Wang Bing, Li Jialiang, Wang Xiaoguang
School of Mathematical Sciences, Dalian University of Technology, China.
Department of Statistics and Applied Probability, Duke University NUS Graduate Medical School, Singapore Eye Research Institute, National University of Singapore, Singapore, Singapore.
Stat Methods Med Res. 2021 Feb;30(2):440-457. doi: 10.1177/0962280220959118. Epub 2020 Sep 24.
The mixture cure model has been widely applied to survival data in which a fraction of the observations never experience the event of interest, despite long-term follow-up. In this paper, we study the Cox proportional hazards mixture cure model where the covariate effects on the distribution of uncured subjects' failure time may jump when a covariate exceeds a change point. The nonparametric maximum likelihood estimation is used to obtain the semiparametric estimates. We employ a two-step computational procedure involving the Expectation-Maximization algorithm to implement the estimation. The consistency, convergence rate and asymptotic distributions of the estimators are carefully established under technical conditions and we show that the change point estimator is consistency. The out of bootstrap and the Louis algorithm are used to obtain the standard errors of the estimated change point and other regression parameter estimates, respectively. We also contribute a test procedure to check the existence of the change point. The finite sample performance of the proposed method is demonstrated via simulation studies and real data examples.
混合治愈模型已被广泛应用于生存数据，在这类数据中，尽管进行了长期随访，但仍有一部分观测值从未经历过感兴趣的事件。在本文中，我们研究了Cox比例风险混合治愈模型，其中当一个协变量超过一个变化点时，协变量对未治愈受试者失败时间分布的影响可能会发生跳跃。使用非参数最大似然估计来获得半参数估计。我们采用一种涉及期望最大化算法的两步计算程序来实现估计。在技术条件下仔细建立了估计量的一致性、收敛速度和渐近分布，并且我们证明了变化点估计量是一致的。分别使用自助法和Louis算法来获得估计变化点和其他回归参数估计的标准误差。我们还贡献了一个检验程序来检查变化点的存在性。通过模拟研究和实际数据示例展示了所提出方法的有限样本性能。
