Restricted spatial models for the analysis of geographic and racial disparities in the incidence of low birthweight in Pennsylvania.

The incidence of low birthweight is a common measure of public health due to the increased risk of complications associated with infants having low and very low birthweights. Moreover, many factors that increase the risk of an infant having a low birthweight can be linked to the mother's socioeconomic status, leading to large racial/ethnic disparities in its incidence. Our objective is thus to analyze the incidence of low and very low birthweight in Pennsylvania counties by race/ethnicity. Due to the small number of births in many Pennsylvania counties when stratified by race/ethnicity, our methods must walk a fine line: While we wish to leverage spatial structure to improve the precision of our estimates, we also wish to avoid oversmoothing the data, which can yield spurious conclusions. As such, we develop a framework by which we can measure (and control) the informativeness of our spatial model. To analyze the data, we first model the Pennsylvania birth data using the conditional autoregressive model to demonstrate the extent to which it can lead to oversmoothing. We then reanalyze the data using our proposed framework and highlight its ability to detect (or not detect) evidence of racial/ethnic disparities in the incidence of low birthweight.

Evaluating the informativeness of the Besag-York-Mollié CAR model.

The use of the conditional autoregressive framework proposed by Besag, York, and Mollié (1991; BYM) is ubiquitous in Bayesian disease mapping and spatial epidemiology. While it is understood that Bayesian inference is based on a combination of the information contained in the data and the information contributed by the model, quantifying the contribution of the model relative to the information in the data is often non-trivial. Here, we provide a measure of the contribution of the BYM framework by first considering the simple Poisson-gamma setting in which quantifying the prior's contribution is quite clear. We then propose a relationship between gamma and lognormal priors that we then extend to cover the framework proposed by BYM. Following a brief simulation study in which we illustrate the accuracy of our lognormal approximation of the gamma prior, we analyze a dataset comprised of county-level heart disease-related death data across the United States. In addition to demonstrating the potential for the BYM framework to correspond to a highly informative prior specification, we also illustrate the sensitivity of death rate estimates to changes in the informativeness of the BYM framework.