  Babies born with low and very low birthweights -- i.e., birthweights below
2,500 and 1,500 grams, respectively -- have an increased risk of complications
compared to other babies, and the proportion of babies with a low birthweight
is a common metric used when evaluating public health in a population. While
many factors increase the risk of a baby having a low birthweight, many can be
linked to the mother's socioeconomic status, which in turn contributes to large
racial disparities in the incidence of low weight births. Here, we employ
Bayesian statistical models to analyze the proportion of babies with low
birthweight in Pennsylvania counties by race/ethnicity. Due to the small number
of births -- and low weight births -- in many Pennsylvania counties when
stratified by race/ethnicity, our methods must walk a fine line. On one hand,
leveraging spatial structure can help improve the precision of our estimates.
On the other hand, we must be cautious to avoid letting the model overwhelm the
information in the data and produce spurious conclusions. As such, we first
develop a framework by which we can measure (and control) the informativeness
of our spatial model. After demonstrating the properties of our framework via
simulation, we analyze the low birthweight data from Pennsylvania and examine
the extent to which the commonly used conditional autoregressive model 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 disparities
in the incidence of low birthweight.
