Calculation of Age–adjusted and Spatially Smoothed Mortality Rates

Rationale for Spatial Smoothing 

Although county death rates provide a high degree of spatial specificity, rates in counties with small populations and few deaths can be unstable. This problem is particularly relevant when examining geographic disparities among racial and ethnic groups because many counties have small or nonexistent populations of minority groups. We used two approaches to reduce the statistical instability of county death rates: (1) temporal aggregation for specified time periods and (2) application of a statistical procedure known as spatial smoothing. 

We chose to spatially smooth death rates using a spatial moving average. Deaths (numerators) and population counts (person–year denominators) for each county were combined with the deaths and population counts of the immediate neighboring counties (i.e., contiguous counties) and then divided to produce an average rate. Thus, a single county's mortality rate actually represents an average of the rates of that county and all its contiguous neighbors. 

Calculation of Death Rates 

Spatially smoothed and age–adjusted death rates were calculated at the county level by gender for each of the following racial and ethnic groups: American Indians and Alaska Natives, Asians and Pacific Islanders, blacks, Hispanics, and whites. Rates were also calculated for the total U.S. population.

For each county, the number of deaths (numerators) and population counts (denominators) for 10–year age groups (i.e., ages 35–44, 45–54, 55–64, 65–74, 75–84, and greater than or equal to 85 years) were summed for the specified time periods. County numerators and denominators were then combined with numerators and denominators of all neighboring counties. Neighboring counties were defined solely by contiguity (as opposed to distance). The combined numerators were divided by the combined denominators to produce spatially smoothed, age–specific (i.e., by 10–year age group) death rates. These spatially smoothed rates were then directly age–adjusted to the 2000 U.S. standard population for the age groups 35 years and older. These calculations were repeated separately by gender for each of the racial and ethnic groups.  Please note: The heart disease death rates for 1991–1995 that are published in our early atlases were age–adjusted to the 1970 U.S. standard population.  However, the online maps for 1991–1995 have been updated using the 2000 standard population. 

Two constraints were applied to the calculation of county death rates for each racial and ethnic group. For a particular racial and ethnic group (e.g., American Indians and Alaska Natives ages 35 years and older), a death rate was not calculated for any county for which the total number of deaths for that group in that county plus its neighbors was fewer than 20 during the specified time period.¹ To avoid calculating rates for counties that had no members of a particular population group but whose neighbors had significant populations, rates were calculated only for counties with a population count of 5 or more during the specified time period (i.e., person–years were greater than or equal to 5). Information on Hispanic ethnicity was not routinely collected on death certificates in Oklahoma during 1991–1998 or before 1993 in New Hampshire. Consequently, we removed all counties in Oklahoma and New Hampshire from the contiguity matrix when we spatially smoothed the rates for Hispanics, and no death rates for Hispanics were calculated for Oklahoma and New Hampshire.

Standard Population Weights

Because we calculated directly age–adjusted death rates for people ages greater than or equal to 35 years and not for the entire age range of the population, we had to recalculate the standard weights for the 2000 U.S. standard population. New weights for age groups 35–44 through greater than or equal to 85 years were calculated using a two–step procedure. First, we calculated the sum of the original 2000 standard weights for 10–year age groups 35–44 through greater than or equal to 85 years. Second, for each age group, we divided the original weight by the sum of the weights for ages greater than or equal to 35 years. The resulting quotients are the new standard population weights. The weights were rounded to two decimal places and used to calculate directly age–adjusted death rates for people ages greater than or equal to 35 years.

Reporting of Hispanic Origin on Death Certificates in New York City 

Heart Disease

During 1991–1993, information on Hispanic origin was not reported on approximately 22 percent of heart disease death certificates for women and men aged 35 years and older residing in New York City. During 1994–1995, the percent of death certificates that were missing information on Hispanic origin dropped to less than 3 percent. Based on a detailed examination of the New York City death certificate data for our five–year study period, we concluded that the majority of the deaths with "unknown" Hispanic origin occurred among non–Hispanics. As evident in the following table, the percent of heart disease deaths for Hispanic men and women rose only slightly between 1991–1993 and 1994–1995, while the percent of heart disease deaths for non–Hispanic men and women rose markedly after reporting improved in 1994. From 1991–1993 to 1994–1995, the average annual number of heart disease deaths increased 7 percent for Hispanics and 22 percent for non–Hispanics, while the number of deaths with unknown Hispanic origin declined 96 percent.

However, since a small proportion of the deaths with missing Hispanic origin data did occur among Hispanics, it is almost certain that the heart disease death rates reported here for Hispanics are modestly (but not severely) underestimated. In addition, the extent of underestimation may have varied among the five city boroughs; therefore prudence should be exercised in comparing individual county rates.

Stroke

During 1991–1993, information on Hispanic origin was not reported on an average 18% of stroke death certificates for adults ages 35 years and older residing in New York City. During 1994–1998, the percentage of death certificates missing this information decreased to <3%. After examining New York City death certificate data for 1991–1998, we concluded that most deaths with "unknown" Hispanic origin occurred among non–Hispanic adults. Our calculations indicated that the percentage of stroke deaths among Hispanic adults increased slightly from 1991–1993 to 1994–1998, whereas the percentage of stroke deaths for non–Hispanic adults increased markedly after reporting improved in 1994. However, because a proportion of the deaths with missing Hispanic origin data occurred among Hispanic adults, the stroke death rates reported here for Hispanic adults are likely underestimated. Erroneous reporting of Hispanics as white on death certificates also causes rates to be underestimated for Hispanics (see Section 1). The extent of underestimation may have varied among the five city boroughs, so readers should be prudent when comparing county rates.

Contiguity Matrix for Alaska

We used the contiguity matrix for all U.S. counties from the 1996 Area Resource File database to perform spatial smoothing of mortality rates. However, this database did not include information for counties in Alaska because Alaska was considered to be a single geographic unit. Because we are interested in the geographic patterns of mortality within the state, we created our own contiguity matrix for the counties in Alaska.

Mapping the Mortality Rates

On each map, counties were grouped into five categories of approximately equal number (quintiles) based on the county distribution of smoothed and age–adjusted death rates. Counties were first ranked from lowest to highest based on death rates. The lowest one–fifth of counties were assigned to the first quintile; counties with death rates between the 20th and 40th percentiles were assigned to the second quintile; between the 40th and 60th percentiles to the third quintile; between the 60th and 80th percentiles to the fourth quintile; and the highest one–fifth of counties were assigned to the highest quintile. The use of quintiles for mapping is appropriate for smoothed death rates and helps the reader avoid over–interpreting the data.

Because the death rates varied by race and ethnicity, the quintile cutpoints are different for each of the national and state maps, and the range of values represented by a given quintile varies from map to map. To determine whether the mortality rates were absolutely higher or lower for one race and ethnicity group than for another, the reader must study the relevant legends and compare the cutpoints. It is well worth making a mental note of the range of county death rates for each group when comparing geographic patterns across maps.

Reference

1. Hoyert DL, Arias E, Smith BL, Murphy SL, Kochanek KD. Deaths: final data for 1999. National Vital Statistics Reports 2001;49(8):110.
    

Date last reviewed: 05/12/2006
Content source: Division for Heart Disease and Stroke Prevention, National Center for Chronic Disease Prevention and Health Promotion