Our primary analytic approach for describing socioeconomic gradients by area-based socioeconomic measures has been to use geocodes to append area-based socioeconomic data to case records, to stratify these records into discrete categories based on ABSM, and to aggregate numerators and denominators over areas, within levels defined by ABSM. This method avoids the problem of unstable rates arising from small areas by assuming that cases and population denominators from areas with similar socioeconomic characteristics can be legitimately combined into the same strata. An alternative approach, which preserves the spatial information of the geocodes, is discussed in the section on multilevel analyses.

The following steps are used to generate age-standardized disease rates stratified by area-based socioeconomic measures, once the case data have been geocoded and appropriate ABSMs have been generated from census data.

• Aggregate the case data into numerators (age cells within areas/geocodes).
• Aggregate population denominator data into age cells within areas/geocodes.
• Merge the numerators and denominators with ABSMs, by area/geocode.
• Aggregate over areas into strata defined by categorical ABSM and age category.
• Generate age-standardized rates and other summary measures.

Clicking on "Case Example & SAS Programming" will take you to a step by step comparison of the analytic methods, the relevant task of the Case Example, and sample SAS code.

Data from public health databases are typically formatted such that each record represents one person (or case report). Once these data have been geocoded, they need to be aggregated before linking to denominator and ABSM data. Before aggregating, however, one should exclude all records that are not geocoded, do not meet the case definition, or are missing data on the important covariates (e.g. age, in the case of simple age-standardized analyses; age, sex, and race/ethnicity in the case of more complex stratified analyses).

One can think of the basic unit of aggregation as a cell, defined by age and other covariates, within an area/geocode. Once aggregated, this cell within an area can be linked to a relevant population denominator. The cell contains a count of all cases within that area that meet the specified age and other covariate criteria. Since our goal is eventually to create rates, we call this count of cases the “numerator.”

Example:
We intend to age-standardize in 5 broad age categories, 0-14, 15-24, 25-44, 45-64, 65+. Therefore, we need to aggregate the records in each census tract into cells defined by the corresponding ages. As an example, consider the following 23 records from census tracts 25009250500 and 25009250800.

Denominator data at the census tract level typically come from the decennial census. In 1990, the US Census reported population counts by age in 31 categories (<1, 1-2, 3-4, 5, 6, 7-9, 10-11, 12-13, 14, 15, 16, 17, 18, 19, 20, 21, 22-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-61, 62-64, 65-69, 70-74, 75-79, 80-84, 85+). In the 1990 US Census STF3, age specific population counts were reported in table P013. Variable P0130001 gave the count of residents <1 year old, P0130002 gave the count of residents 1-2 years old, etc.

For the purposes of age standardization, these age categories need to be re-aggregated to match the age categories used for categorizing case data (numerators, above) and the age categories from the standard million reference population. Additionally, when using case data from multiple years, in order to calculate an average annual incidence rate, one needs to use a person-time denominator (population count multiplied by number of years of case data). For example, in the case of the Massachusetts all-cause mortality data, we have three years worth of cases (1989-1991). Therefore, we multiply the population count in each age category by 3.

Example:
For census tract 25009250800 in 1990, we wish to age standardize using the same five broad age categories as in the numerator example above (0-14, 15-24, 25-44, 45-64, 65+):

In order to collapse these variables into the five broad age categories, we have to sum up census variables as follows:

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SUM OF (P0130010 -- P0130017)

Once the numerators and denominators have the same structure (AREAKEY x AGECAT), they can be merged together, along with the ABSM data (by AREAKEY). For age cells within areas where no cases were reported, we set the numerator to zero.

Example:

Numerator dataset:

0-14

0-14

Next, in order to generate rates for categories of a specific ABSM, it is necessary to aggregate OVER areas into strata defined by AGECAT and ABSM. Numerators and denominators from census tracts with missing ABSM data for a particular ABSM are typically excluded from that analysis.

Example:
In Suffolk County, Massachusetts, there are a total of 189 census tracts. We wish to examine all cause mortality rates by poverty, with poverty categorized into 4 strata (0-4.9%, 5-9.9%, 10-19.9%, and 20-100%).

Thus, to obtain the mortality rates in the least impoverished stratum (0.0-4.9% below poverty), we need to aggregate the cases and the population at risk OVER the ten census tracts in that stratum (preserving the age structure WITHIN each poverty stratum so that we can age standardize in the following step, below). For the next poverty stratum (5.0-9.9%) we need to aggregate the cases and the population denominator over 37 census tracts, and so on. Cases and population at risk in the three census tracts with missing poverty data are excluded from the analysis.

This yields the following table:

1. Age-standardized incidence rates
The standard practice of public health departments in reporting population rates of mortality and disease incidence is to calculate age-standardized rates, which facilitates comparisons between regions or subgroups of interest. The age-standardized rate is interpretable as the rate that would be observed in a population if that population had the same age distribution as a given reference population. Standardization by the direct method involves taking a weighted average of the age specific incidence rates observed in the area or subgroup of interest, where the weights come from a standard age distribution, such as the year 2000 standard million.1

"Standard million" reference populations are available based on the US population age distribution for 1940, 1970, 1980, 1990, and 2000. Here we present the standard million in 11 age categories.

For our project, we used five broad age categories to age standardize, in order to obtain more stable rates in each age stratum, particularly for outcomes with sparse data. The relationship between our five categories and the standard eleven categories is illustrated in the table below.

Example:
To calculate the age-standardized all cause mortality rates in each of the four poverty strata in Suffolk County, we start with the age-specific mortality data. In each poverty stratum, the age standardized mortality rate is calculated as a weighted sum of the age-specific mortality rates, with the weights for each age stratum defined by the Year 2000 standard million.

Example:
In the analysis of mortality due to homicide and legal intervention among Hispanic women in Massachusetts, the estimated rate in the least impoverished group is zero, since there were no deaths reported in census tracts with 0-4.9% below poverty. In the table below, the normal approximation method yields a confidence interval of (0,0) for the rate in the least impoverished group, as well (as “impossible” negative lower limits on the rates in the 5.0-9.9% poverty stratum, as we saw above). The gamma method also yields a (0,0) interval for the rate in the least impoverished group, so we have corrected the entry for the upper confidence limit as described above. Using the “exact” upper limit on the count of 3.689, we divide this by the denominator (40,182) to give an upper limit of 9.2 per 100,000.

,9.2)

Example:
To compare the age-standardized incidence rates in the most and least impoverished census tracts in Suffolk County, we start with the age-specific data for these two strata (note: for ease of presentation, we present variances in scientific notation in the table below):

5. Relative Index of Inequality (RII)
Comparisons of socioeconomic gradients based on categorical ABSM may be complicated by differences in the population distributions of area-based socioeconomic measures. For example, it may be expected that the classifications producing smaller groups at the margins would lead to larger incidence rate ratios, comparing the most deprived to the most affluent, because finer discrimination of extremes of socioeconomic position is achieved. The relative index of inequality (RII) has been proposed as a measure which explicitly addresses this problem.5-7 Assuming ordinality of the ABSM categories, the RII is calculated by regressing the incidence rate in each ABSM category on the total proportion of the population that is more deprived in the socioeconomic hierarchy. Because the RII combines information about the magnitude of the socioeconomic gradient with information about the distribution of the socioeconomic variable in the population, it can be conceptualized as a measure of "total population input".

In practice, this latter quantity is represented by the cumulative distribution function (cdf). We approximate the cdf for the jth level of a given ABSM by summing the proportion of the population represented by the categories ABSM1, …, ABSMj-1, and adding one-half the proportion of the population represented by the category ABSMj.

Example:
In order to calculate the RII for poverty and all cause mortality in Massachusetts, we begin by calculating the approximate cumulative distribution function as follows:

Example:
The column of red numbers shows the expected number of cases in each poverty stratum.

Example:
To calculate the population attributable fraction of all cause mortality due to poverty, we begin by tabulating the cases and population person-time at risk in each poverty stratum j within each age group i. Within each age group, the case fraction CFij is the number of cases in that poverty stratum, divided by the total number of cases within the age group. The incidence rate ratio IRRij for a particular poverty stratum, relative to the reference category of the least impoverished group, is calculated by dividing the rate in that poverty stratum by the rate in the least impoverished group. For each age stratum, we calculate a separate age-specific PAF, as seen in the column of red numbers in the table below. These age-specific PAFs range from 5% to 23%.

To aggregate these PAFs across age strata, we weight the contribution of each age stratum by the proportion of cases in that age stratum. As seen in the table below, this results in an aggregated population attributable fraction PAFagg of 11%.