Jointly optimal bandwidth selection for the planar kernel-smoothed density-ratio

Davies, Tilman M.

doi:10.1016/j.sste.2013.04.001

Cited by 10 publications

(11 citation statements)

References 22 publications

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“…This is a more intuitive approach compared to the fixed kernel estimation (Kelsall and Diggle, 1995) because the amount of smoothing is inversely related to the population density, which is never homogeneous in a study area. An important issue of this approach is the choice of the optimal bandwidth, which provides an overall level of smoothing for the density-ratio and is still the subject of much research in this field (Davies and Hazelton, 2010; Davies, 2013a). Regarding the selection of global and pilot bandwidths, in our study we computed and compared two relative risk surfaces based upon a common global bandwidth selected by the OS selector but with different pilot bandwidths.…”

Section: Discussionmentioning

confidence: 99%

“…So we decided to compute and show relative risk surfaces with OS global and pilot bandwidths. Features observed in illustrative examples and simulation studies in Davies 2013 has indicated the promising performance of OS as a seemingly sensible option for selection of risk function bandwidths (Davies, 2013b). A limitation of the KDE method is that it does not support adjustment of known risk factors that may vary spatially and confound results.…”

Section: Discussionmentioning

confidence: 99%

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Spatial variation in mortality risk for hematological malignancies near a petrochemical refinery: A population-based case-control study

Salvo

Meneghini

Vieira

et al. 2015

Environmental Research

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Introduction The study investigated the geographic variation of mortality risk for hematological malignancies (HMs) in order to identify potential high-risk areas near an Italian petrochemical refinery. Material and methods A population-based case-control study was conducted and residential histories for 171 cases and 338 sex- and age-matched controls were collected. Confounding factors were obtained from interviews with consenting relatives for 109 HM deaths and 267 controls. To produce risk mortality maps, two different approaches were applied. We mapped (1) adptive kernel density relative risk estimation (KDE) for case-control studies which estimates a spatial relative risk function using the ratio between cases and controls’ densities, and (2) estimated odds ratios for case-control study data using generalized additive models (GAMs) to smooth the effect of location, a proxy for exposure, while adjusting for confounding variables. Results No high-risk areas for HM mortality were identified among all subjects (men and women combined), by applying both approaches. Using the adaptive KDE approach, we found a significant increase in death risk only among women in a large area 2–6 km southeast of the refinery and the application of GAMs also identified a similarly-located significant high-risk area among women only (global p-value<0.025). Potential confounding risk factors we considered in the GAM did not alter the results. Conclusion Both approaches identified a high-risk area close to the refinery among women only. Those spatial methods are useful tools for public policy management to determine priority areas for intervention. Our findings suggest several directions for further research in order to identify other potential environmental exposures that may be assessed in forthcoming studies based on detailed exposure modeling.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Spatial variation in mortality risk for hematological malignancies near a petrochemical refinery: A population-based case-control study

Salvo

Meneghini

Vieira

et al. 2015

Environmental Research

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“…Numerical results have shown (25) to avoid undersmoothing and thus be capable of outperforming (23) and (24), although it is important to be wary of the aforementioned ad hoc nature of the plug-in selector. 55 In principle, the approximations to the MISE and weighted MISE that lead to (23) and (24) can be applied to select a jointly optimal h 0 for the spatially adaptive relative risk estimator. This is achieved by replacing instances of̃h,f h and g h in these 2 equations bŷh 0 ,f h 0 andĝ h 0 .…”

Section: Jointly Optimal Bandwidthsmentioning

confidence: 99%

Tutorial on kernel estimation of continuous spatial and spatiotemporal relative risk

Davies

Marshall

Hazelton

2017

Statistics in Medicine

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Kernel smoothing is a highly flexible and popular approach for estimation of probability density and intensity functions of continuous spatial data. In this role, it also forms an integral part of estimation of functionals such as the density-ratio or "relative risk" surface. Originally developed with the epidemiological motivation of examining fluctuations in disease risk based on samples of cases and controls collected over a given geographical region, such functions have also been successfully used across a diverse range of disciplines where a relative comparison of spatial density functions has been of interest. This versatility has demanded ongoing developments and improvements to the relevant methodology, including use spatially adaptive smoothers; tests of significantly elevated risk based on asymptotic theory; extension to the spatiotemporal domain; and novel computational methods for their evaluation. In this tutorial paper, we review the current methodology, including the most recent developments in estimation, computation, and inference. All techniques are implemented in the new software package sparr, publicly available for the R language, and we illustrate its use with a pair of epidemiological examples.

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“…Davies et al (2016) show that using different bandwidth parameters might lead in potentially misleading methodological artefacts in the resulting estimates. Different bandwidth selection methods for the optimal estimation of relative risk ρ are discussed in Lawson and Williams (1993); Kelsall and Diggle (1995a,b); Diggle et al (2005); Hazelton (2008); Davies and Hazelton (2010); Davies (2013); Davies and Baddeley (2018). An overview of various estimators and bandwidth selection methods is also provided by .…”

Section: Relative Riskmentioning

confidence: 99%

“…Some jointly optimal bandwidth selection methods including minimising the approximate mean integrated squared error (MISE) of the log-transformed risk surface (Kelsall and Diggle, 1995a), a weighted-by-control MISE (Hazelton, 2008) and a crude plug-in approximation to the asymptotic MISE (Davies, 2013) are implemented in R package sparr ).…”

Section: Relative Riskmentioning

confidence: 99%

Spatial and spatio-temporal point patterns on linear networks

Moradi¹

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Jointly optimal bandwidth selection for the planar kernel-smoothed density-ratio

Cited by 10 publications

References 22 publications

Spatial variation in mortality risk for hematological malignancies near a petrochemical refinery: A population-based case-control study

Spatial variation in mortality risk for hematological malignancies near a petrochemical refinery: A population-based case-control study

Tutorial on kernel estimation of continuous spatial and spatiotemporal relative risk

Spatial and spatio-temporal point patterns on linear networks

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