Count

Crude Rates

FAQs for Crude Rates

Age and Sex_ Specific Rates

 Age-Adjusted Rates

FAQs for Age-Adjusted Rates

 

More Information on Age Adjustment… 

 

A. Counts

When communicating with health planning groups or legislators, sometimes the total number of health events conveys an important message. The total number of health events such as death, birth, hospitalization can also convey the magnitude of the prevention effort required, or the health care that may need to be provided. Table 1 shows some examples.

Table 1: Number of Deaths by Selected Cause and Sex, Utah, 1991

Disease

Total

Men

Women

Cardiovascular Disease

3660

1781

1879

Suicide

265

229

53

Breast Cancer

195

0

195

Lung Cancer

332

210

122

 

B. Crude Rates

Usually, the count alone has little meaning unless the size of the population from which it is derived is known. A rate is a fraction, in which the numerator is the number of people in whom an event occurred during a certain period of time, and the denominator is the total number of people in the population at risk for the same period of time. Table 2 shows an example of crude rate calculations for heart disease by local health department districts. The example, which is a three year time period, averages the number of deaths occurring per year divided by the population to produce the crude death rates for the period.

 

Table 2: Crude Death Rate for Heart Disease by Local Health Department District, Utah, 1989-1991*

Average Number of Deaths per year

LHD District

Average Population

Crude Death Rate**

167

Bear River

108,959

153.3

144

Central

52,702

273.2

215

Davis

189,663

113.4

1114

Salt Lake

731,665

152.3

96

Southeast

50,051

191.8

185

Southwest

84,386

219.2

15

Summit

15,798

94.9

44

Tooele

26,800

164.2

189

Uintah

35,925

175.4

335

Utah

265,334

126.3

16

Wasatch

10,265

155.9

328

Weber-Morgan

165,211

198.5

*Numbers may differ slightly from other published reports because of rounding

**Per 100,000 persons

 


 FAQs for Crude Rates:

Combining Years.

Q: I am looking at death rates for a five-year period. What should I use for a population denominator?

A: You are combining rates by summing them, then use the sum of the population counts over the same period, and the same geographic area. If you are combining rates by taking an average, then take an average of the population counts for the same time periods and geographic area.


 

C.Age and Sex Specific Rates

An age-specific rate is calculated by dividing the total number of health events for the specific age-group of interest by the total population in that age group. In Table 3, the age-specific rates for suicide are shown. The example demonstrates that the greatest number of suicides occur in the young, whereas the highest rate occurs among elderly men. The example below also shows how useful age- and sex-specific rates can be. Not only are the suicide death rates much higher among men, the rate of suicide increases among men with age, but not among women.

 

Table 3: Suicide Mortality Rates by Age and Sex, Utah, 1990*

Age-Group

Suicide

Deaths

Women

Population

Women

Rate**

Suicide Deaths

Men

Population

Men

Rate**

<15

2

263,161

0.8

4

277,399

1.4

15-44

33

395,725

8.3

139

397,021

35.0

45-64

4

125,633

3.2

49

120,132

40.8

65+

2

85,706

2.3

32

64,319

49.8

*Numbers may differ slightly from other published reports because of rounding

**Per 100,000 persons

 

D. Age-Adjusted Rates

A crude rate is a valuable measure, but can be problematic when comparing rates for different populations. The crude mortality rate for a population depends on the rate in each age group as well as on the proportion of people in each age group. Therefore, the crude rate for most causes of death will be higher in populations with a large proportion of elderly individuals, and lower in populations with a large proportion of young individuals (as in Utah). One way to compare two populations is to compare the age-specific rates, but that may be cumbersome.

An adjusted rate is an overall summary measure that helps control for demographic differences between populations. The most commonly used adjusted rate is the age-adjusted rate, which controls for age differences between two or more populations. When comparing across geographic areas, some method of age-adjusting is typically used to control for area-to-area differences in health events that can be explained by differing age distributions of the area populations. For example, an area that has an older population will have higher crude (not age-adjusted) rates for cancer, even though its exposure levels and cancer rates for specific age groups are the same as those of other areas. One might incorrectly attribute the high cancer rates to some characteristic of the area other than age. Age-adjusted rates control for age effects, allowing better comparability of rates across areas. Age-adjustment may also be used to control for age effects when comparing across several years of data, as the age distribution of the population changes over time.

Direct standardization adjusts the age-specific rates observed in the small area to the age distribution of a standard population (Lilienfeld & Stolley, 1994). Indirect standardization is based on standard mortality and morbidity ratios (SMR), and adjusts the age-specific rates found in the standard population to the age distribution of the small area or sub-population.

In 1998, the Centers for Disease Control and Prevention released new standard population weights for age-adjustment,, replacing the 1940 U.S. standard population weights that had been used for the previous several decades. Table 4., below, contains the standard population weights published by the CDC. They represent the proportion of the U.S. 2000 population in each age group, and sum to 1.0. Only rates adjusted to the same standard population can be compared. For instance, you may not compare rates age-adjusted using the U.S. 1940 standard population with rates that were age-adjusted using the U.S. 2000 population.

 

Table 4. US2000 Standard Population Weights
for Age Standardization

Age Group

US2000 Pop'n Projection, in Thousands

Weight

All Ages

274,634

1.000000

1

Under 1 Year

3,795

0.013818

2

1 - 4 years

15,192

0.055317

3

5 - 14 years

39,977

0.145565

4

15 - 24 years

38,077

0.138646

5

25 - 34 years

37,233

0.135573

6

35 - 44 years

44,659

0.162613

7

45 - 54 years

37,030

0.134834

8

55 - 64 years

23,961

0.087247

9

65 - 74 years

18,136

0.066037

10

75 - 84 years

12,315

0.044842

11

85 years and over

4,259

0.015508

 

Directly Age-Adjusted Rates

The age-specific rates for each age group in the study population are multiplied by the proportion of people in the same age group in the standard population distribution. The sum of these products is the age-adjusted, or age-standardized rate. The age-adjusted rate can be considered an average of each of the individual age-specific rates, but rather than being a simple average, it is a weighted average with each age-specific rate weighted by the proportion of people in that age group in the standard population.

Tables 5a. and 5b. demonstrate the method used by IBIS-Q in calculating age-adjusted rates. Notice that using crude death rates in Tables 5a. and 5b., one might conclude that persons in Southwest Health District have a higher underlying risk for Diabetes death than those living in Davis Health District. What do you conclude from the age-adjusted death rates? Alright, that's a trick question. Although the Davis age-adjusted rate is somewhat higher, the two rates are probably close enough to be considered essentially the same. You could use confidence intervals to assist in interpreting these data.

 

Table 5a. Age-adjusted rates for Diabetes Mellitus, Davis Health District, 1999

Age Group

Number of Deaths by Age Group

Population Counts by Age Group (1)

Age-Specific Death Rate (2)

US2000 Std Pop Weight

Cross Products (3)

Under 1 Year

0

4,773

-

0.013818

-

1 - 4 years

0

17,053

-

0.055317

-

5 - 14 years

0

42,070

-

0.145565

-

15 - 24 years

0

42,347

-

0.138646

-

25 - 34 years

1

35,488

2.82

0.135573

0.38

35 - 44 years

3

35,023

8.57

0.162613

1.39

45 - 54 years

1

25,366

3.94

0.134834

0.53

55 - 64 years

3

15,889

18.88

0.087247

1.65

65 - 74 years

20

10,608

188.54

0.066037

12.45

75 - 84 years

16

5,617

284.85

0.044842

12.77

85 years and over

7

1,204

581.40

0.015508

9.02

All Ages

51

235,438

21.66 (4)

1.000000

38.19

(5)

 

Table 5b. Age-adjusted rates for Diabetes Mellitus, Southwest Health District, 1999

Age Group

Number of Deaths by Age Group

Population Counts by Age Group (1)

Age-Specific Death Rate (2)

US2000 Std Pop Weight

Cross Products (3)

Under 1 Year

0

2,819

-

0.013818

-

1 - 4 years

0

10,093

-

0.055317

-

5 - 14 years

0

21,343

-

0.145565

-

15 - 24 years

0

22,357

-

0.138646

-

25 - 34 years

0

20,844

-

0.135573

-

35 - 44 years

3

17,658

16.99

0.162613

2.76

45 - 54 years

1

12,506

8.00

0.134834

1.08

55 - 64 years

5

7,487

66.78

0.087247

5.83

65 - 74 years

7

6,803

102.90

0.066037

6.79

75 - 84 years

17

5,682

299.19

0.044842

13.42

85 years and over

6

1,703

352.32

0.015508

5.46

All Ages

39

129,295

30.16 (4)

1.000000

35.34

(5)

1. Utah Governor's Office of Planning and Budget projections published in January 2000.

2. Rate per 100,000 = (Age-specific death count * 100,000) / Age-specific population count

3. Age-specific death rate * US2000 Std Pop Weight

4. Crude death rate

5. Death rate age-adjusted to U.S. 2000 standard population.

 

According to Curtin & Klein, "One of the problems with ADR is that rates based on small numbers of deaths will exhibit a large amount of random variation. A very rough guideline is that there should be at least 25 total deaths over all age groups." When fewer than 25 health events occurred over a time period, you mayconsider combining years, or using indirect age-adjustment.

Age adjustment is not appropriate if the age-specific death rates in the population of interest do not have a consistent relationship. For example, if death rates among younger persons is increasing, but death rates among older persons is decreasing. One's conclusion of the trend in this death rate would be different, depending on which standard population is used. A younger standard population (such as the US 1940) would show an increase, whereas an older standard population (such as the US 2000) would show a decrease, or no change at all. One's selection of the standard population should not affect the comparisons. For more information, see Curtis & Klein.3

When reporting age-adjusted rates, always report the standard population used, and when comparing results to other data, be sure to document that the data were adjusted to the same population. The age-adjusted rate is hypothetical, and is useful only for comparing populations, either over time, by geographic area, by sex or by racial/ethnic subgroups. Although age-adjustment may be used with large age sub-groups of the population, such as adults (e.g., age 18+), it is not meaningful to age-adjust "age-specific" rates (e.g., age 18-24).


FAQs for Age-Adjustment:

Event Rates for a Subpopulation.

Q: I am looking at death rates for female breast cancer. Which standard population should I use, females in US 2000 or all persons?

A: Theoretically, it doesn't matter, as long as you use the same standard population for all your analyses. But the recommended standard population is now the U.S. 2000 total population, even for analyses that apply only to a particular sex, race, or other subgroup.

Age Subpopulations.

Q: I am looking at adults, only. If I use the weights in Table 4, above, they will not sum to one. Is that okay?

A: No. The weights must always sum to one. Weights for certain age subgroups have been published by the CDC. But you may also recompute the proportions in Table 4, using only your age subgroup.

Age/Sex Adjusted Rates.

Q: I have a report that uses age AND SEX adjusted rates. Why doesn't IBIS-Q produce age and sex adjusted rates?

A: It is sometimes appropriate to adjust by other variables besides age. IBIS-Q doesn't do it because there is little demand for it at the Utah Department of Health.

Age-Adjusted Confidence Intervals.

Q: Can I use the confidence interval for the crude rate with the age-adjusted rate?

A: No, a new confidence interval for the age-adjusted rate must be calculated. Methods for calculation of this confidence interval may be found in Anderson and Klein, 1998.1


Indirectly Age-Adjusted Rates

The direct method can present problems when population sizes are particularly small. Calculating directly standardized rates requires calculating age-group-specific rates, and for small areas these age-specific rates may be based on one or two events. In such cases, indirect standardization of rates may be used.

Indirectly standardized rates are based on the standard mortality or morbidity ratio (SMR) and the crude rate for a standard population. Indirect standardization adjusts the overall standard population rate to the age distribution of the small area (Lilienfeld & Stolley, 1994). It is technically appropriate to compare indirectly standardized rates only with the rate in the standard population, not with each other. Below is an example where an SMR is computed for Utah, 1998.

 

Table 6. Indirectly Standardized Death Rate for Utah, 1998, Using
the U.S. 1998 Standard Population

U.S. 1998 Age-Specific All Cause Death Rates (1)

Utah 1998 Population Distribution (2)

Number of Deaths Expected in Utah (3)

Males

Under 1 Year

195.7

22,624

44.3

Males

1 - 4 years

37.6

83,217

31.3

Males

5 - 14 years

23.4

188,957

44.2

Males

15 - 24 years

119.3

193,664

231.0

Males

25 - 34 years

151.7

157,750

239.4

Males

35 - 44 years

258.5

146,754

379.4

Males

45 - 54 years

542.8

105,488

572.6

Males

55 - 64 years

1296.9

62,194

806.6

Males

65 - 74 years

3143.7

45,258

1,422.8

Males

75 - 84 years

7019.2

25,864

1,815.4

Males

85 years and over

16763.3

6,558

1,099.3

Females

Under 1 Year

163.4

21,503

35.1

Females

1 - 4 years

31.4

78,660

24.7

Females

5 - 14 years

16.2

179,326

29.1

Females

15 - 24 years

43.5

195,130

84.9

Females

25 - 34 years

68.1

149,050

101.6

Females

35 - 44 years

141.5

148,190

209.7

Females

45 - 54 years

309.6

106,819

330.7

Females

55 - 64 years

788.4

65,336

515.1

Females

65 - 74 years

1967.7

51,514

1,013.6

Females

75 - 84 years

4831.9

35,429

1,711.9

Females

85 years and over

14427.4

13,186

1,902.4

Totals

2,082,471

12,645.2

(4)

(12,645.2*100000) / 2,082,471 =

607.2

(5)

1. U.S. rate per 100,000 from CDC Wonder

2. Utah Governor's Office of Planning and Budget projections published in January 2000.

3. Age-specific death count, assuming risk in Utah is identical to that in the U.S.

4. The expected number of deaths for Utah, 1998 is 12,645

5. The indirectly standardized death rate for all deaths for Utah, 1998 is 607.2

The actual number of deaths in Utah during 1998 was 11,784. The ratio of the actual deaths to the expected deaths is the Standard Mortality Ratio (SMR). In this case, the SMR = 11,784 / 12,645.2, or 0.93. A Standard Mortality Ratio of less than one indicates that the actual risk in Utah is lower than that in the standard population.

1 Anderson RN, Rosenberg HM. Age Standardization of Death Rates: Implementation of the Year 2000 Standard. National vital statistics reports; vol 47 no.3. Hyattsville, Maryland: National Center for Health Statistics. 1998.

2 Klein RJ, Schoenborn CA. Age-Adjustment Using the 2000 Projected U.S. Population. Statistical notes; no.20. Hyattsville, Maryland: National Center for Health Statistics. January 2001.

3 Curtin, LR, Klein, RJ. Direct Standardization (Age-Adjusted Death Rates). Statistical notes; no.6. Hyattsville, Maryland: National Center for Health Statistics. March 1995.

4 Fleis, JL. Statistical methods for rates and proportions. John Wiley and Sons, New York, 1973. As cited in Curtin and Klein, 1995.

5 Klein RJ, Schoenborn CA., 2001.