Symmetric adaptive smoothing regimens for estimation of the spatial relative risk function

The spatial relative risk function is now regarded as a standard tool for visualising spatially tagged case-control data. This function is usually estimated using the ratio of kernel density estimates. In many applications, spatially adaptive bandwidths are essential to handle the extensive inhomogeneity in the distribution of the data. Earlier methods have employed separate, asymmetrical smoothing regimens for case and control density estimates. However, we show that this can lead to potentially misleading methodological artefacts in the resulting estimates of the log-relative risk function. We develop a symmetric adaptive smoothing scheme that addresses this problem. We study the asymptotic properties of the new log-relative risk estimator, and examine its finite sample performance through an extensive simulation study based on a number of problems adapted from real life applications. The results are encouraging.

[1]  J. Bithell.  An application of density estimation to geographical epidemiology. , 1990, Statistics in medicine.

[2]  T. Halasa,et al.  Spatiotemporal patterns, annual baseline and movement-related incidence of Streptococcus agalactiae infection in Danish dairy herds: 2000-2009. , 2014, Preventive veterinary medicine.

[3]  Tilman M. Davies,et al.  Inference Based on Kernel Estimates of the Relative Risk Function in Geographical Epidemiology , 2009, Biometrical journal. Biometrische Zeitschrift.

[4]  G. Terrell.  The Maximal Smoothing Principle in Density Estimation , 1990 .

[5]  Martin L Hazelton,et al.  Generalizing the spatial relative risk function. , 2014, Spatial and spatio-temporal epidemiology.

[6]  J. Toribio,et al.  The Influence of Meteorology on the Spread of Influenza: Survival Analysis of an Equine Influenza (A/H3N8) Outbreak , 2012, PloS one.

[7]  Tilman M. Davies,et al.  Spatial and social variables in the Bronze Age Phase 4 cemetery of Ban Non Wat, Northeast Thailand , 2015 .

[8]  Dorothea Lemke,et al.  Comparing adaptive and fixed bandwidth-based kernel density estimates in spatial cancer epidemiology , 2015, International Journal of Health Geographics.

[9]  C. Freuling,et al.  Spatio-temporal analysis of the progression of Aujeszky's disease virus infection in wild boar of Saxony-Anhalt, Germany. , 2013, Geospatial health.

[10]  Yue Chen,et al.  Identifying high-risk regions for schistosomiasis in Guichi, China: a spatial analysis. , 2008, Acta tropica.

[11]  P. Diggle,et al.  Kernel estimation of relative risk , 1995 .

[12]  Tilman M. Davies,et al.  Adaptive kernel estimation of spatial relative risk , 2010, Statistics in medicine.

[13]  Andrew B. Lawson,et al.  An evaluation of non-parametric relative risk estimators for disease maps , 2004, Comput. Stat. Data Anal..

[14]  Martin L. Hazelton,et al.  Boundary kernels for adaptive density estimators on regions with irregular boundaries , 2010, J. Multivar. Anal..

[15]  Martin L. Hazelton,et al.  sparr: Analyzing Spatial Relative Risk Using Fixed and Adaptive Kernel Density Estimation in R , 2011 .

[16]  N. French,et al.  A prospective case–control and molecular epidemiological study of human cases of Shiga toxin-producing Escherichia coli in New Zealand , 2013, BMC Infectious Diseases.

[17]  J. S. Marron,et al.  Variable window width kernel estimates of probability densities , 1988 .

[18]  Ian Abramson.  On Bandwidth Variation in Kernel Estimates-A Square Root Law , 1982 .

[19]  Anthony Leiserowitz,et al.  Who remembers a hot summer or a cold winter? The asymmetric effect of beliefs about global warming on perceptions of local climate conditions in the U.S. , 2013 .

[20]  Adrian Baddeley,et al.  spatstat: An R Package for Analyzing Spatial Point Patterns , 2005 .

[21]  A B Lawson,et al.  Spatial statistical modeling of disease outbreaks with particular reference to the UK foot and mouth disease (FMD) epidemic of 2001. , 2005, Preventive veterinary medicine.

[22]  P. Diggle,et al.  Spatial variation in risk of disease: a nonparametric binary regression approach , 2002 .

[23]  Tilman M. Davies,et al.  Identification of high-risk regions for schistosomiasis in the Guichi region of China: an adaptive kernel density estimation-based approach , 2013, Parasitology.

[24]  Peter Diggle,et al.  The geographical distribution of primary biliary cirrhosis in a well‐defined cohort , 2001, Hepatology.

[25]  P. Diggle.  A point process modeling approach to raised incidence of a rare phenomenon in the vicinity of a prespecified point , 1990 .

[26]  S. Ganesalingam,et al.  A comparison of estimators of the geographical relative risk function , 2014 .

[27]  Modelling dichotomously marked muscle fibre configurations. , 2013, Statistics in medicine.

[28]  S. Cornell,et al.  Dynamics of the 2001 UK Foot and Mouth Epidemic: Stochastic Dispersal in a Heterogeneous Landscape , 2001, Science.