发表机构
Shanxi University; Bristol Myers Squibb; Takeda Pharmaceuticals; University of Pennsylvania（山西大学; 百时美施贵宝; 武田制药; 宾夕法尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种半参数方法，通过二次惩罚将辅助结局信息纳入Cox回归，在效应一致时借用信息，不一致时自适应调整，以降低估计方差并保持有效性。
AI 中文摘要
时间至事件结局通常与辅助结局一起收集，这些辅助结局可能提供关于基线风险的额外信息。我们开发了一种半参数方法，在不指定联合似然的情况下，将此类信息纳入Cox回归。生存结局遵循Cox比例风险模型，连续辅助结局遵循部分线性模型，两者通过二次惩罚连接不同的非参数基线协变量效应。当这些效应一致且结局得分满足信息恒等式和一阶正交条件时，我们推导了惩罚估计量的三明治协方差，并表明对于任何固定的惩罚水平，Cox回归估计量的渐近方差不大于单独估计下的方差。我们进一步刻画了共享效应设置的偏离。阶为\(n^{-1/2}\)的局部差异在极限分布中引起显式均值偏移，产生直接的偏差-方差权衡，而固定差异在非消失惩罚下通常改变总体目标。这些结果激励了一种自适应惩罚，当拟合的协变量效应接近时借用信息，当检测到持续差异时接近单独估计。模拟和真实数据分析证明了所提出方法的有效性和有效性。
英文摘要
Time-to-event outcomes are often collected together with auxiliary outcomes that may provide additional information about baseline risk. We develop a semiparametric approach for incorporating such information into Cox regression without specifying a joint likelihood. The survival outcome follows a Cox proportional hazards model and a continuous auxiliary outcome follows a partially linear model, with separate nonparametric baseline covariate effects linked through a quadratic penalty. When these effects coincide and the outcome scores satisfy the information identities and a first-order orthogonality condition, we derive the sandwich covariance of the penalized estimator and show that, for any fixed penalty level, the asymptotic variance of the Cox regression estimator is no greater than that under separate estimation. We further characterize departures from the shared-effect setting. Local differences of order \(n^{-1/2}\) induce an explicit mean shift in the limiting distribution, yielding a direct bias--variance trade-off, whereas fixed differences generally alter the population target under nonvanishing penalization. These results motivate an adaptive penalty that borrows information when the fitted covariate effects are close and approaches separate estimation when a persistent difference is detected. Simulations and a real world data analysis demonstrate the validity and effectiveness of the proposed method.
