Analysis of panel count data with dependent observation times

In this article, a semiparametric approach is proposed for the regression analysis of panel count data. Panel count data commonly arise in clinical trials and demographical studies where the response variable is the number of multiple recurrences of the event of interest and observation times are not fixed, varying from subject to subject. It is assumed that two processes exist in this data: the first is for a recurrent event and the second is for observation time. Many studies have been done to estimate mean function and regression parameters under the independency between recurrent event process and observation time process. In this article, the same statistical inference is studied, but the situation where these two processes may be related is also considered. The mixed Poisson process is applied for the recurrent event processes, and a frailty intensity function for the observation time is also used, respectively. Simulation studies are conducted to study the performance of the suggested methods. The bladder tumor data are applied to compare previous studie' results.