Reliable event rates for disease mapping

Abstract

When analyzing spatially referenced event data, the criteria for declaring rates as "reliable" is still a matter of dispute. What these varying criteria have in common, however, is that they are rarely satisfied for crude estimates in small area analysis settings, prompting the use of spatial models to improve reliability. While reasonable, recent work has quantified the extent to which popular models from the spatial statistics literature can overwhelm the information contained in the data, leading to oversmoothing. Here, we begin by providing a definition for a "reliable" estimate for event rates that can be used for crude and model-based estimates and allows for discrete and continuous statements of reliability. We then construct a spatial Bayesian framework that allows users to infuse prior information into their models to improve reliability while also guarding against oversmoothing. We apply our approach to county-level birth data from Pennsylvania, highlighting the effect of oversmoothing in spatial models and how our approach can allow users to better focus their attention to areas where sufficient data exists to drive inferential decisions. We then conclude with a brief discussion of how this definition of reliability can be used in the design of small area studies.

Keywords: Bayesian inference; Informative priors; Preterm birth; Small area analyses; Spatial statistics.

Figure 1:

Comparison of the relative precision as a function of the number of events. Panel (a) displays the relative precision at the 0.95 level for various underlying event rates, and Panel (b) displays the relative precision for various levels of reliability for an event rate of ${\pi }_i=0.01$.

Figure 2:

Comparison of the estimated model informativeness parameters, ${\widehat{a}}_{0;rt}$, from the Pennsylvania preterm birth analysis; median county-level counts provided for reference.

Figure 3:

Comparison of the posterior distributions of rate parameters, ${\pi }_{irt}$, under the standard and restricted CAR models for white and black mothers in selected counties.

Figure 4:

Comparison of the preterm birth rates for white and Asian mothers in 2019 from the standard and restricted CAR models.

Figure 5:

Comparison of the relative precision of the race/ethnicity-specific estimates from 2019 under the standard and restricted CAR models.

Figure 6:

Comparison of the level of reliability of the estimates of the preterm birth rate for Asian mothers in 2019 under the standard and restricted CAR models.