Reliable event rates for disease mapping

TL;DR

This paper proposes a new definition of reliable event rate estimates for disease mapping, introduces a Bayesian spatial model to improve reliability while avoiding oversmoothing, and demonstrates its application on county birth data.

Contribution

It provides a formal definition of reliability for event rate estimates and develops a Bayesian framework to enhance reliability without oversmoothing in small area analysis.

Findings

The new reliability definition applies to both crude and model-based estimates.

The Bayesian approach improves reliability by incorporating prior information.

Application to Pennsylvania birth data illustrates reduced oversmoothing.

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.