Recent Advancements in Kernel Estimation of Spatial Relative Risk

• Activity Number: 647
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Tilman Davies* and Martin L. Hazelton and Khair Jones
• Companies: University of Otago and Massey University and Massey University
• Keywords: Kernel smoothing ; relative risk ; spatial ; density-ratio ; adaptive bandwidth

Abstract

Estimation of the continuous risk of disease contraction over some spatial region $W$ is a core objective in applications in geographical epidemiology. Such pursuits require knowledge of the probability densities of both the infected and uninfected (at-risk) populations ($f$ and $g$ respectively). Their ratio, $r=f/g$, indicates spatial areas of increased and decreased risk with peaks and troughs respectively. The complexities associated with the often highly heterogeneous nature of the requisite density functions renders nonparametric 2-dimensional kernel density estimation particularly appealing for estimation of $f$ and $g$, given samples of data assumed to have arisen therefrom. However, a number of familiar practical problems associated with kernel smoothing are present, even exacerbated, in this density-ratio estimation. In this work, we use applied examples to discuss the latest research into the so-called relative risk estimator. Our findings indicate that this density-ratio estimation is considerably aided by using a variable (adaptive) smoothing regimen that can be symmetrized to stabilize the resulting surfaces, without disturbing beneficial asymptotic properties.