发表机构
School of Banking and Finance Management Development Institute of Singapore in Tashkent（塔什干新加坡金融管理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究分析仿射随访污染下Cox回归的最小假系数，推导精确基准，发现强污染导致缩减与饱和，行政删失引发过冲，分组改变几何，并给出影响函数与方差估计。
AI 中文摘要
在受试者完成的随访期间汇总的协变量有时被纳入Cox回归，如同在基线时观察到的那样。这种做法引入了未来的事件或删失信息，并改变了估计目标及其抽样行为。我们分析了一个仿射类，其中真实的基线协变量被已实现的随访时间所污染。将偏似然视为观测数据估计准则，我们推导出总体得分并刻画其唯一的最小假系数。精确的连续时间基准显示，在强污染下存在尺度缩减和饱和，而行政删失破坏了这种缩减并可能产生过冲。将退出时间与Breslow结分组会改变几何形状：系数具有单一驼峰，并最终回到零，尽管诱导的关联发散。我们还推导了一个观测数据影响函数，并展示了为什么基于模型的方差可能过小或过大。在所述条件下，受试者水平的三明治法能一致地估计最小假目标周围的不确定性，但它并不修正目标本身。
英文摘要
Covariates summarized over a subject's completed follow-up are sometimes entered into Cox regression as though observed at baseline. This practice incorporates future event or censoring information and changes both the estimand and its sampling behavior. We analyze an affine class in which a genuine baseline covariate is contaminated by realized follow-up time. Treating partial likelihood as an observed-data estimation criterion, we derive the population score and characterize its unique least-false coefficient. Exact continuous-time benchmarks show scale reduction and saturation under strong contamination, while administrative censoring destroys the reduction and may produce overshoot. Grouping exit times with Breslow ties changes the geometry: the coefficient has a single hump and eventually returns to zero even though the induced association diverges. We also derive an observed-data influence function and show why model-based variance can be either too small or too large. A subject-level sandwich consistently estimates uncertainty around the least-false target under the stated conditions, but it does not correct the target itself.
