Dealing with risk discontinuities to estimate cancer mortality risks when the number of small areas is large

Many statistical models have been developed during the last years to smooth risks in disease mapping. However, most of these modeling approaches do not take possible local discontinuities into consideration or if they do, they are computationally prohibitive or simply do not work when the number of small areas is large. In this paper, we propose a two-step method to deal with discontinuities and to smooth noisy risks in small areas. In a first stage, a novel density-based clustering algorithm is used. In contrast to previous proposals, this algorithm is able to automatically detect the number of spatial clusters, thus providing a single cluster structure. In the second stage, a Bayesian hierarchical spatial model that takes the cluster configuration into account is fitted, which accounts for the discontinuities in disease risk. To evaluate the performance of this new procedure in comparison to previous proposals, a simulation study has been conducted. Results show competitive risk estimates at a much better computational cost. The new methodology is used to analyze stomach cancer mortality data in Spanish municipalities.

Characterizing and Modeling Temporal and Spatial Trends in Rainfall Extremes

A hierarchical spatial model for daily rainfall extremes that characterizes their temporal variation due to interannual climatic forcing as well as their spatial pattern is proposed. The model treats the parameters of at-site probability distributions for rainfall extremes as “data” that are likely to be spatially correlated and driven by atmospheric forcing. The method is applied to daily rainfall extremes for summer and winter half years over the Swan–Avon River basin in Western Australia. Two techniques for the characterization of at-site extremes—peaks-over-threshold (POT) analysis and the generalized extreme value (GEV) distribution—and three climatic drivers—the El Niño–Southern Oscillation as measured by the Southern Oscillation index (SOI), the Southern Hemisphere annular mode as measured by an Antarctic Oscillation index (AOI), and solar irradiance (SI)—were considered. The POT analysis of at-site extremes revealed that at-site thresholds lacked spatial coherence, making it difficult to determine a smooth spatial surface for the threshold parameter. In contrast, the GEV-based analysis indicated smooth spatial patterns in daily rainfall extremes that are consistent with the predominant orientation of storm tracks over the study area and the presence of a coastal escarpment near the western edge of the basin. It also indicated a linkage between temporal trends in daily rainfall extremes and those of the SOI and AOI. By applying the spatial models to winter and summer extreme rainfalls separately, an apparent increasing trend in return levels of summer rainfall to the northwest and decreasing trends in return levels of winter rainfall to the southwest of the region are found.