Assignment: AGE ADJUSTMENT
When analyzing epidemiologic data, researchers often wish to adjust for the influence of some variable so that the "true" effect of other variables can be seen more clearly. Consider the example of a study to determine if gray hair is related to mortality risk. Two statements stand out in this study:
1. People with gray hair have a higher death rate when compared to other people.
2. People with gray hair are older than others people.
Because of this second statement the meaning of statement one is obscure. The possible link between gray hair and mortality risk is confused by the effect of age on mortality risk. Age is considered a confounding factor that needs to be accounted for to accurately assess the impact of gray hair on mortality rates. Epidemiologists use many tools to sort through information and overcome this confusion of information by adjusting data. The purpose of data adjustment is to disentangle the relationship so that we can evaluate a variables effect free from confusion and distortion. For the gray hair investigation, adjustment would permit us to determine whether persons of the same age who have gray hair have different mortality risks. (Sempos 1989)
Confounding Variables
Confounding variables are variables whose effects confuse the true relationships between factors and diseases. This is why there is a need for data adjustment. In order for a variable to be considered a confounding variable, it must be related to the disease or condition of interest and to the risk factor being investigated (Miettinen 1970). But if the possible confounding variable is truly related only to the disease of interest, it may still be desirable to adjust for it (Mantel 1986). One reason is the adjustment could possibly reduce the sampling variance of the comparison that is being investigated.
Adjustments
A common example of data adjustment is the age adjustment of mortality rates. While the age adjustment technique is most often applied to mortality (death) rates, it could also be applied to incidence of disease, prevalence, or any other kind of proportional rates. Age adjustment allows comparison of mortality risk for various groups free from the distortion of one group having a different age distribution than another. There are two types of age adjustments in relation to mortality rates -- direct and indirect age adjustments.
Direct Adjustment
Direct adjustment, or direct standardization, is to superimpose the age distribution of a standard population on the two study groups to be compared. Standardized rates are then calculated for each population, making use of the standard age distribution. These adjusted rates are then compared, and any difference between them can no longer be due to difference in age distribution because age has been taken into account. The direct method uses two inputs called age-specific rates and standard population.
Age-Specific Rates
A set of age-specific death rates for each study group is needed. If they are not already available, they can be computed from various kinds of counts.
Standard Population
Select a population that is relevant to the data. Within wide ranges of choice, the population chosen as a standard usually does not make much difference. If comparing only two groups choices for a standard population include the sum of populations of the groups to be compared, the population of one of the groups in the comparison, or a large population (such as that of the United States) (Abramson 1988). A common standard is the A1940 standard million typically used by the National Center for Health Statistics and the 1970 US population, used often by the National Cancer Institute. When making comparisons of local death rates to nationally reported, age adjusted rated, it is imperative that the local data be age adjusted to the exact same standard population as the national data.
Indirect Adjustment
Sometimes direct-adjustment cannot be carried out because the age-specific rates in the groups to be adjusted are not available or, in at least some age classes, are based on such small numbers as to be completely unreliable. Indirect adjustment does not require age-specific rates of a population but does require the following:
1. Age distribution of each study group to be adjusted.
2. Total deaths in each study group to be adjusted.
3. Age-specific death rates for a standard population.
Items 1 and 3 are used to calculate how many deaths would be expected in each age category for the study groups. This observed/expected ratio is a relative, indirect, age-adjusted rate. (Selvin 1991)
Age-Adjustments
Age-adjustment is an important part of the analysis of mortality and incidence rates since age almost always influences disease risk and is the most important factor impacting the likelihood of death. Thus, age adjustment corrects for differences in age distributions among groups to be compared so that observed differences in adjusted rates would then be attributable to the influence of factors other than age.
The two populations in Table 1 are made up with identical age-specific rates but with different age structures. Population II has a larger number of older people, which leads to a higher crude mortality rate (5.86 deaths per 1000 people at risk, compared to 4.57 per 1000 for population I). Notice the risk of death (age-specific mortality) is clearly the same for both populations since the age-specific rates are the same for both groups. This means that the risk of dying is the same in both populations.
|
|
Population I
|
Population II
|
|
Age
|
Deaths
|
Population
|
Age-Specific Mortality per 1000
|
Deaths
|
Population
|
Age-Specific Mortality per 1000
|
|
40-50
|
1
|
1,000
|
1
|
1
|
1,000
|
1
|
|
50-60
|
3
|
1,500
|
2
|
10
|
5,000
|
2
|
|
60-70
|
8
|
2,000
|
4
|
40
|
10,000
|
4
|
|
70-80
|
20
|
2,500
|
8
|
160
|
20,000
|
8
|
|
Total
|
32
|
7,000
|
|
211
|
36,000
|
|
Crude Rate: Total death / total population x 1000 =
32/7000 x 1000 = 4.57 per 1000 people for population I
211/36,000 x 1000 = 5.86 per 1000 people for population II
Age-specific rates for 60-70 age group:
(number of deaths for 60-70 age group / population aged 60-70) x 1000 =
8/2000 x 1000 = 4 per 1000 for population I
40/10000 x 1000 = 4 per 1000 for population II
Expected deaths: (Age-specific rate for each age group in a population X standard population in that age group). If rates are given in values per some constant (such as 1000), divide the answer by that constant when calculating the expected deaths.
If you add the two populations (I and II) together to make a standard population, then the number of expected deaths would be identical for each age group:
|
|
Population I
|
Population II
|
|
Age
|
Deaths
|
Population
|
Age-Specific Mortality per 1000
|
Deaths
|
Population
|
Age-Specific Mortality per 1000
|
|
40-50
|
1
|
2,000
|
2
|
1
|
2,000
|
2
|
|
50-60
|
2
|
6,500
|
13
|
2
|
6,500
|
13
|
|
60-70
|
4
|
12,000
|
48
|
4
|
12,000
|
48
|
|
70-80
|
8
|
22,500
|
180
|
8
|
22,500
|
180
|
|
Total
|
|
43,000
|
243
|
|
43,500
|
243
|
Age-adjusted rates: Number of expected deaths in a population/total standard population:
(total expected deaths / total standard population) x 1000 =
243/43,000 x 1000 = 5.65 per 1000 for both populations
Crude rates supply simple, direct summaries of a set of age-specific disease data but fail to reflect risk accurately to compare groups that differ in age (or other) distributions. Crude rates are to be used as a general guide only. In this case, the crude rate indicates the risk is less in population I, but in reality the risk is identical in both populations. The age-adjusted rates show the accurate risk for the two populations B the risk of dying is the same in the two populations.
Note: Age adjustments are the most common type of adjustment but race, sex and many more effects can be adjusted.
Age Adjustment Exercise:
Table 2 U.S. Cancer mortality for the years 1960 and 1990
|
|
1960
|
1990
|
|
Age
|
Population
|
Deaths
|
Rate*
|
Population
|
Deaths
|
Rate*
|
|
<1
|
906,897
|
14
|
1.5
|
1,784,033
|
34
|
1.9
|
|
1-4
|
3,794,573
|
87
|
2.3
|
7,065,148
|
219
|
3.1
|
|
5-14
|
10,003,544
|
320
|
3.2
|
15,658,730
|
783
|
5.0
|
|
15-24
|
10,629,526
|
670
|
6.3
|
10,482,916
|
839
|
8.0
|
|
25-34
|
9,645,330
|
2,074
|
21.5
|
10,939,972
|
2,057
|
18.8
|
|
35-44
|
8,249,558
|
8,109
|
98.3
|
10,563,872
|
10,226
|
96.8
|
|
45-54
|
7,294,330
|
13,684
|
187.6
|
9,114,202
|
16,807
|
184.4
|
|
55-64
|
5,022,499
|
30,346
|
604.2
|
6,850,263
|
44,540
|
650.2
|
|
65-74
|
2,920,220
|
39,201
|
1342.4
|
4,702,482
|
65,242
|
1387.4
|
|
75-84
|
1,019,504
|
33,893
|
3324.5
|
1,874,619
|
60,232
|
3213.0
|
|
85+
|
142,532
|
9,364
|
6570.1
|
330,915
|
21,414
|
6471.0
|
|
Total
|
59,628,513
|
137,762
|
231.0
|
79,367,152
|
222,393
|
280.2
|
* Rates per 100,000
Question:
1. What is the crude cancer death rate in
a. 1960? 137,762/59,628,513x100,000=231.03 Per 100,000 1960
b. 1990? 222,393/79,367,152x100,000=280.21 Per 100,00 1990
2. Which time period has the higher crude death rate?
1990 has the highest crude death rate
3. When you look at the age specific rates, does it appear that one year has a consistently higher rate? Yes, 1990 has a consistently higher age specific rate.
In Table 3, fill in the number of people in each age group in the standard population, the age specific cancer death rate from the 1960 and 1990 populations, and calculate the expected number of deaths due to cancer for 1960 and 1990. Use the 1940 standard million population as the Standard Population.
Table 3
|
Age
|
Number in Standard Pop.
|
1960 Rate Exp.
|
1960 Deaths
|
1990 Rate Exp.
|
1990 Deaths
|
|
<1
|
|
|
|
|
|
|
1-4
|
|
|
|
|
|
|
5-14
|
|
|
|
|
|
|
15-24
|
|
|
|
|
|
|
25-34
|
|
|
|
|
|
|
35-44
|
|
|
|
|
|
|
45-54
|
|
|
|
|
|
|
55-64
|
|
|
|
|
|
|
65-74
|
|
|
|
|
|
|
75-84
|
|
|
|
|
|
|
85+
|
|
|
|
|
|
|
Total
|
|
|
|
|
|
* Rates per 100,000
4. What is the total number of people in Standard Population?
5. What was the number of Expected Deaths in 1960?
6. What was the Age Adjusted Cancer Mortality Rate in 1960?
7. What was the number of Expected Deaths in 1990?
8. What was the Age Adjusted Cancer Mortality Rate in 1990?
9. How do the crude and age adjusted rates compare?
10. Why would death rates need to be adjusted for variables like age (or sex or race, etc)?
11. How do you know when it is necessary to age adjust rates?
In Table 4, fill in the number of people in each age group in the standard population, the age specific cancer death rate from the 1960 and 1990 populations, and calculate the expected number of deaths due to cancer for 1960 and 1990. Use the 2000 standard million population as the Standard Population
Table 4
|
Age
|
Number in Standard Pop.
|
1960 Rate Exp.
|
1960 Deaths
|
1990 Rate Exp.
|
1990 Deaths
|
|
<1
|
|
|
|
|
|
|
1-4
|
|
|
|
|
|
|
5-14
|
|
|
|
|
|
|
15-24
|
|
|
|
|
|
|
25-34
|
|
|
|
|
|
|
35-44
|
|
|
|
|
|
|
45-54
|
|
|
|
|
|
|
55-64
|
|
|
|
|
|
|
65-74
|
|
|
|
|
|
|
75-84
|
|
|
|
|
|
|
85+
|
|
|
|
|
|
|
Total
|
|
|
|
|
|
* Rates per 100,000
12. What was the number of Expected Deaths in 1960? ________________
13. What was the Age Adjusted Cancer Mortality Rate in 1960?
14. What was the number of Expected Deaths in 1990? ________________
15. What was the Age Adjusted Cancer Mortality Rate in 1990?
16. Discuss how the two sets of adjusted rates compare with each other and with the unadjusted rates.
|
STANDARD MILLION AGE DISTRIBUTION
|
|
BASED ON 1940 U.S. POPULATION
|
|
Age Group
|
Number
|
|
Under 1 year
|
15,343
|
|
1-4 years
|
64,718
|
|
5-14 years
|
170,355
|
|
15-24 years
|
181,677
|
|
25-34 years
|
162,066
|
|
35-44 years
|
139,237
|
|
45-54 years
|
117,811
|
|
55-64 years
|
80,294
|
|
65-74 years
|
48,426
|
|
75-84 years
|
17,303
|
|
85 years and over
|
2,770
|
|
All ages
|
1,000,000
|
|
STANDARD MILLION AGE DISTRIBUTION
|
|
BASED ON 2000 U.S. POPULATION
|
|
Age Group
|
Number
|
|
Under 1 year
|
13,818
|
|
1-4 years
|
55,317
|
|
5-14 years
|
145,565
|
|
15-24 years
|
138,646
|
|
25-34 years
|
135,573
|
|
35-44 years
|
162,613
|
|
45-54 years
|
134,834
|
|
55-64 years
|
87,247
|
|
65-74 years
|
66,037
|
|
75-84 years
|
44,842
|
|
85 years and over
|
15,508
|
|
All ages
|
1,000,000
|