AI 中文总结
该研究提出两阶段核偶极子拆分SVM生存树方法，分离空间与临床生存风险，在LeukSurv数据及模拟中可准确识别风险区域，优于未调整空间分析与平滑基准方法。
AI 中文摘要
恢复生存的地理变异需要将空间风险与患者的临床特征分离开来，而该问题因本身具有空间结构的预后协变量而变得复杂。我们开发了一种用于该分离的非参数两阶段方法。仅对协变量拟合的临床生存树提供叶节点Nelson-Aalen累积风险残差，将删失生存结构转换为临床调整后的尺度，且无需对临床风险施加函数形式；对这些残差在坐标上拟合的第二棵树则可恢复空间结构。两个阶段均为核偶极子拆分生存树，因此所得空间风险图为分段常数，具有尖锐的、可能弯曲的边界。我们确定残差恢复空间信号的条件：在乘性脆弱性和外生性条件下，给定位置时残差不含临床协变量，且按脆弱性随机排序。脆弱性拉普拉斯指数的展开量化了其近似指数性并确定了主导余项。这些结果假设第一阶段的一致性而非模型类别，因此该构造可扩展至其他生存估计量。在LeukSurv白血病数据上，该方法与贝叶斯高斯随机场脆弱性在风险升高区域的结果一致，同时解决了平滑表面平均所忽略的尖锐邻接关系，而未调整的空间分析会将临床变异错误归因于位置。在具有已知区域的模拟中（包括对不同程度外生性违反的遍历），我们确定了两种贡献不再可分离的点，且当接近该点时，平滑基准会平行退化。
英文摘要
Recovering geographic variation in survival requires separating spatial risk from patients' clinical characteristics, a problem complicated by prognostic covariates that are themselves spatially structured. We develop a nonparametric two-stage method for this separation. A clinical survival tree fit to the covariates alone supplies leaf Nelson-Aalen cumulative hazard residuals, transferring the censored survival structure to a clinically adjusted scale without imposing a functional form on the clinical hazard, and a second tree fit to these residuals on the coordinates recovers the spatial structure. Both stages are kernel dipole-splitting survival trees, so the resulting spatial risk map is piecewise constant, with sharp, possibly curved boundaries. We establish when the residuals recover the spatial signal: under a multiplicative frailty and an exogeneity condition, they are free of the clinical covariates given location and stochastically ordered by the frailty. An expansion of the frailty Laplace exponent quantifies their approximate exponentiality and identifies the leading remainder. These results assume consistency of the first stage rather than a model class, so the construction extends to other survival estimators. On the LeukSurv leukemia data the method agrees with a Bayesian Gaussian random field frailty about where risk is elevated while resolving sharp adjacencies the smooth surface averages away, and an unadjusted spatial analysis misattributes clinical variation to location. Simulations with known zones, including a sweep through graded violations of exogeneity, locate the point at which the two contributions cease to be separately identifiable, with the smooth benchmark degrading in parallel as that point is approached.
Comments37 pages, 6 figures, 3 tables, submitted to Spatial Statistics
