Hu Xiangbin, Liu L I, Zhang Ying, Zhao Xingqiu
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China.
School of Mathematics and Statistics, Wuhan University, Wuhan, China.
Bernoulli (Andover). 2023 Nov;29(4):2828-2853. doi: 10.3150/22-bej1565. Epub 2023 Aug 22.
We study a semiparametric model for robust analysis of panel count data with an informative terminal event. To explore the explicit effect of the terminal event on recurrent events of interest, we propose a conditional mean model for a reversed counting process anchoring at the terminal event. Treating the distribution function of the terminal event as a nuisance functional parameter, we develop a predicted least squares-based two-stage estimation procedure with the spline-based sieve estimation technique, and derive the convergence rate of the proposed estimator. Furthermore, overcoming the difficulties caused by the convergence rate slower than , we establish the asymptotic normality for the estimator of the finite-dimensional parameter and a functional of the estimator of the infinite-dimensional parameter. The proposed method is evaluated through extensive simulation studies and illustrated with an application to the Longitudinal Healthy Longevity Survey study on elder people in China.
我们研究了一个半参数模型，用于对具有信息性终端事件的面板计数数据进行稳健分析。为了探究终端事件对感兴趣的复发事件的明确影响，我们提出了一个以终端事件为锚点的反向计数过程的条件均值模型。将终端事件的分布函数视为一个干扰函数参数，我们利用基于样条筛估计技术开发了一种基于预测最小二乘法的两阶段估计程序，并推导了所提出估计量的收敛速度。此外，克服了收敛速度慢于 的困难，我们建立了有限维参数估计量和无限维参数估计量的泛函的渐近正态性。通过广泛的模拟研究对所提出的方法进行了评估，并通过应用于中国老年人纵向健康长寿调查研究进行了说明。
