Spatial Difference Boundary Detection for Multiple Outcomes Using Bayesian Disease Mapping

Abstract

Summary Regional aggregates of health outcomes over delineated administrative units (e.g., states, counties, and zip codes), or areal units, are widely used by epidemiologists to map mortality or incidence rates and capture geographic variation. To capture health disparities over regions, we seek “difference boundaries” that separate neighboring regions with significantly different spatial effects. Matters are more challenging with multiple outcomes over each unit, where we capture dependence among diseases as well as across the areal units. Here, we address multivariate difference boundary detection for correlated diseases. We formulate the problem in terms of Bayesian pairwise multiple comparisons and seek the posterior probabilities of neighboring spatial effects being different. To achieve this, we endow the spatial random effects with a discrete probability law using a class of multivariate areally referenced Dirichlet process models that accommodate spatial and interdisease dependence. We evaluate our method through simulation studies and detect difference boundaries for multiple cancers using data from the Surveillance, Epidemiology, and End Results Program of the National Cancer Institute.

Bayesian finite-population inference with spatially correlated measurements

“…Extensions to multivariate responses and spatio-temporal data may also serve useful, particularly when examining health outcomes. Finally, learning about spatial difference boundaries (Gao et al, 2022) from finite population estimates for regionally aggregated health outcomes is witnessing growing interest among public health researchers and will comprise future investigations.…”

Bayesian modeling with spatial curvature processes

“…For regionally aggregated data, it identifies boundaries delineating neighboring regions and has been used to study health disparities (Lu & Carlin 2005, Li et al 2015, Gao et al 2022) and ecological boundaries (Fitzpatrick et al 2010). For point-referenced data, where variables are mapped at locations within an Euclidean coordinate frame with a sufficiently smooth spatial surface, it refers to estimating spatial gradients and identifying boundaries representing large gradients , Qu et al 2021.…”

Discussion of “Optimal Test Procedures for Multiple Hypotheses Controlling the Familywise Expected Loss” by Willi Maurer, Frank Bretz, and Xiaolei Xun

“…Developments in Li et al. (2015) (also see Gao et al., 2022, for a more recent multivariate extension) exploit Dirichlet processes (DPs) to model $$\bm {\phi }$$ without parametric specifications. Letting $$\delta _{\theta _k}$$ be the Dirac measure located at $$\theta _k$$ and modeling $$\bm {\phi }$$ as an unknown distribution $$G_n$$, which itself is modeled as a DP, yields …”

“…Spatial components $$\bm {\gamma } = (\gamma _{1}, \gamma _{2}\dots , \gamma _{n})^{{\rm {T}}}$$ are dependent and are modeled jointly with covariance matrix $$\bm {\Sigma }_\gamma$$. The matrix $$\bm {\Sigma }_\gamma$$ introduces spatial proximity‐based associations and can be specified from a proper conditional autoregression (CAR) (see, e.g., Cressie, 1993; MacNab, 2016, 2018; Rue & Held, 2005, for a variety of specifications) or a DAGAR prior on $$\bm {\gamma }$$ (Datta et al., 2019; Gao et al., 2022). Each $$F^{(i)}(\cdot )$$ denotes the cumulative distribution functions of the marginal distribution of the corresponding $$\gamma _{i}$$.…”

“…An immediate concern is that these spatial random effects are typically endowed with a multivariate Gaussian distribution using Markov random fields or Gaussian processes and, being continuous distributions, the posterior probability of any two random effects being equal will be zero. Modeling spatial random effects with discrete jumps, step changes, and discontinuities have been addressed in diverse settings (see, e.g., Gao et al, 2022;Hanson et al, 2015;Li et al, 2012Li et al, , 2015Rushworth et al, 2017;Santafé et al, 2021).…”