Boundary analysis of cancer maps may highlight areas where causative exposures change through geographic space, the presence of local populations with distinct cancer incidences, or the impact of different cancer control methods. Too often, such analysis ignores the spatial pattern of incidence or mortality rates and overlooks the fact that rates computed from sparsely populated geographic entities can be very unreliable. This paper proposes a new methodology that accounts for the uncertainty and spatial correlation of rate data in the detection of significant edges between adjacent entities or polygons. Poisson kriging is first used to estimate the risk value and the associated standard error within each polygon, accounting for the population size and the risk semivariogram computed from raw rates. The boundary statistic is then defined as half the absolute difference between kriged risks. Its reference distribution, under the null hypothesis of no boundary, is derived through the generation of multiple realizations of the spatial distribution of cancer risk values. This paper presents three types of neutral models generated using methods of increasing complexity: the common random shuffle of estimated risk values, a spatial re-ordering of these risks, or p-field simulation that accounts for the population size within each polygon. The approach is illustrated using age-adjusted pancreatic cancer mortality rates for white females in 295 US counties of the Northeast (1970-1994). Simulation studies demonstrate that Poisson kriging yields more accurate estimates of the cancer risk and how its value changes between polygons (i.e. boundary statistic), relatively to the use of raw rates or local empirical Bayes smoother. When used in conjunction with spatial neutral models generated by p-field simulation, the boundary analysis based on Poisson kriging estimates minimizes the proportion of type I errors (i.e. edges wrongly declared significant) while the frequency of these errors is predicted well by the p-value of the statistical test.

中文翻译：

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在癌症死亡率地图的边界分析中考虑速率不稳定性和空间模式。

癌症地图的边界分析可能会突出显示致病暴露随地理空间变化的区域、具有不同癌症发病率的当地人群的存在或不同癌症控制方法的影响。此类分析常常忽略发病率或死亡率的空间模式，并忽略从人口稀少的地理实体计算的比率可能非常不可靠的事实。本文提出了一种新方法，该方法在检测相邻实体或多边形之间的重要边缘时考虑了速率数据的不确定性和空间相关性。泊松克里金法首先用于估计每个多边形内的风险值和相关标准误差，考虑人口规模和根据原始利率计算的风险半变异函数。然后将边界统计量定义为克里金风险之间绝对差值的一半。它的参考分布，在无边界的零假设下，是通过对癌症风险值空间分布的多重实现产生的。本文介绍了使用越来越复杂的方法生成的三种类型的中性模型：估计风险值的常见随机洗牌、这些风险的空间重新排序或考虑每个多边形内人口规模的 p 场模拟。该方法使用美国东北部 295 个县 (1970-1994) 中白人女性的年龄调整胰腺癌死亡率来说明。模拟研究表明，泊松克里金法可以更准确地估计癌症风险及其值在多边形之间的变化（即 边界统计），相对于使用原始率或局部经验贝叶斯更平滑。当与 p 场模拟生成的空间中性模型结合使用时，基于泊松克里金估计的边界分析可最大限度地减少 I 类错误的比例（即错误地声明为重要的边缘），而这些错误的频率可以通过 p-统计检验的价值。