超越均值：用于协变量平衡诊断的加权k样本综合方差比统计量
Beyond the Mean: A Weighted k-Sample Omnibus Variance-Ratio Statistic for Covariate Balance Diagnostics
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- University of California, San Francisco（加州大学旧金山分校）
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中文总结 AI 辅助
提出FVR统计量，将Rubin方差比推广至k组，用于检测协变量离散度不平衡，模拟显示其能有效跟踪估计偏差并已实现于Stata命令。
中文摘要 AI 辅助
Rubin方差比（VR）通过检测离散度中的协变量不平衡来补充标准化均值差，但针对多于两组的组别，尚无专门构建的综合扩展。我们引入了FVR，一种对成对对数方差比进行规模加权二次组合的统计量，将VR推广至k组，同时提供了几何均值和最大成对方差比作为比较基准。FVR在k=2时与Rubin的VR存在精确关系，其数学结构直接平行于Cohen的f。在涵盖四种方差驱动偏差机制、k=3、4、6以及样本量从200到10,000的蒙特卡洛模拟中，FVR和几何均值统计量通常至少与最大统计量一样好地跟踪下游估计偏差。当许多组共享非常小的样本时，FVR保留了显著更多的信号，而绝对偏差阈值在N=200时不稳定。在各种机制中，FVR<0.10相当令人放心，高于约0.30的值通常表示需要关注，中间值则取决于具体情况。该统计量在Stata命令varatio中针对任意分析权重实现，并通过一个多值处理应用加以说明。
英文摘要
Rubin's variance ratio (VR) complements the standardized mean difference by detecting covariate imbalance in spread, but no purpose-built omnibus extension exists for more than two groups. We introduce FVR, a size-weighted quadratic combination of pairwise log-variance-ratios that generalizes VR to k groups, together with geometric-mean and maximum pairwise variance-ratio comparators. FVR has an exact relationship to Rubin's VR at k = 2 and a mathematical structure directly parallel to Cohen's f. In Monte Carlo simulations spanning four variance-driven bias mechanisms, k = 3, 4, 6, and sample sizes from 200 to 10,000, FVR and the geometric-mean statistic generally tracked downstream estimation bias at least as well as the maximum statistic. FVR retained substantially more signal when many groups shared a very small sample, while absolute-bias thresholds were unstable at N = 200. Across mechanisms, FVR < 0.10 was reasonably reassuring, values above approximately 0.30 generally indicated concern, and intermediate values were context-dependent. The statistic is implemented for arbitrary analysis weights in the Stata command varatio and illustrated using a multivalued-treatment application.
