Department of Biostatistics, Brown University, Providence, RI, U.S.A.
Stat Med. 2012 Nov 10;31(25):2998-3010. doi: 10.1002/sim.5454. Epub 2012 Jul 16.
Untestable assumptions about the association between survival and censoring times can affect the validity of estimates of the survival distribution including the Kaplan-Meier (KM) nonparametric maximum likelihood estimate (MLE). This paper explores the sensitivity of the KM curve to nonignorable censoring by extending the index of local sensitivity to nonignorability (ISNI; Troxel et al., Statistica Sinica, 14, 1221-1237, 2004; Zhang and Heitjan, Biometrics, 62, 1260-1268, 2006) to the case of a nonparametric survival model. The method involves, first, specifying a coarse-data selection model to describe the association between the failure and censoring processes and then evaluating the slope of the nonparametric survival MLE ordinate with respect to a nonignorability parameter in the neighborhood of the ignorable model. We define the nonparametric MLE of the survival curve for a fixed value of the nonignorability parameter and show in a simulation that ISNI analysis effectively captures local sensitivity to nonignorability. The method measures sensitivity in the sense of identifying functionals of the nonparametric MLE that nonignorability, if present, can affect substantially. We demonstrate the method with an application to a trial comparing mechanical assistance to optimal medical management in the treatment of end-stage heart failure.
关于生存和删失时间之间关联的未经检验的假设会影响生存分布的估计值的有效性，包括 Kaplan-Meier（KM）非参数最大似然估计（MLE）。本文通过将非可忽略性局部灵敏度指数（ISNI；Troxel 等人，Statistica Sinica，14，1221-1237，2004；Zhang 和 Heitjan，Biometrics，62，1260-1268，2006）扩展到非参数生存模型的情况，探讨了 KM 曲线对不可忽略性删失的敏感性。该方法首先指定一个粗数据选择模型来描述失效和删失过程之间的关联，然后评估在可忽略模型的邻域内非参数生存 MLE 纵坐标相对于不可忽略性参数的斜率。我们为不可忽略性参数的固定值定义了生存曲线的非参数 MLE，并在模拟中表明，ISNI 分析有效地捕捉了不可忽略性的局部敏感性。该方法从识别非参数 MLE 的函数的角度来衡量敏感性，如果存在不可忽略性，则可以对其产生实质性的影响。我们通过对一项比较机械辅助治疗与最佳药物治疗末期心力衰竭的试验的应用来说明该方法。
