TY - JOUR

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

AU - Kelsall, Julia E.

AU - Diggle, Peter J.

PY - 1995/11/15

Y1 - 1995/11/15

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.

U2 - 10.1002/sim.4780142106

DO - 10.1002/sim.4780142106

M3 - Journal article

VL - 14

SP - 2335

EP - 2342

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 1097-0258

IS - 21-22

ER -