Liu L I, Su Wen, Yin Guosheng, Zhao Xingqiu, Zhang Ying
School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, 430072, China.
Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong.
Bernoulli (Andover). 2022 Nov;28(4):2968-2997. doi: 10.3150/21-bej1444. Epub 2022 Aug 17.
Panel count data typically refer to data arising from studies with recurrent events, in which subjects are observed only at discrete time points rather than under continuous observations. We investigate a general situation where a recurrent event process is eventually truncated by an informative terminal event and we are particularly interested in behaviors of the recurrent event process near the terminal event. We propose a reversed mean model for estimating the mean function of the recurrent event process. We develop a two-stage sieve likelihood-based method to estimate the mean function, which overcomes the computational difficulties arising from a nuisance functional parameter involved in the likelihood. The consistency and the convergence rate of the two-stage estimator are established. Allowing for the convergence rate slower than the standard rate, we develop the general weak convergence theory of -estimators with a nuisance functional parameter, and then apply it to the proposed estimator for deriving the asymptotic normality. Furthermore, a class of two-sample tests is developed. The proposed methods are evaluated with extensive simulation studies and illustrated with panel count data from the Chinese Longitudinal Healthy Longevity Study.
面板计数数据通常指来自具有复发事件研究的数据，在这类研究中，仅在离散时间点而非连续观测下观察受试者。我们研究一种一般情况，即复发事件过程最终被一个信息性终末事件截断，并且我们特别关注终末事件附近复发事件过程的行为。我们提出一种反向均值模型来估计复发事件过程的均值函数。我们开发了一种基于筛似然的两阶段方法来估计均值函数，该方法克服了似然中涉及的一个讨厌泛函参数所带来的计算困难。建立了两阶段估计量的一致性和收敛速度。考虑到收敛速度慢于标准速度，我们发展了带有讨厌泛函参数的估计量的一般弱收敛理论，然后将其应用于所提出的估计量以推导渐近正态性。此外，还开发了一类两样本检验。所提出的方法通过广泛的模拟研究进行评估，并用中国老年健康长寿纵向研究的面板计数数据进行说明。
