Semiparametric and nonparametric methods for the analysis of panel count data

Panel count data are one type of event-history data concerning recurrent events. Ideally for an event-history study, subjects should be monitored continuously, so for the events that may happen recurrently over time, the exact time of each event occurrence is recordable. Data obtained in such cases are commonly referred to as recurrent event data (Cook and Lawless, 2007). In reality, however, subjects may only be observed at their clinical visits or discrete times. As a result, instead of observing the exact event times, one only knows the numbers of events that happen between the observation times. Such interval-censored recurrent event data are usually referred to as panel count data (Kalbfleisch and Lawless, 1985; Sun and Kalbfleisch, 1995; Thall and Lachin, 1988). The primary interest with panel count data is about the underlying recurrent event process. Meanwhile for the analysis, one needs to consider the times when the observations occur, which can be regarded as realizations of an observation process with follow-up times. This dissertation consists of four parts. In the first part, we will consider regression analysis of panel count data with dependent observation processes while the follow-up times may be subject to a terminal event like death. A semiparametric transformation model is presented for the mean function of the underlying recurrent event process among survivals. To estimate the regression parameters, an estimating equation approach is proposed and the inverse survival probability weighting technique is used. In addition, the asymptotic distribution of the proposed estimate is derived and a model checking procedure is presented. Simulation studies are conducted to evaluate finite sample properties of the proposed approach, and the approach is applied to a bladder cancer study. The second part will focus on regression analysis of multivariate panel count data in the presence of a terminal event. Both the observation process and the terminal event may be correlated with recurrent event process