Testing for Spatial Correlation in Nonstationary Binary Data, with Application to Aberrant Crypt Foci in Colon Carcinogenesis

Tatiyana V. Apanasovich, Simon Sheather, Joanne R. Lupton, Natasa Popovic, Nancy D. Turner, Robert S. Chapkin, Leslie A. Braby, Raymond J. Carroll

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


In an experiment to understand colon carcinogenesis, all animals were exposed to a carcinogen, with half the animals also being exposed to radiation. Spatially, we measured the existence of what are referred to as aberrant crypt foci (ACF), namely, morphologically changed colonic crypts that are known to be precursors of colon cancer development. The biological question of interest is whether the locations of these ACFs are spatially correlated: if so, this indicates that damage to the colon due to carcinogens and radiation is localized. Statistically, the data take the form of binary outcomes (corresponding to the existence of an ACF) on a regular grid. We develop score-type methods based upon the Matern and conditionally autoregressive (CAR) correlation models to test for the spatial correlation in such data, while allowing for nonstationarity. Because of a technical peculiarity of the score-type test, we also develop robust versions of the method. The methods are compared to a generalization of Moran's test for continuous outcomes, and are shown via simulation to have the potential for increased power. When applied to our data, the methods indicate the existence of spatial correlation, and hence indicate localization of damage.

Original languageEnglish
Pages (from-to)752-761
Number of pages10
Issue number4
StatePublished - Dec 2003


  • Aberrant crypt foci
  • Binary data
  • Carcinogenesis
  • Colon cancer
  • Conditionally autoregressive models
  • Moran's test
  • Robustness
  • Score tests
  • Spatial statistics

ASJC Scopus subject areas

  • Statistics and Probability
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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