When Do Surrogate Metrics Work? A Finite-Sample Comparison Under Realistic Failure Modes
替代指标何时有效？现实失效机制下的有限样本比较AI 解读 ↓
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替代指标何时有效？现实失效机制下的有限样本比较
- 研究问题
- 长期结果尚未成熟、仅早期入组者具有结果标签时，替代指标与预测辅助估计如何权衡效率、稳健性和违例可检测性？
- 方法与思路
- 作者跨多种失效机制比较七类估计量，推导固定预测器下的 PPI++ 方差与交叉拟合联合分布，并构造差异诊断。
- 材料陈述的贡献
- 摘要称替代指标违例可能损害覆盖率却难被诊断发现；PPI 方法在随机标注下较稳健，但稀有结果仍有有限样本问题。
- 阅读关注点
- 应核对滚动入组与随机标注的区别、固定预测器方差的适用范围，以及诊断功效、覆盖率和偏差的联合表现。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实；摘要中的随机标注结论不能直接推广至按入组时间标注的情形。
原文摘要
Online experiments must often be evaluated before long-term outcomes mature. Under rolling enrollment, these outcomes are observed only for early enrollees, while short-term surrogates are available for everyone. We compare seven estimators across eleven data-generating processes, spanning partial mediation, drift, outcome sparsity, and enrollment-time labeling, with up to $R = 2,000$ replications over more than 500 method-by-scenario cells. We find a sharp robustness-efficiency tradeoff: the surrogate index delivers large efficiency gains when surrogacy holds but its coverage collapses under violations, while PPI-family methods stay asymptotically valid under random labeling at smaller gains. We give the finite-sample variance of PPI++ in the all-units parameterization for a fixed predictor, a joint asymptotic distribution for the two estimators under cross-fitting, and a Hausman-type estimator-disagreement diagnostic, then quantify the detection-damage gap: in the partial-mediation design, where we locate both edges, a band of violations destroys surrogate-index coverage yet is too small to detect on most datasets. On the 64,000-customer Hillstrom experiment the diagnostic rarely flags a violation that biases the surrogate index, and a Cauchy-kernel hybrid of the two estimators inherits 10.7% relative bias; on the 14-million-user Criteo experiment the violation is detected, and subsampling traces detection turning on with scale as damage persists. PPI++ has limits: at a rare-conversion $n = 30,000$ Criteo subsample its empirical coverage is 85.0%. We recommend prespecifying PPI++ with the exact variance as the primary analysis under random labeling and adequate labeled outcome counts, reading the diagnostic as a warning, not a certificate, and treating the surrogate index as a sensitivity analysis.