Zucker David M, Spiegelman Donna
Department of Statistics, Hebrew University, Mount Scopus, 91905 Jerusalem, Israel.
Stat Med. 2008 May 20;27(11):1911-33. doi: 10.1002/sim.3159.
We consider Cox proportional hazards regression when the covariate vector includes error-prone discrete covariates along with error-free covariates, which may be discrete or continuous. The misclassification in the discrete error-prone covariates is allowed to be of any specified form. Building on the work of Nakamura and his colleagues, we present a corrected score method for this setting. The method can handle all three major study designs (internal validation design, external validation design, and replicate measures design), both functional and structural error models, and time-dependent covariates satisfying a certain 'localized error' condition. We derive the asymptotic properties of the method and indicate how to adjust the covariance matrix of the regression coefficient estimates to account for estimation of the misclassification matrix. We present the results of a finite-sample simulation study under Weibull survival with a single binary covariate having known misclassification rates. The performance of the method described here was similar to that of related methods we have examined in previous works. Specifically, our new estimator performed as well as or, in a few cases, better than the full Weibull maximum likelihood estimator. We also present simulation results for our method for the case where the misclassification probabilities are estimated from an external replicate measures study. Our method generally performed well in these simulations. The new estimator has a broader range of applicability than many other estimators proposed in the literature, including those described in our own earlier work, in that it can handle time-dependent covariates with an arbitrary misclassification structure. We illustrate the method on data from a study of the relationship between dietary calcium intake and distal colon cancer.
当协变量向量包括容易出错的离散协变量以及无误差的协变量（可能是离散的或连续的）时，我们考虑Cox比例风险回归。允许离散的容易出错的协变量中的错误分类为任何指定形式。基于中村及其同事的工作，我们针对此设置提出了一种校正得分方法。该方法可以处理所有三种主要的研究设计（内部验证设计、外部验证设计和重复测量设计）、功能和结构误差模型以及满足特定“局部误差”条件的随时间变化的协变量。我们推导了该方法的渐近性质，并指出如何调整回归系数估计的协方差矩阵以考虑错误分类矩阵的估计。我们给出了在具有已知错误分类率的单个二元协变量的威布尔生存模型下的有限样本模拟研究结果。这里描述的方法的性能与我们在先前工作中研究的相关方法相似。具体而言，我们的新估计器的表现与完整的威布尔最大似然估计器一样好，在某些情况下甚至更好。我们还给出了从外部重复测量研究中估计错误分类概率的情况下我们方法的模拟结果。我们的方法在这些模拟中通常表现良好。新估计器比文献中提出的许多其他估计器具有更广泛的适用性，包括我们自己早期工作中描述的那些估计器，因为它可以处理具有任意错误分类结构的随时间变化的协变量。我们用一项关于膳食钙摄入量与远端结肠癌关系的研究数据说明了该方法。
