Background: Cancer mortality maps are used by public health officials to identify areas of excess and to guide surveillance and control activities. Quality of decision-making thus relies on an accurate quantification of risks from observed rates which can be very unreliable when computed from sparsely populated geographical units or recorded for minority populations. This paper presents a geostatistical methodology that accounts for spatially varying population sizes and spatial patterns in the processing of cancer mortality data. Simulation studies are conducted to compare the performances of Poisson kriging to a few simple smoothers (i.e. population-weighted estimators and empirical Bayes smoothers) under different scenarios for the disease frequency, the population size, and the spatial pattern of risk. A public-domain executable with example datasets is provided.Results: The analysis of age-adjusted mortality rates for breast and cervix cancers illustrated some key features of commonly used smoothing techniques. Because of the small weight assigned to the rate observed over the entity being smoothed (kernel weight), the population-weighted average leads to risk maps that show little variability. Other techniques assign larger and similar kernel weights but they use a different piece of auxiliary information in the prediction: global or local means for global or local empirical Bayes smoothers, and spatial combination of surrounding rates for the geostatistical estimator. Simulation studies indicated that Poisson kriging outperforms other approaches for most scenarios, with a clear benefit when the risk values are spatially correlated. Global empirical Bayes smoothers provide more accurate predictions under the least frequent scenario of spatially random risk.Conclusion: The approach presented in this paper enables researchers to incorporate the pattern of spatial dependence of mortality rates into the mapping of risk values and the quantification of the associated uncertainty, while being easier to implement than a full Bayesian model. The availability of a public-domain executable makes the geostatistical analysis of health data, and its comparison to traditional smoothers, more accessible to common users. In future papers this methodology will be generalized to the simulation of the spatial distribution of risk values and the propagation of the uncertainty attached to predicted risks in local cluster analysis.

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. 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. The 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. A 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.

Background: Smoothing methods have been developed to improve the reliability of risk cancer estimates from sparsely populated geographical entities. Filtering local details of the spatial variation of the risk leads however to the detection of larger clusters of low or high cancer risk while most spatial outliers are filtered out. Static maps of risk estimates and the associated prediction variance also fail to depict the uncertainty attached to the spatial distribution of risk values and does not allow its propagation through local cluster analysis. This paper presents a geostatistical methodology to generate multiple realizations of the spatial distribution of risk values. These maps are then fed into spatial operators, such as in local cluster analysis, allowing one to assess how risk spatial uncertainty translates into uncertainty about the location of spatial clusters and outliers. This novel approach is applied to age-adjusted breast and pancreatic cancer mortality rates recorded for white females in 295 US counties of the Northeast (1970–1994). A public-domain executable with example datasets is provided.Results: Geostatistical simulation generates risk maps that are more variable than the smooth risk map estimated by Poisson kriging and reproduce better the spatial pattern captured by the risk semivariogram model. Local cluster analysis of the set of simulated risk maps leads to a clear visualization of the lower reliability of the classification obtained for pancreatic cancer versus breast cancer: only a few counties in the large cluster of low risk detected in West Virginia and Southern Pennsylvania are significant over 90% of all simulations. On the other hand, the cluster of high breast cancer mortality in Niagara county, detected after application of Poisson kriging, appears on 60% of simulated risk maps. Sensitivity analysis shows that 500 realizations are needed to achieve a stable classification for pancreatic cancer, while convergence is reached for less than 300 realizations for breast cancer.Conclusion: The approach presented in this paper enables researchers to generate a set of simulated risk maps that are more realistic than a single map of smoothed mortality rates and allow the propagation of cancer risk uncertainty through local cluster analysis. Coupled with visualization and querying capabilities of geographical information systems, animated display of realizations can highlight areas that depart consistently from the general behavior observed across the region, guiding further investigation and control activities.

Complete Spatial Randomness (CSR) is the null hypothesis employed by many statistical tests for spatial pattern, such as local cluster or boundary analysis. CSR is however not a relevant null hypothesis for highly complex and organized systems such as those encountered in the environmental and health sciences in which underlying spatial pattern is present. This paper presents a geostatistical approach to filter the noise caused by spatially varying population size and to generate spatially correlated neutral models that account for regional background obtained by geostatistical smoothing of observed mortality rates. These neutral models were used in conjunction with the local Moran statistics to identify spatial clusters and outliers in the geographical distribution of male and female lung cancer in Nassau, Queens, and Suffolk counties, New York, USA. We developed a typology of neutral models that progressively relaxes the assumptions of null hypotheses, allowing for the presence of spatial autocorrelation, non-uniform risk, and incorporation of spatially heterogeneous population sizes. Incorporation of spatial autocorrelation led to fewer significant ZIP codes than found in previous studies, confirming earlier claims that CSR can lead to over-identification of the number of significant spatial clusters or outliers. Accounting for population size through geostatistical filtering increased the size of clusters while removing most of the spatial outliers. Integration of regional background into the neutral models yielded substantially different spatial clusters and outliers, leading to the identification of ZIP codes where SMR values significantly depart from their regional background. The approach presented in this paper enables researchers to assess geographic relationships using appropriate null hypotheses that account for the background variation extant in real-world systems. In particular, this new methodology allows one to identify geographic pattern above and beyond background variation. The implementation of this approach in spatial statistical software will facilitate the detection of spatial disparities in mortality rates, establishing the rationale for targeted cancer control interventions, including consideration of health services needs, and resource allocation for screening and diagnostic testing. It will allow researchers to systematically evaluate how sensitive their results are to assumptions implicit under alternative null hypotheses.