Penalized estimation of general frailty Poisson models for recurrent count events

We study spline-based efficient estimation of frailty models for panel count data using a penalization technique. An easy-to-implement and computationally efficient two-stage iterative expectation-maximization algorithm is proposed for the analysis. A general quasi-likelihood estimation that does not specify the stochastic model of the underlying counting process is developed to provide flexibility for model fitting. A powerful score test is discussed to detect the presence of overdispersion in count data. The proposed methods are assessed via an extensive simulation and further illustrated by analyzing data from a non-melanoma skin cancer chemoprevention study.