Maximum likelihood estimation for semiparametric regression models with panel count data

Panel count data, in which the observation for each study subject consists of the number of recurrent events between successive examinations, are commonly encountered in industrial reliability testing, medical research and other scientific investigations. We formulate the effects of potentially time-dependent covariates on one or more types of recurrent events through nonhomogeneous Poisson processes with random effects. We employ nonparametric maximum likelihood estimation under arbitrary examination schemes, and develop a simple and stable EM algorithm. We show that the resulting estimators of the regression parameters are consistent and asymptotically normal, with a covariance matrix that achieves the semiparametric efficiency bound and can be estimated using profile likelihood. We evaluate the performance of the proposed methods through simulation studies and analysis of data from a skin cancer clinical trial.