Abstract
Quantifying the distributions of disease risk in space and time jointly is a key element for understanding spatio-temporal phenomena while also having the potential to enhance our understanding of epidemiologic trajectories. However, most studies to date have neglected time dimension and focus instead on the “average” spatial pattern of disease risk, thereby masking time trajectories of disease risk. In this study we propose a new idea titled “spatio-temporal kernel density estimation (stKDE)” that employs hybrid kernel (i.e., weight) functions to evaluate the spatio-temporal disease risks. This approach not only can make full use of sample data but also “borrows” information in a particular manner from neighboring points both in space and time via appropriate choice of kernel functions. Monte Carlo simulations show that the proposed method performs substantially better than the traditional (i.e., frequency-based) kernel density estimation (trKDE) which has been used in applied settings while two illustrative examples demonstrate that the proposed approach can yield superior results compared to the popular trKDE approach. In addition, there exist various possibilities for improving and extending this method.
Highlights
Modern epidemiology is founded on spatial analysis that can be traced back to the classical paradigm of John Snow’s work on cholera in the middle of nineteenth century [1]
Sabel et al studied the spatial pattern of motor neurone disease risk in Finland [10], Prince et al examined the geographic risk of primary biliary cirrhosis in a region of north-east England [11], Wheeler detected the childhood leukemia clustering and clusters in the US state of Ohio [12], Berke generated the relative risk maps of pseudorabies-seropositive (Aujeszky’s disease) pig herds in an animal-dense region of Germany [13], while Zhang et al assessed the schistosomiasis risk in a region of Anhui province in China [3]
For the sample sizes considered, the MISE of trKDE tends to decrease for a given level of the ordered variable as the sample size increases as one would naturally expect
Summary
Modern epidemiology is founded on spatial analysis that can be traced back to the classical paradigm of John Snow’s work on cholera in the middle of nineteenth century [1]. The kernel density estimation (KDE) based spatial relative risk function (sRRF) have attracted much attention because of its flexibility in applications and its minimal assumptions regarding the underlying data structure [3]. In 1990, Bithell first introduced the method of kernel density ratio between cases and controls into the field of epidemiology for describing the spatial relative risks [4,5]. The ratio of adaptive kernel density estimation has been proposed to depict the spatial variation of disease risk [8,9]. The risk pattern in discrete time dimension has always been neglected [2]
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