Estimating County-Level Mortality Rates Using Highly Censored Data From CDC WONDER

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This figure displays maps of the age-standardized rates from the raw data, the approach of Tiwari et al (8), the Poisson-gamma model of equation 4, and the MCAR model described in relation to equation 5. The maps of the estimates from the raw data and the Poisson-gamma model look similar and contain many extreme rates, ie, rates at the high end or low end of the spectrum. Because of the smoothing used in the approach of Tiwari et al (8), the map of its rates tends to show similar rates in each of a state’s more rural counties. Finally, the map of the estimates from the MCAR model exhibit the same general trend observed in the other 3 maps, but with more gradual transitions between regions with high rates and regions with low rates.

Figure 1.
Estimates of age-standardized heart disease mortality rates from 1980. A, Crude age-standardized rates based solely on the data. B, Estimates obtained by using the approach of Tiwari et al (8). C, Estimated posterior medians from the Poisson-gamma model. D, Estimated posterior medians from the multivariate conditional autoregressive model (MCAR). Data source: Centers for Disease Control and Prevention (18).

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Figure 2 compares maps of the rate estimates from the 3 approaches for the age groups 35 to 44 and 85 or older. Because of the high rate of suppression, the substitution approach of Tiwari et al (8) for those aged 35 to 44 assigns nearly every county in each state the same value. The Poisson-gamma model also struggles with this age-group, producing estimates that are quite high for many rural parts of the country. In contrast to these approaches, the MCAR model produces estimates that are much more spatially smooth (ie, gradual changes from high to low rates) for this age-group. Moving on to the estimates from the 85 and older age-group, we find a bit more similarity between the substitution approach and the Poisson-gamma model — this is not too surprising, given the higher death counts and thus lower rate of suppression. Again, the MCAR model produces estimates for the 85 or older age-group that exhibit much more spatial smoothing. Finally, from an epidemiologic perspective, the MCAR estimates from the 35 to 44 age-group exhibit high rates in Appalachia and the Deep South, while the MCAR estimates from the 85 or older age-group exhibit high rates in New England and the Rust Belt region. These broader trends are more apparent in the maps of the MCAR estimates than in the maps from the other 2 approaches because of the lack of smoothing in the estimates they produce.

Figure 2.
Comparison of 3 approaches for estimating age-standardized heart disease mortality rates for 2 age groups (adults aged 35 to 44 and adults aged ≥85) from 1980. A, Estimates for adults aged 35 to 44 obtained by using the approach of Tiwari et al (8). B, Estimated posterior medians for adults aged 35 to 44 from the Poisson-gamma model. C, Estimated posterior medians for adults aged 35 to 44 from the multivariate conditional autoregressive model (MCAR). D, Estimates for adults aged ≥85 obtained by using the approach of Tiwari et al (8). E, Estimated posterior medians for adults aged ≥85 from the Poisson-gamma model. F, Estimated posterior medians for adults aged ≥85 from the multivariate conditional autoregressive model (MCAR). Data source: Centers for Disease Control and Prevention (18).

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