Age adjustment of diabetes prevalence: Use of 2010 US Census data

Abstract

Background:

There is a growing interest in using the 2010 US Census data for age adjustment after the Census data are officially released. This report discusses the rationale, procedures, demonstrations, and caveats of age adjustment using the 2010 US Census data.

Methods:

Empirical data from the Behavioral Risk Factor Surveillance System and the 2010 US Census age composition were used in demonstrations of computing the age-adjusted prevalence of diagnosed diabetes by race/ethnicity, across various geographic regions, and over time.

Results:

The use of the 2010 US Census data yielded higher age-adjusted prevalence of diagnosed diabetes than using the 2000 projected US population data. The differences persisted across geographic regions, among racial/ethnic groups, and over time. Sixteen age compositions were generated to facilitate the use of the 2010 Census data in age adjustment. The SAS survey procedures and SUDAAN software programs yielded similar age-adjusted prevalence estimates of diagnosed diabetes.

Conclusions:

Using the 2010 US Census data tends to yield a higher age-adjusted measure than using the 2000 projected US population data. Consistent use of a standard population and age composition is recommended once they are chosen for age adjustment.

Introduction

Public health professionals and data analysts often need to compare the rates (e.g. mortality, incidence, or prevalence) of chronic diseases or conditions (e.g. cardiovascular disease, cancer, diabetes, and metabolic syndrome) or health risk factors (e.g. smoking, heavy drinking, and physical inactivity) and to compare the means of health indicators measured on a continuous scale (e.g. body mass index, blood pressure, and blood cholesterol concentrations) across various racial/ethnic groups, over time, or across different geographic regions. Age has been recognized as the most important non-modifiable risk factor for many causes of death and for incidence and prevalence of many chronic diseases or conditions.¹ Age compositions may differ among various subpopulations, across different geographic regions, and over time.² Therefore, the aim of direct age adjustment is to apply observed age-specific estimates of a measure to age composition of a hypothetical ‘standard’ population to eliminate differences in crude measures in the populations of interest that result from differences in the age composition of the populations.

The 2000 projected US population data have been recommended as a standard population for computing age-adjusted (or age-standardized) death rates and indicators in Healthy People 2010 in the United States in the past decade.^3–5 There is growing interest in using the 2010 US Census data for age adjustment after the census data are officially released. Furthermore, it may be more realistic to use the 2010 US Census data for age-adjustment because they represent the most recent actual age compositions of the US population. Therefore, the objective of this report was to discuss the rationale and procedures of computing age-adjusted measures using the 2010 US Census data as a standard population, and to illustrate the differences in age-adjusted estimates that results from using different standard populations. Data from the Behavioral Risk Factor Surveillance System (BRFSS) were used in demonstrations of computing the age-adjusted prevalence of diagnosed diabetes by race/ethnicity, across various geographic regions, and over time.

Methods

Data

The summary data of the 2010 US Census were obtained from the US Census Bureau.⁶ According to the 2010 Census data, the US population increased by 9.7% from the year 2000 (281.4 million) to the year 2010 (308.7 million).² The median age increased from 35.3 years in 2000 to 37.2 years in 2010. The population grew faster among the older ages than among the younger ages.²

Empirical data from the BRFSS, a cross-sectional telephone survey conducted by the Centers for Disease Control and Prevention (CDC) and state health departments, were used to compute age-adjusted prevalence. The BRFSS uses a multistage cluster design that is based on random digit dialing to select a representative sample from each state’s civilian non-institutionalized adults aged 18 years or older. Diabetes status was determined by asking participants, ‘Have you ever been told by a doctor that you have diabetes?’ Responses were coded as follows: 1, yes; 2, yes, but female told only during pregnancy (i.e. gestational diabetes); 3, no; 7, don’t know/not sure; or 9, refused during 1995−2003. An additional response 4 (‘no, prediabetes or borderline diabetes’) was added to the questionnaire during 2004−2010. Gestational diabetes and prediabetes were considered as ‘no’ diabetes. A detailed description of the BRFSS survey design and sampling procedures is available elsewhere.⁷

Direct age adjustment

In epidemiologic studies, two methods of age adjustment are used, namely direct and indirect age adjustment.^3,4 In this report, we focus on direct age adjustment. Both an external population age composition and the internal age composition of available sample data can be used as a hypothetical ‘standard’ population age composition to eliminate the effects of any differences in age composition on the measures between the two or more populations being compared. The equation summarizing the computation of an age-adjusted measure (AAM)³ is:

$$AAM={\sum }_{i=1}^k\left(m_i\times w_{si}\right)$$ (1)

where i through k represents age groups, m_i represents a statistic measure for age group i (a rate or a mean), and w_si represents a standard population age-adjustment weight in age group i. The variance of age-adjusted measure³ is estimated as:

$$\text{var}\left(AAM\right)={\sum }_{i=1}^k{w_{si}}^2\times \text{var}\left(m_i\right)$$ (2)

Data demonstration and analysis

We generated a master list and 16 age compositions for different age periods with population size and age adjustment weights based on the 2010 US Census data that are commonly used in major health data systems for Healthy People 2010 objectives.⁵ Similar age composition structures as proposed in the report by Klein and Schoenborn⁵ were used to maintain consistency. We demonstrated direct calculation of age-adjusted prevalence of diagnosed diabetes between non-Hispanic whites and Hispanics using the 2011 BRFSS data. We compared the trends in age-adjusted prevalence of diagnosed diabetes from 1995 to 2010 using the 2010 Census data and the 2000 projected US population as standard populations. We also compared the age-adjusted prevalence of diagnosed diabetes using the two age compositions across the 50 states and District of Columbia (DC).

The SUDAAN DESCRIPT (Release 10.0; Research Triangle Institute, Research Triangle Park, NC, USA) and SAS SURVEYREG (SAS version 9.3; SAS Institute, Cary, NC, USA) procedures were used for computing age-adjusted prevalence and standard errors and to account for the complex design of the BRFSS data. Sample weights were used to account for the varying probabilities of complex sampling design and non-response.

Results

To facilitate use of the 2010 US Census data for age adjustment in various age periods and for different objectives, the 16 age compositions generated based on the master list are presented in Table 1. All other variations of age compositions may be created based on the master list (Appendix I), in which population size and age adjustment weights in single year and 5-year groups from age <1 year to ≥90 years are shown in males, females, and both sexes.

Table 1.

Selected age compositions and age-adjustment weights based on the 2010 US census summary population data

Age	Population	Adjustment weight	Age	Population	Adjustment weight
Composition #1			Composition #2
All ages	308 745 538	1.000000	All ages	308 745 538	1.000000
<12 years	48 836 975	0.158179	<18 years	74 181 467	0.240267
12–19 years	34 430 581	0.111518	18–44 years	112 806 642	0.365371
20–29 years	42 687 848	0.138262	45–64 years	81 489 445	0.263937
30–39 years	40 141 741	0.130016	65–74 years	21 713 429	0.070328
40–49 years	43 599 555	0.141215	≥75 years	18 554 555	0.060097
50–59 years	41 962 930	0.135914
60–69 years	29 253 187	0.094749
70–79 years	16 595 961	0.053753
≥80 years	11 236 760	0.036395
Composition #3			Composition #4
≥2 years	300 823 315	1.000000	≥2 years	300 823 315	1.000000
2–5 years	16 335 997	0.054304	2–17 years	66 259 244	0.220260
6–11 years	24 578 755	0.081705	18–44 years	112 806 642	0.374993
12–19 years	34 430 581	0.114454	45–64 years	81 489 445	0.270888
20–29 years	42 687 848	0.141903	65–74 years	21 713 429	0.072180
30–39 years	40 141 741	0.133440	≥75 years	18 554 555	0.061679
40–49 years	43 599 555	0.144934
50–59 years	41 962 930	0.139494
60–69 years	29 253 187	0.097244
70–79 years	16 595 961	0.055168
≥80 years	11 236 760	0.037353
Composition #5			Composition #6
≥18 years	234 564 071	1.000000	≥18 years	234 564 071	1.000000
18–29 years	51 773 937	0.220724	18–24 years	30 672 088	0.130762
30–39 years	40 141 741	0.171133	25–34 years	41 063 948	0.175065
40–49 years	43 599 555	0.185875	35–44 years	41 070 606	0.175093
50–59 years	41 962 930	0.178898	45–64 years	81 489 445	0.347408
60–69 years	29 253 187	0.124713	≥65 years	40 267 984	0.171672
70–79 years	16 595 961	0.070752
≥80 years	11 236 760	0.047905
Composition #7			Composition #8
≥20 years	225 477 982	1.000000	≥20 years	225 477 982	1.000000
20–29 years	42 687 848	0.189322	20–44 years	103 720 553	0.460003
30–39 years	40 141 741	0.178030	45–64 years	81 489 445	0.361408
40–49 years	43 599 555	0.193365	≥65 years	40 267 984	0.178589
50–59 years	41 962 930	0.186107
60–69 years	29 253 187	0.129739
70–79 years	16 595 961	0.073603
≥80 years	11 236 760	0.049835
Composition #9			Composition #10
≥25 years	203 891 983	1.000000	≥40 years	142 648 393	1.000000
25–34 years	41 063 948	0.201401	40–49 years	43 599 555	0.305644
35–44 years	41 070 606	0.201433	50–64 years	58 780 854	0.412068
45–64 years	81 489 445	0.399670	≥65 years	40 267 984	0.282288
≥65 years	40 267 984	0.197497
Composition #11			Composition #12
≥45 years	121 757 429	1.000000	≥50 years	99 048 838	1.000000
45–49 years	22 708 591	0.186507	50–64 years	58 780 854	0.593453
50–64 years	58 780 854	0.482770	≥65 years	40 267 984	0.406547
≥65 years	40 267 984	0.330723
Composition #13			Composition #14
≥65 years	40 267 984	1.000000	<65 years	268 477 554	1.000000
65–74 years	21 713 429	0.539223	<18 years	74 181 467	0.276304
≥75 years	18 554 555	0.460777	18–44 years	112 806 642	0.420172
			45–64 years	81 489 445	0.303524
Composition #15			Composition #16
18–64 years	194 296 087	1.000000	<18 years	74 181 467	1.000000
18–24 years	30 672 088	0.157863	<5 years	20 201 362	0.272324
25–34 years	41 063 948	0.211347	5–11 years	28 635 613	0.386021
35–44 years	41 070 606	0.211382	12–17 years	25 344 492	0.341655
45–64 years	81 489 445	0.419409

Bolded values indicate the total or subtotal numbers by age groups.

The direct calculations of age-adjusted prevalence and its standard error of diagnosed diabetes between non-Hispanic whites and Hispanics using Eqns 1 and 2 are illustrated in Table 2. The age composition #5 in Table 1 is selected for the illustration. The numbers in Columns A and F are crude prevalence rates of diagnosed diabetes in each age group among non-Hispanic whites and Hispanics, respectively. The numbers in Columns B and G are standard errors for crude prevalence rates of diagnosed diabetes in each age group among non-Hispanic whites and Hispanics, respectively. The numbers in Columns C and H are age-adjustment weights for each age group adopted from the age composition #5 in Table 2. The numbers in Columns D and I are computed using Eqn 1 in each age group, respectively. The numbers in Columns E and J are computed using the Eqn 2 in each age group, respectively. The age-adjusted prevalence of diagnosed diabetes among non-Hispanic whites is 8.1%, which is the sum of values in Column D in each age group. The standard error of age-adjusted prevalence of diagnosed diabetes among non-Hispanic whites is 0.07%, which is the square root of sum of values in Column E in each age group. Similarly, the age-adjusted prevalence of diagnosed diabetes and its standard error among Hispanics are 13.8% and 0.36%, respectively. Compared with the crude prevalence, the age-adjusted prevalence among non-Hispanic whites is lower than the non-adjusted prevalence (from 9.1% to 8.1%), whereas age-adjusted prevalence among Hispanics is higher than the non-adjusted prevalence (from 10.1% to 13.8%).

Table 2.

Direct calculation of age-adjusted prevalence of diabetes between non-Hispanic whites and Hispanics, 2011 Behavioral Risk Factor Surveillance System

Age (years)	Non-Hispanic whites					Hispanics
	Diabetes		Age-adjustment weight	A × C	B2 × C2	Diabetes		Age-adjustment weight	F × H	G2 × H2
	%	SE				%	SE
	A	B	C	D	E	F	G	H	I	J
18–29	1.1	0.1	0.220724	0.2	0.000430	1.3	0.2	0.220724	0.3	0.002305
30–39	2.7	0.2	0.171133	0.5	0.000724	4.7	0.5	0.171133	0.8	0.006827
40–49	6.1	0.2	0.185875	1.1	0.001185	10.5	0.8	0.185875	2.0	0.019624
50–59	10.4	0.2	0.178898	1.9	0.001288	19.3	1.0	0.178898	3.5	0.032786
60–69	17.5	0.2	0.124713	2.2	0.000914	29.6	1.4	0.124713	3.7	0.032553
70–79	20.5	0.3	0.070752	1.5	0.000470	30.1	1.9	0.070752	2.1	0.017264
80+	16.1	0.3	0.047905	0.8	0.000278	31.2	2.9	0.047905	1.5	0.019094
Total	9.1	0.1	1.000000	8.1*	0.072727*	10.1	0.3	1.000000	13.8*	0.361183†

^*Age-adjusted prevalence (AAP) was calculated using Eqn 1 (see text for details).

^†The standard error (SE) was calculated as $\sqrt{\text{var}\left(AAP\right)}$, where the variance of AAP was estimated using Eqn 2 (see text for details).

Crude and age-adjusted prevalences of diagnosed diabetes among adults from 1995 to 2010 using the annual BRFSS data are shown in Figure 1. The magnitude in age-adjusted prevalence of diagnosed diabetes using the 2010 US Census data was larger than that using the 2000 projected US population at each year of the BRFSS survey. However, the trend in age-adjusted prevalence appeared to be similar when two standard populations were used.

Figure 1.

Trends of diabetes prevalence among adults aged ≥18 years in the US, Behavioral Risk Factor Surveillance System 1995–2010. (---), crude prevalence (linear trend: t = 71.5, P < 0.0001); (·····), age-adjusted prevalence using the 2000 projected US population (linear trend: t = 62.0, P < 0.0001); (-----), age-adjusted prevalence using the 2010 US Census population (linear trend: t = 62.6, P < 0.0001).

Crude and age-adjusted prevalences of diagnosed diabetes among adults across the 50 states and DC in 2010 are given in Table 3. The age-adjusted prevalences using the 2000 projected US population were lower than those estimated using the 2010 US Census data for all states and DC combined (P < 0.0001). The absolute difference in age-adjusted prevalence of diabetes among 50 states and DC ranged from 0.27% to 0.69% (all P > 0.10), and the relative difference ranged from 3.37% to 7.41%. The age-adjusted prevalence estimates of diagnosed diabetes by race/ethnicity using the SUDAAN DESCRIPT and SAS SURVEYREG procedures are identical (Appendix II). However, the standard errors of age-adjusted prevalence estimates differed slightly between the two software programs, which yielded slightly different 95% confidence intervals.

Table 3.

Comparison of crude and age-adjusted prevalence of diagnosed diabetes by state, 2011 Behavioral Risk Factor Surveillance System

State	n	Crude prevalence [% (SE)]	AAP using 2010 US Census data [% (SE)]	AAP using 2000 projected US population [% (SE)]	Absolute difference*	Relative difference (%)†
All	485694	9.73 (0.08)	9.51 (0.08)	9.01 (0.07)	−0.50‡	−5.53
Alabama	7542	11.66 (0.46)	11.23 (0.43)	10.67 (0.43)	−0.56	−5.21
Alaska	3445	7.86 (0.72)	8.62 (0.73)	8.22 (0.74)	−0.41	−4.95
Arizona	6156	9.52 (0.64)	9.42 (0.62)	9.02 (0.62)	−0.39	−4.35
Arkansas	4590	11.06 (0.59)	10.68 (0.57)	10.14 (0.58)	−0.55	−5.39
California	16843	8.91 (0.29)	8.86 (0.28)	8.33 (0.26)	−0.53	−6.36
Colorado	13239	6.63 (0.29)	6.81 (0.28)	6.55 (0.29)	−0.27	−4.07
Connecticut	6640	9.33 (0.46)	8.79 (0.41)	8.21 (0.39)	−0.58	−7.12
Delaware	4672	9.66 (0.55)	9.1 (0.51)	8.62 (0.51)	−0.48	−5.56
District of Columbia	4395	9.12 (0.58)	9.96 (0.56)	9.54 (0.56)	−0.42	−4.45
Florida	11995	10.44 (0.39)	9.3 (0.36)	8.65 (0.34)	−0.64	−7.41
Georgia	9732	10.13 (0.37)	10.65 (0.36)	9.97 (0.35)	−0.68	−6.78
Hawaii	7416	8.32 (0.41)	8.01 (0.39)	7.58 (0.39)	−0.44	−5.76
Idaho	5908	9.34 (0.51)	9.37 (0.5)	8.85 (0.49)	−0.52	−5.91
Illinois	5418	9.69 (0.55)	9.71 (0.53)	9.4 (0.54)	−0.32	−3.37
Indiana	8262	10.13 (0.4)	9.93 (0.38)	9.43 (0.38)	−0.50	−5.34
Iowa	7216	8.18 (0.35)	7.66 (0.32)	7.18 (0.3)	−0.49	−6.81
Kansas	20508	9.53 (0.23)	9.37 (0.22)	8.88 (0.22)	−0.48	−5.46
Kentucky	10566	10.71 (0.41)	10.39 (0.39)	9.81 (0.39)	−0.58	−5.91
Louisiana	10776	11.85 (0.43)	11.78 (0.42)	11.32 (0.42)	−0.45	−4.01
Maine	12937	9.53 (0.3)	8.54 (0.27)	8.1 (0.27)	−0.43	−5.36
Maryland	9830	9.42 (0.41)	9.29 (0.38)	8.85 (0.38)	−0.44	−4.98
Massachusetts	21571	8.02 (0.27)	7.77 (0.25)	7.41 (0.25)	−0.36	−4.92
Michigan	10802	10.03 (0.38)	9.55 (0.36)	9.14 (0.36)	−0.42	−4.56
Minnesota	15112	7.28 (0.28)	7.17 (0.28)	6.88 (0.27)	−0.29	−4.24
Mississippi	8779	12.28 (0.42)	12.19 (0.39)	11.51 (0.39)	−0.69	−5.97
Missouri	6308	10.17 (0.48)	9.8 (0.46)	9.33 (0.46)	−0.47	−5.08
Montana	10137	7.94 (0.37)	7.33 (0.34)	7.03 (0.34)	−0.30	−4.32
Nebraska	25132	8.36 (0.24)	8.16 (0.23)	7.69 (0.22)	−0.46	−6.02
Nevada	5316	10.39 (0.79)	10.65 (0.79)	10.19 (0.77)	−0.46	−4.55
New Hampshire	6186	8.6 (0.41)	8.12 (0.39)	7.69 (0.39)	−0.43	−5.60
New Jersey	14895	8.76 (0.31)	8.43 (0.29)	7.95 (0.28)	−0.48	−6.00
New Mexico	9232	9.97 (0.38)	9.8 (0.37)	9.34 (0.37)	−0.45	−4.87
New York	7399	10.27 (0.44)	10.03 (0.42)	9.44 (0.41)	−0.59	−6.27
North Carolina	11319	10.73 (0.41)	10.49 (0.39)	9.95 (0.38)	−0.54	−5.40
North Dakota	5185	8.27 (0.42)	8.13 (0.4)	7.67 (0.4)	−0.46	−6.03
Ohio	9672	9.91 (0.38)	9.42 (0.36)	8.9 (0.35)	−0.51	−5.76
Oklahoma	8467	11.11 (0.41)	10.9 (0.4)	10.36 (0.39)	−0.55	−5.27
Oregon	6121	9.2 (0.46)	8.64 (0.43)	8.22 (0.44)	−0.42	−5.12
Pennsylvania	11173	9.44 (0.36)	8.68 (0.33)	8.24 (0.33)	−0.44	−5.29
Rhode Island	6344	8.4 (0.42)	8.08 (0.4)	7.72 (0.4)	−0.36	−4.68
South Carolina	12518	11.7 (0.41)	11.33 (0.4)	10.83 (0.4)	−0.51	−4.69
South Dakota	8166	9.48 (0.57)	8.98 (0.54)	8.61 (0.53)	−0.37	−4.29
Tennessee	5818	11.16 (0.74)	10.72 (0.68)	10.1 (0.65)	−0.61	−6.04
Texas	14565	10.17 (0.39)	10.7 (0.39)	10.16 (0.38)	−0.54	−5.28
Utah	12430	6.67 (0.26)	7.78 (0.27)	7.39 (0.27)	−0.38	−5.17
Vermont	6945	7.64 (0.36)	7.08 (0.35)	6.76 (0.35)	−0.32	−4.69
Virginia	6428	10.4 (0.54)	10.32 (0.51)	9.74 (0.5)	−0.58	−5.97
Washington	14461	8.83 (0.33)	8.74 (0.32)	8.34 (0.32)	−0.40	−4.84
West Virginia	5228	12.07 (0.49)	11.1 (0.45)	10.6 (0.45)	−0.50	−4.69
Wisconsin	5203	8.3 (0.49)	7.95 (0.46)	7.53 (0.44)	−0.42	−5.55
Wyoming	6696	8.13 (0.48)	7.99 (0.46)	7.57 (0.45)	−0.42	−5.60

^*Difference between age-adjusted prevalence (AAP) using the 2000 projected US population and AAP using the 2010 US Census data.

^†Calculated as the difference in two AAP values divided by the prevalence using the 2000 projected US population data.

^‡P < 0.0001; t-tests were used to test for equality between the two AAPs. All P-values for the absolute differences in the two prevalences for individual states were >0.10 (ranging from 0.13 to 0.69).

Examples of the SUDAAN DESCRIPT procedure for testing the linear and quadratic trends in age-adjusted prevalence during the 18 survey years (from 1995 to 2010) are illustrated in Appendix III. Examples of the SUDAAN DESCRIPT and SAS SURVEYREG procedures for computing age-adjusted prevalence by race/ethnicity (non-Hispanic white, non-Hispanic black, Hispanic, and non-Hispanic other) are illustrated in Appendices IV and V, respectively.

Discussion

This report illustrates the use of a new alternative standard population for age adjustment using the 2010 US Census data. The master list of single year and 5-year age group population size and age-adjustment weights were provided to facilitate generation of a specific age composition to fulfill a special need. The selected 16 age compositions were generated to facilitate use of standard population for various objectives. Compared with results using the 2010 US Census data as the standard population, age-adjusted prevalence of diagnosed diabetes using the 2000 projected US population tend to be smaller in magnitude, although the overall trends over time appeared to be similar.

Age adjustment is common practice among health professionals. From the perspective of epidemiologic studies, age adjustment is a means of controlling for the possible confounding effects of age when age is associated with a health outcome (e.g. diagnosed diabetes or blood pressure) and there are differences in age compositions among subpopulations being compared. A crude rate reflects the ‘absolute’ disease burden in a region or a time period; it is useful for making health policies. An age-adjusted rate reflects the ‘relative’ disease burden when comparing two or more regions, time periods, or specific subpopulations based on a standard population; it is useful for evaluating program effects, secular trends, and disparities after eliminating the confounding effects of age. The use of an available standard population is to facilitate comparisons across different studies, in diverse populations, or over time.

The 2000 projected US population has been used as a standard population for age adjustment in the US in the past decade.^3–5 The use of a single age-adjustment standard by federal agencies may be helpful in facilitating comparisons of health indicators among federal and state health agencies.³ In addition, the World Health Organization (WHO) has constructed a world standard population for age adjustment,⁸ which has been used in European countries and other countries outside the US. Although there is no theoretical justification for using one population standard over another, using different standard populations may impact the magnitude and, to some extent, the trend of age-adjusted measures (e.g. death rates).^3,4 Consistent with previous reports,^3,4 our results suggest that using an earlier population age composition tends to yield a lower age-adjusted measure than using the most recent population age compositions. Because diabetes prevalence is higher among older people than among younger people,² using an earlier or younger population age composition with a lower proportion of older ages could yield a lower age-adjusted prevalence.

It is arbitrary whether to choose the 2010 US Census data, as suggested in this report, the 2000 projected US population,⁵ the WHO world standard population,⁸ or a specific standard population created by a health professional or data analyst. However, there are several considerations when one chooses a standard population for computing age-adjusted measures. First, because age-adjusted measures using different standard population are not comparable, a standard population should be used consistently in all comparisons once it is chosen. Second, a standard population should have a similar age composition as the study population. A standard population with abnormal or unnatural age composition relative to the study population should be avoided. Therefore, one of the selected 16 age compositions with a reasonable age structure according to the sample size and crude prevalence (or mean) estimates in each age group could be used for age adjustment in the US. Third, a pooled standard population may be used when comparing measures across different countries to minimize variance. The WHO world standard population accounts for the average age composition structure of the world population and time series of observation and eliminates the impact of historical events, such as wars and famine, on the age composition of certain populations.⁸ Therefore, a pooled standard population of two or more countries or the WHO world standard population may be used as a standard population when one compares measures between two or more countries.

It is of note that both the SUDAAN DESCRIPT and SAS SURVEYREG procedures yielded identical age-adjusted prevalence estimates of diagnosed diabetes but slightly different standard errors for the prevalence estimates. It has been shown that when the analysis includes all participants with no missing data for all analytic variables and the Taylor variance estimation method is used, SUDAAN and SAS survey procedures yield identical estimates.⁹ However, when certain strata have only one primary sampling unit or cluster, SUDAAN and SAS survey procedures may yield different results because the two software programs use different variance estimation methods: SUDAAN uses the difference between the stratum’s value and the overall population mean to estimate the variance, whereas SAS estimates the variance by zero.⁹

It is worth commenting on the caveats for age adjustment. First, an age-adjusted measure is a hypothetical measure. It does not reflect the actual status in the populations. However, an age-adjusted measure could be useful to evaluate the effects of health risks other than age on the health outcome among subpopulations or over time. Second, age-adjusted measures may mask interesting differences in age-specific measures. For example, if there is an age by time interaction, it is inappropriate to report age-adjusted rates or means.¹⁰ Instead, age-specific trends may be reported separately when an age by time interaction exits. Third, age-adjusted measures may not be comparable when different population standard or age composition structures are used. Applying different population standards or age composition to the same data could result in different results and interpretations. Thus, it is imperative and critical to ensure the use of identical standard populations when comparing age-adjusted health indicators between state and federal agencies, among subpopulations, across data systems, or over time.

In conclusion, direct age adjustment is a common practice in public health data analysis and epidemiologic studies. It requires selection of a standard population. The same standard population and age composition should be used consistently once they are chosen. The 2000 projected US population recommended by the National Center for Health Statistics has been used in the US in the past decade. With the official release of the 2010 Census data, there is a growing interest in using the most recent population data as a standard population for age adjustment in health survey data analysis. For readers who are interested in using the most recent age compositions to adjust their data for age, this report demonstrates the use of the 2010 US Census age composition and provides detailed procedures on how to compute age-adjusted measures.

Significant findings of the study:

This methodological guide provides detailed steps as to how to perform age adjustments of diabetes prevalence using the 2010 US Census population data. It also highlights the importance of using selected standard population for computing age-adjusted rates.

What this study adds:

This is the first study that demonstrates the use of the 2010 US Census population data for age adjustment when comparing diabetes prevalence by time, region, and subpopulations.

Appendix I. Master list: The 2010 US Census population and age-adjustment weights

	Both sexes		Male		Female
Age	Population	Adjustment weight	Population	Adjustment weight	Population	Adjustment weight
Total population (all ages)	308 745 538	1.000000	151 781 326	1.000000	156 964 212	1.000000
Under 5 years	20 201 362	0.065430	10 319 427	0.067989	9 881 935	0.062957
Under 1 year	3 944 153	0.012775	2 014 276	0.013271	1 929 877	0.012295
1 year	3 978 070	0.012885	2 030 853	0.013380	1 947 217	0.012405
2 years	4 096 929	0.013270	2 092 198	0.013784	2 004 731	0.012772
3 years	4 119 040	0.013341	2 104 550	0.013866	2 014 490	0.012834
4 years	4 063 170	0.013160	2 077 550	0.013688	1 985 620	0.012650
5–9 years	20 348 657	0.065908	10 389 638	0.068451	9 959 019	0.063448
5 years	4 056 858	0.013140	2 072 094	0.013652	1 984 764	0.012645
6 years	4 066 381	0.013171	2 075 319	0.013673	1 991 062	0.012685
7 years	4 030 579	0.013055	2 057 076	0.013553	1 973 503	0.012573
8 years	4 046 486	0.013106	2 065 453	0.013608	1 981 033	0.012621
9 years	4 148 353	0.013436	2 119 696	0.013965	2 028 657	0.012924
10–14 years	20 677 194	0.066972	10 579 862	0.069705	10 097 332	0.064329
10 years	4 172 541	0.013514	2 135 996	0.014073	2 036 545	0.012975
11 years	4 114 415	0.013326	2 103 264	0.013857	2 011 151	0.012813
12 years	4 106 243	0.013300	2 100 145	0.013837	2 006 098	0.012781
13 years	4 118 013	0.013338	2 104 914	0.013868	2 013 099	0.012825
14 years	4 165 982	0.013493	2 135 543	0.014070	2 030 439	0.012936
15 to 19 years	22 040 343	0.071387	11 303 666	0.074473	10 736 677	0.068402
15 years	4 242 820	0.013742	2 177 022	0.014343	2 065 798	0.013161
16 years	4 316 139	0.013980	2 216 034	0.014600	2 100 105	0.013380
17 years	4 395 295	0.014236	2 263 153	0.014911	2 132 142	0.013584
18 years	4 500 855	0.014578	2 305 473	0.015189	2 195 382	0.013987
19 years	4 585 234	0.014851	2 341 984	0.015430	2 243 250	0.014291
20–24 years	21 585 999	0.069915	11 014 176	0.072566	10 571 823	0.067352
20 years	4 519 129	0.014637	2 308 319	0.015208	2 210 810	0.014085
21 years	4 354 294	0.014103	2 223 198	0.014647	2 131 096	0.013577
22 years	4 264 642	0.013813	2 177 797	0.014348	2 086 845	0.013295
23 years	4 198 571	0.013599	2 140 799	0.014104	2 057 772	0.013110
24 years	4 249 363	0.013763	2 164 063	0.014258	2 085 300	0.013285
25–29 years	21 101 849	0.068347	10 635 591	0.070072	10 466 258	0.066679
25 years	4 262 350	0.013805	2 161 308	0.014240	2 101 042	0.013385
26 years	4 152 305	0.013449	2 097 088	0.013817	2 055 217	0.013094
27 years	4 248 869	0.013762	2 140 651	0.014104	2 108 218	0.013431
28 years	4 215 249	0.013653	2 118 605	0.013958	2 096 644	0.013357
29 years	4 223 076	0.013678	2 117 939	0.013954	2 105 137	0.013412
30–34 years	19 962 099	0.064656	9 996 500	0.065861	9 965 599	0.063490
30 years	4 285 668	0.013881	2 160 802	0.014236	2 124 866	0.013537
31 years	3 970 218	0.012859	1 988 155	0.013099	1 982 063	0.012627
32 years	3 986 847	0.012913	1 994 476	0.013140	1 992 371	0.012693
33 years	3 880 150	0.012567	1 936 863	0.012761	1 943 287	0.012380
34 years	3 839 216	0.012435	1 916 204	0.012625	1 923 012	0.012251
35–39 years	20 179 642	0.065360	10 042 022	0.066161	10 137 620	0.064586
35 years	3 956 434	0.012815	1 980 916	0.013051	1 975 518	0.012586
36 years	3 802 087	0.012315	1 890 595	0.012456	1 911 492	0.012178
37 years	3 934 445	0.012743	1 953 386	0.012870	1 981 059	0.012621
38 years	4 121 880	0.013350	2 049 720	0.013504	2 072 160	0.013201
39 years	4 364 796	0.014137	2 167 405	0.014280	2 197 391	0.013999
40–44 years	20 890 964	0.067664	10 393 977	0.068480	10 496 987	0.066875
40 years	4 383 274	0.014197	2 191 249	0.014437	2 192 025	0.013965
41 years	4 114 985	0.013328	2 047 818	0.013492	2 067 167	0.013170
42 years	4 076 104	0.013202	2 028 653	0.013366	2 047 451	0.013044
43 years	4 105 105	0.013296	2 035 990	0.013414	2 069 115	0.013182
44 years	4 211 496	0.013641	2 090 267	0.013772	2 121 229	0.013514
45–49 years	22 708 591	0.073551	11 209 085	0.073850	11 499 506	0.073262
45 years	4 508 868	0.014604	2 237 450	0.014741	2 271 418	0.014471
46 years	4 519 761	0.014639	2 230 982	0.014699	2 288 779	0.014582
47 years	4 535 265	0.014689	2 238 248	0.014747	2 297 017	0.014634
48 years	4 538 796	0.014701	2 237 734	0.014743	2 301 062	0.014660
49 years	4 605 901	0.014918	2 264 671	0.014921	2 341 230	0.014916
50–54 years	22 298 125	0.072222	10 933 274	0.072033	11 364 851	0.072404
50 years	4 660 295	0.015094	2 300 354	0.015156	2 359 941	0.015035
51 years	4 464 631	0.014461	2 190 766	0.014434	2 273 865	0.014487
52 years	4 500 846	0.014578	2 207 246	0.014542	2 293 600	0.014612
53 years	4 380 354	0.014188	2 141 354	0.014108	2 239 000	0.014264
54 years	4 291 999	0.013901	2 093 554	0.013793	2 198 445	0.014006
55–59 years	19 664 805	0.063693	9 523 648	0.062746	10 141 157	0.064608
55 years	4 254 709	0.013781	2 073 473	0.013661	2 181 236	0.013896
56 years	4 037 513	0.013077	1 956 141	0.012888	2 081 372	0.013260
57 years	3 936 386	0.012750	1 905 355	0.012553	2 031 031	0.012939
58 years	3 794 928	0.012291	1 834 808	0.012088	1 960 120	0.012488
59 years	3 641 269	0.011794	1 753 871	0.011555	1 887 398	0.012024
60–64 years	16 817 924	0.054472	8 077 500	0.053218	8 740 424	0.055684
60 years	3 621 131	0.011729	1 745 507	0.011500	1 875 624	0.011949
61 years	3 492 596	0.011312	1 679 077	0.011062	1 813 519	0.011554
62 years	3 563 182	0.011541	1 712 692	0.011284	1 850 490	0.011789
63 years	3 483 884	0.011284	1 672 329	0.011018	1 811 555	0.011541
64 years	2 657 131	0.008606	1 267 895	0.008353	1 389 236	0.008851
65–69 years	12 435 263	0.040277	5 852 547	0.038559	6 582 716	0.041938
65 years	2 680 761	0.008683	1 273 310	0.008389	1 407 451	0.008967
66 years	2 639 141	0.008548	1 248 276	0.008224	1 390 865	0.008861
67 years	2 649 365	0.008581	1 248 906	0.008228	1 400 459	0.008922
68 years	2 323 672	0.007526	1 087 296	0.007164	1 236 376	0.007877
69 years	2 142 324	0.006939	994 759	0.006554	1 147 565	0.007311
70–74 years	9 278 166	0.030051	4 243 972	0.027961	5 034 194	0.032072
70 years	2 043 121	0.006617	945 611	0.006230	1 097 510	0.006992
71 years	1 949 323	0.006314	900 148	0.005931	1 049 175	0.006684
72 years	1 864 275	0.006038	853 726	0.005625	1 010 549	0.006438
73 years	1 736 960	0.005626	787 863	0.005191	949 097	0.006047
74 years	1 684 487	0.005456	756 624	0.004985	927 863	0.005911
75–79 years	7 317 795	0.023702	3 182 388	0.020967	4 135 407	0.026346
75 years	1 620 077	0.005247	721 008	0.004750	899 069	0.005728
76 years	1 471 070	0.004765	647 804	0.004268	823 266	0.005245
77 years	1 455 330	0.004714	631 884	0.004163	823 446	0.005246
78 years	1 400 123	0.004535	602 458	0.003969	797 665	0.005082
79 years	1 371 195	0.004441	579 234	0.003816	791 961	0.005045
80–84 years	5 743 327	0.018602	2 294 374	0.015116	3 448 953	0.021973
80 years	1 308 511	0.004238	543 559	0.003581	764 952	0.004873
81 years	1 212 865	0.003928	494 870	0.003260	717 995	0.004574
82 years	1 161 421	0.003762	462 983	0.003050	698 438	0.004450
83 years	1 074 809	0.003481	419 831	0.002766	654 978	0.004173
84 years	985 721	0.003193	373 131	0.002458	612 590	0.003903
85–89 years	3 620 459	0.011726		0.008393	2 346 592	0.014950
85 years	914 723	0.002963	336 819	0.002219	577 904	0.003682
86 years	814 211	0.002637	293 120	0.001931	521 091	0.003320
87 years	712 908	0.002309	249 803	0.001646	463 105	0.002950
88 years	640 619	0.002075	217 436	0.001433	423 183	0.002696
89 years	537 998	0.001743	176 689	0.001164	361 309	0.002302
90 years and over	1 872 974	0.006066	515 812	0.001671	1 357 162	0.004396

Bolded values indicate the total or subtotal numbers by age groups.

Note, the 2010 US Census population data are available from http://factfinder2.census.gov/faces/tableservices/jsf/pages/productview.xhtml?pid=DEC_10_SF1_QTP2&prodType=table (accessed 12 December 2012).

When using the master list to generate additional age composition categories not presented in Table 2, the age-adjustment weights need to be recalculated using the appropriate subtotals as denominator and the adjustment weight must add to 1.

Appendix II. Comparison of age-adjusted prevalence estimates of diagnosed diabetes between SUDAAN and SAS, the 2011 Behavioral Risk Factor Surveillance System

	SUDAAN PROC DESCRIPT			SAS PROC SURVEYREG
Race/ethnicity	Diabetes (%)	SE	95% CI	Diabetes (%)	SE	95% CI
NH white	8.117509	0.072688	7.975041–8.259977	8.117509	0.072688	7.975040–8.259978
NH black	14.870951	0.298228	14.286424–15.455478	14.870951	0.298238	14.286403–15.455498
Hispanic	13.807271	0.360795	13.100113–14.514429	13.807271	0.360782	13.100138–14.514404
NH other	10.939010	0.400601	10.153832–11.724188	10.939010	0.400610	10.153814–11.724206

NH, non-Hispanic; SE, standard error; CI, confidence interval.

Appendix III. SUDAAN codes for testing linear and quadratic trends in age-adjusted prevalence using the 2010 US Census population age-adjustment weights over survey years, Behavioral Risk Factor Surveillance System 1995–2010

proc descript data=dmtrend filetype=SAS design=wr; NEST survyear _STSTR _PSU/psulev=3 MISSUNIT; /* note 1 */ WEIGHT _finalwt; /* note 2 */ var DM; catlevel 1; /* note 3 */ subgroup survyear sex agedist10 race4 DM; level 18 2 7 4 2; tables sex; stdvar agedist10; stdwgt 0.220724 0.171133 0.185875 0.178898 0.124713 0.070752 0.047905; /* note 4 */ poly survyear=2; /* note 5 */ subpopn age>=18 & _state<=56; setenv rowwidth = 2 colwidth = 10 rowspce=0 colspce=2 topmgn=0 pagesize=60; print nsum PERCENT SEPERCENT T_pct P_pct/nsumfmt = F10.0 PERCENTfmt = F20.8 SEPERCENTfmt = F20.8 style=NCHS; title ‘Test for linear and quadratic trends in the prevalence of self-reported diabetes by survey year, age-adjustment using 2010 US Census population’; run;

Note 1: survyear = survey year, an indicator variable representing survey year 1 = 1995, 2 = 1996, 3 = 1997, …, 18 = 2010. The survey year variable is included in the ‘NEST’ statement to obtain appropriate variance estimates.

Note 2: _finalwt = sample weights. The original sample weights in each year are used. This sampling weight reflected landline survey only.

Note 3: catlevel statement can be omitted for continuous variables, just put the variable in the var statement (e.g. ‘var BP’; here, BP stands for blood pressure).

Note 4: either age-adjusted weights or the sample size can be used in this statement.

Note 5: poly statement specifies orthogonal polynomial contrast for linear or quadratic trends.

Appendix IV. SUDAAN codes for computing age-adjusted by race/ethnicity using the 2010 US Census population age-adjustment weights, the 2011 Behavioral Risk Factor Surveillance System

proc descript data=brfss11 filetype=SAS design=wr; nest _STSTR _PSU/missunit; weight _LLCPWT; /* Note 1 */ var DM; catlevel 1; subgroup sex agedist10 race4; level 2 7 4; tables race4; stdvar agedist10; stdwgt 0.220724 0.171133 0.185875 0.178898 0.124713 0.070752 0.047905; subpopn anasamp=2; setenv rowwidth = 2 colwidth = 10 rowspce=0 colspce=2 topmgn=0 pagesize=60; print nsum=‘SAMPLE SIZE’ percent=‘PERCENT’ sepercent=‘S.E.’ /nsumfmt = F6.0 wsumfmt = F10.0 percentfmt = F10.6 sepercentfmt = F10.6 style=NCHS; title ‘Prevalence of diagnosed diabetes by race/ethnicity, age-adjustment using the 2010 US Census population’; run;

Note 1: the sampling weight reflected landline and cellphone surveys combined.

Appendix V. SAS codes for computing age-adjusted prevalence by race/ethnicity using the 2010 US Census population age-adjustment weights, the 2011 Behavioral Risk Factor Surveillance System

PROC SURVEYREG DATA=brfss11 order=internal; strata _STSTR ; cluster _PSU; weight _LLCPWT; class race4 agedist10; model DM01 = race4 * agedist10/NOINT SOLUTION CLPARM;/* note 1 */ domain anasamp; estimate ‘Age-adjusted DM %, White’ race4 * agedist10 22.0724 17.1133 18.5875 17.8898 12.4713 7.0752 4.7905 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; estimate ‘Age-adjusted DM %, Black’ race4 * agedist10 0 0 0 0 0 0 0 22.0724 17.1133 18.5875 17.8898 12.4713 7.0752 4.7905 0 0 0 0 0 0 0 0 0 0 0 0 0 0; estimate ‘Age-adjusted DM %, Hispanics’ race4 * agedist10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22.0724 17.1133 18.5875 17.8898 12.4713 7.0752 4.7905 0 0 0 0 0 0 0; estimate ‘Age-adjusted DM %, Other’ race4 * agedist10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22.0724 17.1133 18.5875 17.8898 12.4713 7.0752 4.7905; title ‘Age-adjusted % of diabetes by race, age composition #5, SAS SURVEYREG, BRFSS 2011’; run;

Note 1: DM01, diagnosed diabetes status coded as 1 = yes, 0 = no.