemma - Too little aggregation: Unstable rates. - Too much aggregation: Geographical variation in

Dilemma - Too little aggregation: Unstable rates. - Too much aggregation: Geographical variation in disease may not follow political boundaries. Solution: Smoothed Maps