### 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) |
---|---|

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 |

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### ASJC Scopus subject areas

- Epidemiology

### Cite this

*Statistics in Medicine*,

*14*(21-22), 2335-2342.

**Non-parametric estimation of spatial variation in relative risk.** / Kelsall, J. E.; Diggle, P. J.

Research output: Contribution to journal › Article

*Statistics in Medicine*, vol. 14, no. 21-22, pp. 2335-2342.

}

TY - JOUR

T1 - Non-parametric estimation of spatial variation in relative risk

AU - Kelsall, J. E.

AU - Diggle, P. J.

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0028790233&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028790233&partnerID=8YFLogxK

M3 - Article

VL - 14

SP - 2335

EP - 2342

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 21-22

ER -