Ge Lei, Zhu Liang, Sun Jianguo
Center for Applied Statistical Research, School of Mathematics, Jilin University, Changchun, China.
Division of Clinical and Translational Sciences, Department of Internal Medicine, University of Texas Health Science Center at Houston, Houston, Texas, USA.
Stat Med. 2021 Feb 28;40(5):1262-1271. doi: 10.1002/sim.8839. Epub 2020 Dec 3.
Panel count data occur often in event history studies and in these situations, one observes only incomplete information, the number of events rather than the occurrence times of each event, about the point processes of interest. Sometimes one may have to face a more complicated type of panel count data, mixed panel count data in which instead of the number of events, one only knows if there is an occurrence of an event. Furthermore, this may depend on the underlying point process of interest or in other words, the point process of interest and the observation type process may be related. To address this, a sieve maximum likelihood estimation approach is proposed with the use of Bernstein polynomials, and for the implementation, an EM algorithm is developed. To assess the finite sample performance of the proposed approach, a simulation study is conducted and suggests that it works well for practical situations. The method is then applied to a motivating example about cancer survivors.
面板计数数据在事件历史研究中经常出现，在这些情况下，人们只能观察到不完整的信息，即关于感兴趣的点过程的事件数量，而不是每个事件的发生时间。有时，人们可能不得不面对一种更复杂的面板计数数据类型，即混合面板计数数据，在这种数据中，人们只知道是否发生了事件，而不是事件的数量。此外，这可能取决于感兴趣的潜在点过程，或者换句话说，感兴趣的点过程和观测类型过程可能是相关的。为了解决这个问题，提出了一种使用伯恩斯坦多项式的筛极大似然估计方法，并为实现该方法开发了一种期望最大化（EM）算法。为了评估所提出方法的有限样本性能，进行了一项模拟研究，结果表明该方法在实际情况下效果良好。然后将该方法应用于一个关于癌症幸存者的激励性例子。
