Analysis of time-to-event data using Cox's proportional hazards (PH) model is ubiquitous in scientific research. A sample is taken from the population of interest and covariate information is collected on everyone. If the event of interest is rare and covariate information is difficult to collect, the nested case-control (NCC) design reduces costs with minimal impact on inferential precision. Under PH, application of the Cox model to data from a NCC sample provides consistent estimation of the hazard ratio. However, under non-PH, the finite-sample estimates corresponding to the Cox estimator depend on the number of controls sampled and the censoring distribution. We propose two estimators based on a binary predictor of interest: one recovers the estimand corresponding to the Cox model under a simple random sample, while the other recovers an estimand that does not depend on the censoring distribution. We derive the asymptotic distribution and provide finite-sample variance estimators.

中文翻译：

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非比例风险下嵌套病例对照设计的估计

使用 Cox 的比例风险 (PH) 模型分析事件发生时间数据在科学研究中无处不在。从感兴趣的人群中抽取样本，并收集每个人的协变量信息。如果感兴趣的事件很少且难以收集协变量信息，则嵌套案例控制 (NCC) 设计可降低成本，同时对推理精度的影响最小。在 PH 下，将 Cox 模型应用于 NCC 样本的数据可提供对风险比的一致估计。然而，在非 PH 下，对应于 Cox 估计的有限样本估计取决于抽样控制的数量和审查分布。我们提出了两个基于感兴趣的二元预测器的估计器：一个在简单的随机样本下恢复与 Cox 模型相对应的估计量，而另一个恢复一个不依赖于审查分布的估计值。我们推导出渐近分布并提供有限样本方差估计量。