Too often racial disparities in health outcomes are evaluated simply by computing the difference or ratio between crude rates, ignoring the lack of reliability of rates recorded for small minority populations, as well as the spatial and temporal dimensions of the data.
This paper went beyond earlier methodological work on quantifying racial disparities [35, 36, 42] by incorporating the temporal dimension through the comparison of time series instead of rates aggregated over a given time period. This comparison relied on the innovative application of joinpoint regression to rates that were stabilized using binomial kriging. A second innovation was the introduction of a new disparity statistic to supplement the tests of parallelism and coincidence available in joinpoint regression for the comparison of time series. A major advantage of this disparity statistic, which measures the number of years where APC confidence intervals did not overlap, is that it can be summed up yearly over all geographical units, providing an estimate of how the spatial extent of racial disparities changed with time. It is noteworthy that unlike previous disparity measures this statistic quantifies disparities in the pace of changes instead of the values of the health outcomes themselves. Within the context of cancer control and surveillance, this statistic facilitates the quantification of how health outcomes for different racial groups changed following strategies to improve cancer prevention and early detection, which should help better understand the causes underlying observed racial disparities in cancer incidence, mortality and morbidity.
A major challenge when working in both the spatial and temporal domains is the issue of scale or resolution. An accurate determination of when the slopes of the linear models fitted to time series undergo statistically significant changes (i.e. number and location of joinpoints) requires data that are reliable and with a good temporal resolution. Joinpoint regression has been traditionally applied to yearly time series at the State or Federal level. Keeping the same temporal resolution while zooming into the county level for example enhanced the small number problem; in particular as the focus is here on minority populations that represent on average only 10% of cases. The issue of rate instability was tackled by using both the rate estimates and standard errors provided by binomial kriging as input to joinpoint regression. A sensitivity analysis showed that kriging-based noise-filtering improved the fit by the joinpoint regression models (i.e. lower residual variability) compared to the modelling of raw rates. Another benefit of using noise-filtered rates was the clearer detection of the drop in the percentage of counties with more favorable changes for black males (i.e. significantly smaller APC) that occurred in the early nineties when PSA screening was introduced.
Another issue associated with the spatialization of joinpoint regression results is the repetition of tests of hypothesis that need to be conducted for each geographical unit, increasing the risk of false positives. Multiple testing correction was here applied using the traditional implementation of the false discovery rate (FDR) approach which is based on the underlying assumption of independence of tests. This assumption might not be appropriate for adjacent geographical units whose kriged estimates are based on common neighbors. Several techniques were proposed recently to account for highly correlated test statistics in the FDR approach [43, 44]. These approaches might however be too conservative since tests for geographical units that are further apart are independent and only adjacent counties were used in binomial kriging. In addition, some authors  hypothesized that the spatial dependence could be controlled by the traditional FDR correction given its statistical properties. More research is needed on this issue of multiple testing correction .
The case-study illustrated very well how the proportion of late-stage diagnosis for a common disease, such a prostate cancer, can change dramatically over time (i.e. 50% decline over 20 years) and display striking geographical and racial disparities within a single State. Thus, a comprehensive picture of the burden of cancer and the impact of various interventions can only be achieved through the simultaneous incorporation of the spatial and temporal dimensions in the visualization and analysis of health outcomes and putative covariates. State-level percentage of late-stage diagnosis decreased 50% since 1981; a decline that started slightly earlier for black males which had historically high rates of late-stage diagnosis. This decline accelerated in the 90's when PSA screening was introduced and stopped abruptly in the early 2000. Analysis at the metropolitan and non-metropolitan levels revealed a recent urban increase in the frequency of late-stage diagnosis for both races, and this trend was significant for white males. This result has important public health implications since it might cause an increase in prostate cancer mortality in the future. Non-metropolitan counties, despite displaying a steady decline in percentage of late-stage diagnosis, are still behind urban areas that generally have higher providers to cases ratio. Larger differences in temporal trends for Whites and Blacks were also observed in these rural counties, as measured by the new disparity statistic. In particular, the group of counties with a Beale index above 6 (i.e. most rural counties) received the maximum value for the racial disparity statistic, indicating that the yearly rate of change was significantly different between races for each of the 25 years.
The annual rate of decrease in prostate cancer late-stage diagnosis and the onset years for significant declines varied greatly among counties and racial groups. This spatial heterogeneity reflects the non-stationarity of the parameters of the time trend model even within the metropolitan and non-metropolitan strata and might warrant the development of a geographically-weighted version of joinpoint regression. Most counties with non-significant average annual percent change (AAPC) were located in the Florida Panhandle for white males, whereas they clustered in south-eastern Florida for black males. The new disparity statistic indicated that the spatial extent of racial disparities reached a peak in 1990 because of an early decline in frequency of late-stage diagnosis observed for black males. This result suggests the existence of racial disparities in the application or availability of PSA testing, in particular as the new screening procedure was introduced.
The present study was mainly methodological and the interpretation of the results suffers from limitations typically associated with ecological studies. As discussed before, the modelling of temporal trends requires some level of spatial aggregation in order to capture enough cases for a reliable estimation of percentages of late-stage diagnosis on an annual basis, which is the main culprit for the MAUP effect. In addition, the use of cases 65 year old and older allowed controlling for one source of individual-level heterogeneity because the entire study population had Medicare coverage. Individual-level data available for the same period are being analyzed to explore the impact of individual characteristics, area-level census measures of education, income, and environmental exposure on prostate cancer mortality, incidence and stage at diagnosis. These data will help conduct joinpoint regression at the sub-county level for heavily populated areas where enough cases are available for geographically detailed analysis and modelling.