## Abstract

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 language | English (US) |
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Pages (from-to) | 2335-2342 |

Number of pages | 8 |

Journal | Statistics in Medicine |

Volume | 14 |

Issue number | 21-22 |

State | Published - 1995 |

Externally published | Yes |

## ASJC Scopus subject areas

- Epidemiology