This paper presents a geostatistical methodology which accounts for spatially varying population size in the processing of cancer mortality data. The approach proceeds in two steps: (1) spatial patterns are first described and modeled using population-weighted semivariogram estimators, (2) spatial components corresponding to nested structures identified on semivariograms are then estimated and mapped using a variant of factorial kriging. The main benefit over traditional spatial smoothers is that the pattern of spatial variability (i.e. direction-dependent variability, range of correlation, presence of nested scales of variability) is directly incorporated into the computation of weights assigned to surrounding observations. Moreover, besides filtering the noise in the data the procedure allows the decomposition of the structured component into several spatial components (i.e. local versus regional variability) on the basis of semivariogram models. A simulation study demonstrates that maps of spatial components are closer to the underlying risk maps in terms of prediction errors and provide a better visualization of regional patterns than the original maps of mortality rates or the maps smoothed using weighted linear averages. The proposed approach also attenuates the underestimation of the magnitude of the correlation between various cancer rates resulting from noise attached to the data. This methodology has great potential to explore scale-dependent correlation between risks of developing cancers and to detect clusters at various spatial scales, which should lead to a more accurate representation of geographic variation in cancer risk, and ultimately to a better understanding of causative relationships.

中文翻译：

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使用阶乘克里格法和人口加权半变异函数探索癌症死亡率之间的尺度相关性。

本文提出了一种地统计学方法，该方法在处理癌症死亡率数据时考虑了空间变化的人口规模。该方法分两个步骤进行：（1）首先使用人口加权半变异函数估计量描述和建模空间模式，（2）然后使用阶乘克里金法的变体估计和映射与在半变异函数上标识的嵌套结构相对应的空间成分。与传统空间平滑器相比，主要优点是空间可变性的模式（即，方向相关的可变性，相关性范围，可变性嵌套标度的存在）直接合并到分配给周围观测值的权重计算中。此外，除了过滤数据中的噪声外，该过程还允许在半变异函数模型的基础上将结构化分量分解为几个空间分量（即局部变量与区域变量）。仿真研究表明，与原始死亡率图或使用加权线性平均值进行平滑处理的图相比，就预测误差而言，空间成分图更接近基础风险图，并且可以更好地显示区域格局。所提出的方法还减弱了因附加在数据上的噪声而导致的各种癌症发生率之间相关性大小的低估。这种方法学具有巨大的潜力，可以探索癌症风险之间的比例相关性，并可以检测各种空间尺度上的簇，