Second-order analysis of inhomogeneous spatial point processes using case-control data

P. J. Diggle, V. Gómez-Rubio, P. E. Brown, A. G. Chetwynd, S. Gooding

Research output: Contribution to journalArticlepeer-review

63 Scopus citations


Methods for the statistical analysis of stationary spatial point process data are now well established, methods for nonstationary processes less so. One of many sources of nonstationary point process data is a case-control study in environmental epidemiology. In that context, the data consist of a realization of each of two spatial point processes representing the locations, within a specified geographical region, of individual cases of a disease and of controls drawn at random from the population at risk. In this article, we extend work by Baddeley, Møller, and Waagepetersen (2000, Statistica Neerlandica 54, 329-350) concerning estimation of the second-order properties of a nonstationary spatial point process. First, we show how case-control data can be used to overcome the problems encountered when using the same data to estimate both a spatially varying intensity and second-order properties. Second, we propose a semiparametric method for adjusting the estimate of intensity so as to take account of explanatory variables attached to the cases and controls. Our primary focus is estimation, but we also propose a new test for spatial clustering that we show to be competitive with existing tests. We describe an application to an ecological study in which juvenile and surviving adult trees assume the roles of controls and cases.

Original languageEnglish (US)
Issue number2
StatePublished - Jun 2007
Externally publishedYes


  • Case-control study
  • Ecology
  • Environmental epidemiology
  • Kernel smoothing
  • Monte Carlo test
  • Nonstationary spatial point process

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Public Health, Environmental and Occupational Health
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Statistics and Probability


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