Abstract
BackgroundGeostatistical techniques that account for spatially varying population sizes and spatial patterns in the filtering of choropleth maps of cancer mortality were recently developed. Their implementation was facilitated by the initial assumption that all geographical units are the same size and shape, which allowed the use of geographic centroids in semivariogram estimation and kriging. Another implicit assumption was that the population at risk is uniformly distributed within each unit. This paper presents a generalization of Poisson kriging whereby the size and shape of administrative units, as well as the population density, is incorporated into the filtering of noisy mortality rates and the creation of isopleth risk maps. An innovative procedure to infer the point-support semivariogram of the risk from aggregated rates (i.e. areal data) is also proposed.ResultsThe novel methodology is applied to age-adjusted lung and cervix cancer mortality rates recorded for white females in two contrasted county geographies: 1) state of Indiana that consists of 92 counties of fairly similar size and shape, and 2) four states in the Western US (Arizona, California, Nevada and Utah) forming a set of 118 counties that are vastly different geographical units. Area-to-point (ATP) Poisson kriging produces risk surfaces that are less smooth than the maps created by a naïve point kriging of empirical Bayesian smoothed rates. The coherence constraint of ATP kriging also ensures that the population-weighted average of risk estimates within each geographical unit equals the areal data for this unit. Simulation studies showed that the new approach yields more accurate predictions and confidence intervals than point kriging of areal data where all counties are simply collapsed into their respective polygon centroids. Its benefit over point kriging increases as the county geography becomes more heterogeneous.ConclusionA major limitation of choropleth maps is the common biased visual perception that larger rural and sparsely populated areas are of greater importance. The approach presented in this paper allows the continuous mapping of mortality risk, while accounting locally for population density and areal data through the coherence constraint. This form of Poisson kriging will facilitate the analysis of relationships between health data and putative covariates that are typically measured over different spatial supports.
Highlights
Geostatistical techniques that account for spatially varying population sizes and spatial patterns in the filtering of choropleth maps of cancer mortality were recently developed
The interpretation and analysis of those choropleth maps faces three major hurdles: 1) the presence of extreme unreliable rates that typically occur for sparsely populated areas and/or less frequent cancers, 2) the visual bias resulting from the aggregation of health data within administrative units of widely different sizes and shapes, and 3) the mismatch of spatial supports for cancer rates and explanatory variables that prevents their direct use in correlation analysis and often implies an aggregation to the coarser geography
Poisson kriging was conducted with the semivariogram model derived through deconvolution or inferred directly from the simulated grid risk values (true point-support model γR(h))
Summary
Geostatistical techniques that account for spatially varying population sizes and spatial patterns in the filtering of choropleth maps of cancer mortality were recently developed. Their implementation was facilitated by the initial assumption that all geographical units are the same size and shape, which allowed the use of geographic centroids in semivariogram estimation and kriging. This paper presents a generalization of Poisson kriging whereby the size and shape of administrative units, as well as the population density, is incorporated into the filtering of noisy mortality rates and the creation of isopleth risk maps. Geostatistical methods range from straightforward point kriging [2,3,4,5] to complex random field models that require distributional assumptions and computationally intensive parameter estimation using Markov Chain Monte Carlo (MCMC) techniques [6,7]
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