title: Non-parametric estimation of spatial variation in relative risk.
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.
authors.affiliation: Mathematics, Lancaster University, UK.
authors.forename: J E
authors.initials: JE
authors.lastname: Kelsall
authors.forename: P J
authors.initials: PJ
authors.lastname: Diggle
mesh_terms: D000397:Air Pollution / Q000009:adverse effects; D015982:Bias; D016000:Cluster Analysis; D004739:England / Q000453:epidemiology; D005260:Female; D006801:Humans; D007231:Infant, Newborn; D007822:Laryngeal Neoplasms / Q000453:epidemiology; D008175:Lung Neoplasms / Q000453:epidemiology; D008297:Male; D015233:Models, Statistical; D009010:Monte Carlo Method; D016012:Poisson Distribution; D011156:Population Density; D015203:Reproducibility of Results; D012306:Risk; D018570:Risk Assessment; D012744:Sex Ratio; D013029:Space-Time Clustering; D018709:Statistics, Nonparametric