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Bayesian wombling for spatial point processes.

Shengde Liang1, Sudipto Banerjee, Bradley P Carlin

  • 1MMC 303, School of Public Health, University of Minnesota, Minneapolis, Minnesota 55455-0392, USA.

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This study introduces novel statistical wombling methods for point-process data, enabling boundary analysis in spatial epidemiology. The techniques help identify significant spatial patterns and missing covariates in disease mapping.

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Area of Science:

  • Spatial statistics
  • Geostatistics
  • Epidemiology

Background:

  • Geographically indexed data analysis often requires identifying regions of rapid spatial change or distinct boundaries.
  • Existing statistical wombling methods are developed for geostatistical and areal data, but not for point-process data.
  • Point-process data presents challenges in likelihood evaluation, hindering boundary analysis.

Purpose of the Study:

  • To extend existing point-level and areal wombling tools to the point-process case for spatial boundary analysis.
  • To obtain full posterior inference for multivariate spatial random effects to identify potential missing covariates.
  • To develop methods for constructing wombled maps and testing postulated boundaries in spatial data.

Main Methods:

  • Extension of point-level and areal wombling techniques to the point-process framework.
  • Utilizing full posterior inference for multivariate spatial random effects.
  • Combining Monte Carlo likelihood approximation with a predictive process for computational efficiency in point-referenced data.
  • Application to colorectal and prostate cancer data in Minnesota.

Main Results:

  • Developed novel statistical wombling methods applicable to point-process data.
  • Enabled the identification of significant boundaries in fitted spatial intensity surfaces.
  • Facilitated the testing of postulated boundaries in point-referenced spatial models.
  • Provided insights into spatial patterns of colorectal and prostate cancer and their relation to screening facility proximity.

Conclusions:

  • The developed methods offer a robust approach to boundary analysis in spatial point-process data.
  • These techniques can reveal significant spatial structures and guide the inclusion of relevant covariates in epidemiological models.
  • The study successfully applied these novel methods to cancer data, demonstrating their practical utility in public health research.