Su Wen, Liu Li, Yin Guosheng, Zhao Xingqiu, Zhang Ying
The University of Hong Kong.
Wuhan University.
Stat Sin. 2024;34:1843-1862. doi: 10.5705/ss.202021.0353.
We study semiparametric regression for a recurrent event process with an informative terminal event, where observations are taken only at discrete time points, rather than continuously over time. To account for the effect of a terminal event on the recurrent event process, we propose a semiparametric reversed mean model, for which we develop a two-stage sieve likelihood-based method to estimate the baseline mean function and the covariate effects. Our approach overcomes the computational difficulties arising from the nuisance functional parameter in the assumption that the likelihood is based on a Poisson process. We establish the consistency, convergence rate, and asymptotic normality of the proposed two-stage estimator, which is robust against the assumption of an underlying Poisson process. The proposed method is evaluated using extensive simulation studies, and demonstrated using panel count data from a longitudinal healthy longevity study and data from a bladder tumor study.
我们研究了具有信息性终端事件的复发事件过程的半参数回归，其中观测仅在离散时间点进行，而非随时间连续进行。为了考虑终端事件对复发事件过程的影响，我们提出了一种半参数反向均值模型，并为此开发了一种基于筛法似然的两阶段方法来估计基线均值函数和协变量效应。我们的方法克服了似然基于泊松过程这一假设中讨厌的泛函参数所带来的计算困难。我们建立了所提出的两阶段估计量的一致性、收敛速度和渐近正态性，该估计量对潜在泊松过程的假设具有鲁棒性。所提出的方法通过广泛的模拟研究进行了评估，并使用了一项纵向健康长寿研究的面板计数数据以及一项膀胱肿瘤研究的数据进行了演示。
