Health Event Counts and Crude, Age-specific, and Age-adjusted Rates
Table of Contents
A. Counts
B. Crude Rates
C. Age- and Sex-specific Rates
D. Age-adjusted Rates
....D.1. Age-adjusted Rates, Direct Method
....D.2. Indirectly Age-adjusted Rates, Indirect Method
E. Deciding Which Measure to Use
References
A. Counts
When communicating with health planning groups or legislators, the total number of health events, or theTable 1: Number of Deaths for Four Leading Causes by Cause and Sex, Utah, 2005
Underlying Cause of Death | Men | Women | Total |
---|---|---|---|
Disease of heart (ICD10: I00-I09, I11, I13, I20-I51) |
1,408 |
1,437 |
2,845 |
Malignant neoplasms (ICD10: C00-C97) |
1,344 |
1,168 |
2,512 |
Injury, Unintentional injuries (ICD10: V01-X59, Y85-Y86) |
466 |
249 |
715 |
Respiratory, chronic lower respiratory diseases (ICD10: J40-J47) | 335 |
257 |
592 |
B. Crude Rates
The count alone will be less useful if you want to compare populations of unequal size. Knowing the population sizes is useful, but computing a rate will allow direct comparison between similar populations. A- A specified time period.
- The numerator, the number of people in whom an event occurred during a given period of time.
- The denominator, the total number of people in the population at risk for the same period of time. This is also referred to as the "person-years at risk."
- A constant. The result of the fraction is usually multiplied by some constant (in this case 100,000) to make the number more legible.
In general, a rate is called a "crude rate" if it has not been adjusted for the age and sex composition of a population.
Table 2 shows an example of crude rate calculations for heart disease by local health 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 District, Utah, 2003-2005
Utah Local Health District | Average Annual Number of Deaths | Average Annual Population Estimate | Crude Death Rate (Deaths per 100,000 Population) |
---|---|---|---|
Bear River LHD | 168 |
147,371 |
113.77 |
Central Utah LHD | 149 |
70,382 |
211.7 |
Davis County LHD | 278 |
269,744 |
102.94 |
Salt Lake Valley LHD | 1,081 |
957,972 |
112.84 |
Southeastern LHD | 83 |
52,936 |
156.79 |
Southwest LHD | 286 |
174,363 |
164.03 |
Summit County LHD | 22 |
35,149 |
61.64 |
Tooele County LHD | 56 |
50,388 |
111.14 |
TriCounty LHD | 68 |
42,277 |
161.63 |
Utah County LHD | 404 |
438,995 |
92.03 |
Wasatch County LHD | 17 |
19,230 |
90.14 |
Weber-Morgan LHD | 312 |
217,939 |
143.16 |
Using the values, above, for Bear River LHD as an example...
- The specified time period is 2003 through 2005.
- The numerator, or the number of events was averaged over the three years, for a value of 167.67 (before rounding).
- The denominator, or the estimated population at risk, was also averaged over the three years. The average of the three July 1 population population estimates was 147,370.67.
- The constant was 100,000.
The calculation for the Bear River LHD heart disease crude death rate for 2003-2005 looks like this:
FAQs for Crude Rates:
Combining Years
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- and sex-specific rates for suicide are shown. The example demonstrates that the greatestThe calculation for an age-specific rate is the same as for a crude rate.
Table 3: Suicide Mortality Rates by Age and Sex, Utah, 2002-2006
Males | Females |
---|
Age Group | Suicide Deaths | Population | Age- and Sex-specific Rate per 100,000 Population | Suicide Deaths | Population | Age- and Sex-specific Rate per 100,000 Population |
---|---|---|---|---|---|---|
<15 | 13 |
1,677,087 |
0.78 |
5 |
1,587,965 |
0.31 |
15-44 | 852 |
2,921,606 |
29.16 |
199 |
2,838,704 |
7.01 |
45-64 | 372 |
1,153,370 |
32.25 |
117 |
1,163,236 |
10.06 |
65+ | 168 |
474,715 |
35.39 |
23 |
587,013 |
3.92 |
D. Age-adjusted Rates
Crude rates are valuable for comparing similar population of different sizes, but the word, "similar" is a key concept, because crude rates can be misleading when comparing rates for populations with different age compositions. The crude mortality rate for a population depends on the mortality rate in each age group as well as on the proportion of people in each age group. For instance, 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. AnAn adjusted rate is an overall summary measure that helps control for age differences between 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 different age distributions in the area populations. For example, an area that has an older population will have higher crude death rates for cancer, even though its exposure levels and cancer rates within specific age groups may be the same as those in 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.
Calculating age-adjusted rates using "direct age standardization" is the same as calculating a weighted average. It adjusts the age-specific rates observed in a given population (such as a county or ethnic group) to the age distribution of a standard population (Lilienfeld & Stolley, 1994). In some cases, such as when there are too few cases to stratify by age, "indirect age standardization" may be used. 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 smaller area or sub-population.
In 1998, the Centers for Disease Control and Prevention (CDC) revised the standard population weights for age-adjustment (Klein & Schoenborn), 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.
Age-adjusted rates should be viewed as
Table 4. U.S. 2000 Standard Population Weights for Age Standardization
Age Group | U.S. 2000 Population Projection (in thousands) |
Weight | |
---|---|---|---|
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 |
D.1. Age-adjusted Rates: Direct Method
To apply direct age-adjustment to a set of rates, the age-specific rate for each age group in the study population is multiplied by the appropriate weight in the standard population. The sum of these products is the directly 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
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 LHD have a higher underlying risk for unintentional injury death compared with the state of Utah. How should the age-adjusted death rates be interpreted? You could use confidence intervals to assist in interpreting these data (IBIS automatically provides 95% confidence intervals for all rates).
Table 5a. Age-adjusted Death Rate for Unintentional Injuries, State of Utah, 2002-2006
Age Group | Number of Deaths (5-Year Sum) | Population Counts (5-Year Sum) (1) | Age- specific Rate (2) | U.S. 2000 Std Pop Weight | Cross Products (3) |
---|---|---|---|---|---|
Under 1 Year | 42 |
250,611 |
16.76 |
0.013818 |
0.231576 |
1 - 4 Years | 121 |
960,731 |
12.59 |
0.055317 |
0.696694 |
5 - 14 Years | 130 |
2,053,710 |
6.33 |
0.145565 |
0.921428 |
15 - 24 Years | 560 |
2,253,594 |
24.85 |
0.138646 |
3.445242 |
25 - 34 Years | 452 |
1,957,687 |
23.09 |
0.135573 |
3.130173 |
35 - 44 Years | 369 |
1,549,029 |
23.82 |
0.162613 |
3.873665 |
45 - 54 Years | 394 |
1,405,684 |
28.03 |
0.134834 |
3.779270 |
55 - 64 Years | 297 |
910,922 |
32.60 |
0.087247 |
2.844630 |
65 - 74 Years | 256 |
564,672 |
45.34 |
0.066037 |
2.993857 |
75 - 84 Years | 396 |
372,361 |
106.35 |
0.044842 |
4.768875 |
85 Years and Over | 443 |
124,695 |
355.27 |
0.015508 |
5.509478 |
All Ages | 3,462 |
12,403,696 |
27.91 (4) |
1 |
Table 5b. Age-adjusted Rate for Unintentional Injuries, Southwest LHD, Utah, 2002-2006
Age Group | Number of Deaths (5-Year Sum) | Population Counts (5-Year Sum) (1) | Age- specific Rate (2) | U.S. 2000 Std Pop Weight | Cross Products (3) |
---|---|---|---|---|---|
Under 1 Year | 5 |
16,753 |
29.85 |
0.013818 |
0.412404 |
1 - 4 Years | 13 |
62,149 |
20.92 |
0.055317 |
1.157092 |
5 - 14 Years | 18 |
135,238 |
13.31 |
0.145565 |
1.937451 |
15 - 24 Years | 51 |
157,563 |
32.37 |
0.138646 |
4.487694 |
25 - 34 Years | 34 |
117,343 |
28.97 |
0.135573 |
3.928212 |
35 - 44 Years | 32 |
94,544 |
33.85 |
0.162613 |
5.503909 |
45 - 54 Years | 23 |
91,791 |
25.06 |
0.134834 |
3.378525 |
55 - 64 Years | 34 |
72,058 |
47.18 |
0.087247 |
4.116681 |
65 - 74 Years | 25 |
64,701 |
38.64 |
0.066037 |
2.551622 |
75 - 84 Years | 28 |
48,070 |
58.25 |
0.044842 |
2.611974 |
85 Years and Over | 39 |
15,410 |
253.08 |
0.015508 |
3.924802 |
All Ages | 302 |
875,620 |
34.49 (4) |
1 |
(1) The Utah Population Estimates Committee (UPEC) and the Governor's Office of Planning and Budget (GOPB), Estimates for Counties by Sex and Single Year of Age. |
(2) Rate per 100,000 = (Age-specific death count * 100,000) / Age-specific population count |
(3) Age-specific death rate * U.S. 2000 Std Pop Weight |
(4) Crude death rate |
(5) |
According to Curtin & Klein, "One of the problems with [direct age adjustment] 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 may consider 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 U.S. 1940) would show an increase, whereas an older standard population (such as the U.S. 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 Curtin & Klein.
When reporting age-adjusted rates, always report the standard population used, and when comparing results to other data, be sure to document that those data were also age-adjusted and report the standard population. The age-adjusted rate is hypothetical, and is useful only for
FAQs for Age-adjustment:
Event Rates for a Subpopulation
When NOT to Age-adjust
- You are comparing populations with similar age distributions, and age-adjustment does not produce a rate that is substantively different from the crude rate.
- You are comparing groups with the same, narrow, age range.
- Do not use direct age-adjustment if you have too few cases (you should have a least 25 events across all age groups).
Age Subpopulations
Age/Sex Adjusted Rates
Confidence Intervals for Age-adjusted Rates
D.2. Age-adjusted Rates: Indirect Method
The direct method can present problems when population sizes are particularly small. Calculating directly standardized rates requires calculating age-group-specific rates, and for Utah 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 death 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.
E. Deciding Which Measure to Use
If your question is: | Then use: |
---|---|
MAGNITUDE: How big is the problem? | Number of events (count) |
PROBABILITY: What is the underlying risk in my population? | Crude rate and confidence interval |
DISPARITY: Is there a difference in risk after controlling for age? | Age-adjusted rate and confidence interval |
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.
6. Lilienfeld, DE and Stolley, PD. Foundations of Epidemiology, 3rd Ed. Oxford University Press, 1994.