The Cox regression model is a popular model for analyzing the relationship between a covariate vector and a survival endpoint. The standard Cox model assumes a constant covariate effect across the entire covariate domain. However, in many epidemiological and other applications, the covariate of main interest is subject to a threshold effect: a change in the slope at a certain point within the covariate domain. Often, the covariate of interest is subject to some degree of measurement error. In this paper, we study measurement error correction in the case where the threshold is known. Several bias correction methods are examined: two versions of regression calibration (RC1 and RC2, the latter of which is new), two methods based on the induced relative risk under a rare event assumption (RR1 and RR2, the latter of which is new), a maximum pseudo-partial likelihood estimator (MPPLE), and simulation-extrapolation (SIMEX). We develop the theory, present simulations comparing the methods, and illustrate their use on data concerning the relationship between chronic air pollution exposure to particulate matter PM10 and fatal myocardial infarction (Nurses Health Study (NHS)), and on data concerning the effect of a subject's long-term underlying systolic blood pressure level on the risk of cardiovascular disease death (Framingham Heart Study (FHS)). The simulations indicate that the best methods are RR2 and MPPLE.

中文翻译：

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具有协变量测量误差和变化点的 Cox 生存回归模型中的估计

Cox 回归模型是一种流行的模型，用于分析协变量向量和生存终点之间的关系。标准 Cox 模型假设在整个协变量域中存在恒定的协变量效应。然而，在许多流行病学和其他应用中，主要关注的协变量受到阈值效应的影响：协变量域内某个点的斜率变化。通常，感兴趣的协变量会受到一定程度的测量误差的影响。在本文中，我们研究了在阈值已知的情况下的测量误差校正。研究了几种偏差校正方法：回归校准的两个版本（RC1 和 RC2，后者是新的），两种基于罕见事件假设下的诱导相对风险的方法（RR1 和 RR2，后者是新的） , 最大伪偏似然估计器 (MPPLE) 和模拟外推 (SIMEX)。我们开发了理论，提出了比较方法的模拟，并说明了它们在有关长期空气污染暴露于颗粒物 PM10 与致命性心肌梗塞（护士健康研究 (NHS)）之间关系的数据以及有关受试者的长期潜在收缩压水平对心血管疾病死亡风险的影响（弗雷明汉心脏研究 (FHS)）。模拟表明最好的方法是 RR2 和 MPPLE。并说明它们在有关长期空气污染暴露于颗粒物 PM10 与致命性心肌梗塞（护士健康研究 (NHS)）之间关系的数据以及有关受试者长期潜在收缩压水平对心血管疾病死亡的风险（弗雷明汉心脏研究 (FHS)）。模拟表明最好的方法是 RR2 和 MPPLE。并说明它们在有关长期空气污染暴露于颗粒物 PM10 与致命性心肌梗塞（护士健康研究 (NHS)）之间关系的数据以及有关受试者长期潜在收缩压水平对心血管疾病死亡的风险（弗雷明汉心脏研究 (FHS)）。模拟表明最好的方法是 RR2 和 MPPLE。