AI 中文总结
该研究针对临床测量值的预后意义随患者修饰因子变化的问题，提出直接映射、策略标准化映射及原点参考映射三种方法，结合Cox模型开发对应估计量，经模拟验证其有限样本性能。
AI 中文摘要
以固定物理单位记录的连续临床测量值，当其效应依赖于患者层面的修饰因子时，对不同患者可能具有不同的预后意义。例如，相同的肿瘤直径在婴儿和成人中可能预示着显著不同的预后，因为患者体型可修饰其预后效应。我们针对时间-事件结局，通过预后等效映射形式化该问题。所得的估计量将在某一修饰因子水平下观测到的测量值，映射至参考修饰因子水平下能产生相同条件预后量的数值。基本操作是令单调条件预后评分相等，并对参考侧曲线求逆。然而，在观察性数据中，治疗可能依据修饰因子和测量值进行选择，因此直接的等效-求逆过程可能同时反映治疗分配的差异以及测量值本身的预后意义差异。因此，除直接方法外，我们还定义了一种策略标准化映射，该映射使用g公式在共同策略下标准化治疗；我们还引入了原点参考映射，其通过比较共同锚点的预后评分变化，从而将修饰因子特异性预后水平与测量值-预后关系中的修饰因子依赖分离开。我们使用Cox模型开发了线性和灵活的求逆估计量，并提供了解析和自助法置信带。模拟研究评估了有限样本性能，并说明了治疗标准化和原点参考如何明确映射的对象。
英文摘要
A continuous clinical measurement recorded in fixed physical units may have different prognostic meaning across patients when its effect depends on a patient-level modifier. For example, the same tumor diameter may imply markedly different prognosis in an infant and an adult, because patient size can modify its prognostic effect. We formalize this problem through prognosis-equivalent mapping for time-to-event outcomes. The resulting estimand maps a measurement value observed at one modifier level to the value under a reference modifier level that yields the same conditional prognostic quantity. The basic operation is to equate a monotone conditional prognostic score and invert the reference-side curve. In observational data, however, treatment may be selected according to the modifier and the measurement, so a direct equate-and-invert procedure may reflect differences in treatment assignment as well as the prognostic meaning of the measurement itself. We therefore define, in addition to a direct approach, a policy-standardized mapping that standardizes treatment under a common policy using the g-formula. We also introduce an origin-referenced mapping that compares changes in prognostic score from a common anchor, thereby separating modifier-specific prognostic levels from modifier dependence in the measurement--prognosis relationship. Using Cox models, we develop linear and flexible inversion estimators with analytic and bootstrap confidence bands. Simulations evaluate finite-sample performance and illustrate how treatment standardization and origin referencing clarify what is being mapped.
