Non-parametric estimation of spatial variation in relative risk

J. E. Kelsall, P. J. Diggle

Research output: Contribution to journalArticlepeer-review

167 Scopus citations


We consider the problem of estimating the spatial variation in relative risks of two diseases, say, over a geographical region. Using an underlying Poisson point process model, we approach the problem as one of density ratio estimation implemented with a non-parametric kernel smoothing method. In order to assess the significance of any local peaks or troughs in the estimated risk surface, we introduce pointwise tolerance contours which can enhance a greyscale image plot of the estimate. We also propose a Monte Carlo test of the null hypothesis of constant risk over the whole region, to avoid possible over-interpretation of the estimated risk surface. We illustrate the capabilities of the methodology with two epidemiological examples.

Original languageEnglish (US)
Pages (from-to)2335-2342
Number of pages8
JournalStatistics in Medicine
Issue number21-22
StatePublished - 1995
Externally publishedYes

ASJC Scopus subject areas

  • Epidemiology


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