用于评估协变量平衡的加权k样本Kolmogorov-Smirnov、Cramer-von Mises和Anderson-Darling检验
Weighted k-Sample Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling Tests for Assessing Covariate Balance
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中文总结 AI 辅助
该研究将协变量平衡的加权分布检验扩展到k≥2组，通过模拟验证了其I型错误与功效特性，并在Stata中实现为相关命令，为多组协变量平衡评估提供了有效工具。
中文摘要 AI 辅助
当前用于协变量平衡的加权分布检验仅局限于两组比较，我们将Kolmogorov-Smirnov、Anderson-Darling和Cramer-von Mises检验扩展到任意数量的加权组（k≥2），利用现有的k样本推广方法和共享的置换推断程序；当k=2时，每个统计量可精确简化为其对应的两组形式。配套的事后成对程序采用四种多重比较调整方法，可在综合检验拒绝后定位哪些组存在差异。在k=3的四场景模拟研究中，I型错误保持接近名义水平，且针对两组建立的比较优势得以保留：Kolmogorov-Smirnov对中心位置的差异最具功效，Anderson-Darling对尾部位置的差异最具功效，Anderson-Darling与Cramer-von Mises对弥散差异的表现相当。不过综合检验的功效始终低于对应的两组设定——这并非因为潜在差异被稀释，而是因为增加组数会扩大原分布本身；因此，当怀疑特定组存在不平衡时，事后程序（其成对统计量无此类惩罚）往往是更灵敏的工具。这些方法已在Stata命令kstest、adtest和cvmtest中实现。
英文摘要
Weighted distributional tests for covariate balance are currently limited to two-group comparisons. We extend the Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises tests to an arbitrary number of weighted groups k >= 2, using existing k-sample generalizations and a shared permutation-inference procedure; each statistic reduces exactly to its two-group counterpart at k = 2. An accompanying post-hoc pairwise procedure with four multiple-comparison adjustments localizes which groups differ following an omnibus rejection. In a four-scenario simulation study at k = 3, Type I error remained close to nominal, and the comparative advantages established for two groups were preserved: Kolmogorov-Smirnov was most powerful against a centrally located discrepancy, Anderson-Darling against a tail-located discrepancy, and Anderson-Darling and Cramer-von Mises performed comparably against a diffuse discrepancy. Omnibus power was nonetheless uniformly lower than in the matching two-group setting - not because the underlying discrepancy is diluted, but because adding groups enlarges the null distribution itself, so the post-hoc procedure, whose pairwise statistics carry no such penalty, is often the more sensitive tool whenever a specific group's imbalance is suspected. The methods are implemented in the Stata commands kstest, adtest, and cvmtest.
