Regression analysis of mixed panel count data with informative indicator processes

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.(2) 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.(3) 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.