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Abstract:
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When analyzing rare event and mortality data, the criteria for declaring rate estimates as “reliable” is still a matter of dispute. What these varying criteria have in common, however, is that they are often infeasible in most small area analysis settings. In this study, we provide a general definition for a “reliable” estimate in a Bayesian framework in which a rate or proportion is defined as reliable at the 1-? level if its posterior median is larger than the width of its (1-?) x 100% equal-tailed credible interval, thereby allowing prior information to improve the precision of our estimates and thus yield more reliable estimates. After describing the properties of this definition via Poisson-gamma, and Binomial-beta conjugate pairing, we extend these criteria to the more general log-normal and logit-normal prior specification commonly used in the disease mapping literature. Following an illustration using data from the County Health Rankings & Roadmaps program, we describe how this work can be used to ensure that prior distributions do not overpower the data in our analyses and to provide guidance with respect to the aggregation of data.
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