In longitudinal studies measurements are often collected on different types of responses for each individual. These may contain several longitudinally measured responses (such as the CD4 count) and the time at which an event occurs (e.g., HIV, death, or dropout from the study). These outcomes are often separately analyzed. Compared to separate modeling, joint modeling and simultaneous analysis allows for more coherent, robust analysis and may produce a better insight into the process under study. However, there has always been difficulty to the analyst that finding a proper multi-variable joint distribution for linking responses. In this article, we survey the zero-inflated property for longitudinal count and time to event data. We apply a member of the family of power series distributions (PSDs) and the Cox proportional hazard regression model (Cox PH) with Weibull baseline hazard rate, respectively, for these correlated responses. Also we consider both right and left censoring mechanisms in time to event process. This modeling strategy leads to expand the class of joint models and presents some new joint models which, as far as we know, have not yet been investigated by other researchers. The parameters in the joint model are estimated by using likelihood techniques.

在纵向研究中，通常会针对每个人的不同类型的反应收集测量值。这些可能包含几个纵向测量的反应（例如 CD4 计数）和事件发生的时间（例如，HIV、死亡或退出研究）。这些结果通常单独分析。与单独建模相比，联合建模和同时分析允许进行更连贯、更稳健的分析，并可以更好地了解所研究的过程。然而，分析人员总是很难找到一个合适的多变量联合分布来关联响应。在本文中，我们调查了纵向计数和事件发生时间数据的零膨胀属性。对于这些相关响应，我们分别应用幂级数分布 (PSD) 和 Cox 比例风险回归模型 (Cox PH) 和 Weibull 基线风险率的成员。我们还考虑了事件过程中的左右审查机制。这种建模策略扩大了联合模型的类别，并提出了一些新的联合模型，据我们所知，其他研究人员尚未研究过这些模型。联合模型中的参数是通过使用似然技术来估计的。尚未被其他研究人员调查。联合模型中的参数是通过使用似然技术来估计的。尚未被其他研究人员调查。联合模型中的参数是通过使用似然技术来估计的。