Chambless Lloyd E, Diao Guoqing
Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27514, USA.
Stat Med. 2006 Oct 30;25(20):3474-86. doi: 10.1002/sim.2299.
Sensitivity, specificity, and area under the ROC curve (AUC) are often used to measure the ability of survival models to predict future risk. Estimation of these parameters is complicated by the fact that these parameters are time-dependent and by the fact that censoring affects their estimation just as it affects estimation of survival curves or coefficients of survival regression models. The authors present several estimators that overcome these complications. One approach is a recursive calculation over the ordered times of events, analogous to the Kaplan-Meier approach to survival function estimation. Another is to first apply Bayes' theorem to write the parameters of interest in terms of conditional survival functions that are then estimated by survival analysis methods. Simulation studies demonstrate that the proposed estimators perform well in practical situations, when compared with an estimator (c-statistic, from logistic regression) that ignores time. An illustration with data from a cardiovascular follow-up study is provided.
敏感性、特异性和ROC曲线下面积（AUC）常被用于衡量生存模型预测未来风险的能力。这些参数的估计较为复杂，原因在于这些参数具有时间依赖性，且删失对其估计的影响，就如同其对生存曲线或生存回归模型系数估计的影响一样。作者提出了几种克服这些复杂情况的估计方法。一种方法是对有序的事件时间进行递归计算，这类似于用于生存函数估计的Kaplan-Meier方法。另一种方法是首先应用贝叶斯定理，根据条件生存函数来表示感兴趣的参数，然后通过生存分析方法对这些条件生存函数进行估计。模拟研究表明，与忽略时间的估计方法（逻辑回归中的c统计量）相比，所提出的估计方法在实际情况中表现良好。文中还给出了一项心血管随访研究数据的示例。
