科恩f值还是均值标准化差异？评估多值处理的协变量平衡
Cohen's f or Mean Standardized Differences? Assessing Covariate Balance with Multivalued Treatments
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中文总结 AI 辅助
该研究对比科恩f值与均值标准化差异（SMD）在多值处理协变量平衡评估中的表现，通过Stata命令esizereg验证，发现科恩f值追踪估计偏差的能力与均值绝对SMD相当，建议报告f及其分解结果。
中文摘要 AI 辅助
评估两个以上处理组间的协变量平衡尚无确定的通用标准：现行做法是对成对标准化均值差异（SMD）取平均或最大值，而科恩f值（科恩d值向两个以上组的经典推广）提供了基于既定效应量框架的替代方案，但二者尚未被正式比较。我们通过社区贡献的Stata命令esizereg将二者推广至任意加权和协变量调整模型，并在包含3、4、6个处理组的模拟研究中，在正确设定和误设定的广义倾向得分加权下验证了它们，将每个统计量与下游处理效应偏差相关联。科恩f值与均值绝对SMD追踪估计偏差的能力相当，合并时相关系数r=0.93，在加权组内相关系数约为0.79；最大绝对SMD通常最弱。在故意对抗性的非线性/交互作用结局模型下，该排序未改变。科恩f值与基于SMD的统计量数值不可比：我们推导了f作为成对SMD的规模加权二次函数的精确表示，并证明了在组规模相等时f与均值绝对SMD之间可达到的最小比值，因此传统SMD阈值不应直接应用于f。我们建议报告f及其按水平和成对分解的结果。
英文摘要
Assessing covariate balance across more than two treatment groups has no established omnibus standard: the prevailing practice averages, or takes the maximum of, pairwise standardized mean differences (SMD), while Cohen's f - the classical generalization of Cohen's d to more than two groups - offers an alternative grounded in an established effect-size framework, but the two have not been formally compared. We extend both to arbitrary weighted and covariate-adjusted models via a community-contributed Stata command, esizereg, and validate them in a simulation study of three, four, and six treatment groups under correctly specified and misspecified generalized-propensity-score weighting, correlating each statistic against downstream treatment-effect bias. Cohen's f tracks estimation bias comparably to mean absolute SMD, both pooled (r = 0.93) and within weighting arm (r approximately 0.79); maximum absolute SMD is generally weakest. This ranking was unchanged under a deliberately adversarial nonlinear/interaction outcome model. Cohen's f and the SMD-based statistics are not numerically comparable: we derive an exact representation of f as a size-weighted quadratic function of the pairwise SMDs and prove the minimum attainable ratio between f and mean absolute SMD under equal group weights, so conventional SMD thresholds should not apply directly to f. We recommend reporting f alongside its per-level and pairwise decomposition.
