Department of Epidemiology and Biostatistics, University of Georgia, Athens, Georgia, USA.
Data Numerica Institute, Bellevue, Washington, USA.
Biometrics. 2023 Mar;79(1):437-448. doi: 10.1111/biom.13595. Epub 2021 Nov 15.
We consider the proportional hazards model in which the covariates include the discretized categories of a continuous time-dependent exposure variable measured with error. Naively ignoring the measurement error in the analysis may cause biased estimation and erroneous inference. Although various approaches have been proposed to deal with measurement error when the hazard depends linearly on the time-dependent variable, it has not yet been investigated how to correct when the hazard depends on the discretized categories of the time-dependent variable. To fill this gap in the literature, we propose a smoothed corrected score approach based on approximation of the discretized categories after smoothing the indicator function. The consistency and asymptotic normality of the proposed estimator are established. The observation times of the time-dependent variable are allowed to be informative. For comparison, we also extend to this setting two approximate approaches, the regression calibration and the risk-set regression calibration. The methods are assessed by simulation studies and by application to data from an HIV clinical trial.
我们考虑比例风险模型，其中协变量包括连续时间相关暴露变量的离散类别，这些类别存在测量误差。在分析中忽略测量误差可能会导致有偏估计和错误的推断。尽管已经提出了各种方法来处理当风险与时间相关变量线性相关时的测量误差，但尚未研究当风险与时间相关变量的离散类别相关时如何进行校正。为了填补文献中的这一空白，我们提出了一种基于对平滑指示函数后离散类别进行近似的平滑校正得分方法。建立了所提出估计量的一致性和渐近正态性。允许时间相关变量的观察时间具有信息性。作为比较，我们还将两种近似方法——回归校正和风险集回归校正扩展到这种情况。通过模拟研究和对 HIV 临床试验数据的应用来评估这些方法。
