This work presents a new model and estimation procedure for the illness-death survival data where the hazard functions follow accelerated failure time (AFT) models. A shared frailty variate induces positive dependence among failure times of a subject for handling the unobserved dependency between the non-terminal and the terminal failure times given the observed covariates. Semi-parametric maximum likelihood estimation procedure is developed via a kernel smoothed-aided EM algorithm, and variances are estimated by weighted bootstrap. The model is presented in the context of existing frailty-based illness-death models, emphasizing the contribution of the current work. The breast cancer data of the Rotterdam tumor bank are analyzed using the proposed and existing illness-death models. The results are contrasted and evaluated based on a new graphical goodness-of-fit procedure. Simulation results and data analysis nicely demonstrate the practical utility of the shared frailty variate with the AFT regression model under the illness-death framework.

翻译：这项工作为疾病-死亡生存数据提供了一个新的模型和估计程序,危险功能遵循加速故障时间(AFT)模型。一个共同的脆弱变差使一个对象的失败时间在处理非终点和终端故障时间之间未观察到的依赖性时产生积极的依赖性,因为观测到的共变情况。半参数最大可能性估计程序是通过内核平滑辅助EM算法开发的,差异由加权靴子估计。该模型是在现有的基于脆弱疾病-死亡模型的背景下展示的,强调当前工作的贡献。鹿特丹肿瘤库的乳腺癌数据使用拟议的和现有的疾病-死亡模型进行分析。结果根据新的图形健康程序进行了对比和评价。模拟结果和数据分析很好地展示了疾病-死亡框架下与AFT回归模型共享的脆弱变异的实际效用。