Proportional rates models for multivariate panel count data

Multivariate panel count data arise when there are multiple types of recurrent events, and the observation for each study subject consists of the number of recurrent events of each type between two successive examinations. We formulate the effects of potentially time-dependent covariates on multiple types of recurrent events through proportional rates models, while leaving the dependence structures of the related recurrent events completely unspecified. We employ nonparametric maximum pseudo-likelihood estimation under the working assumptions that all types of events are independent and each type of event is a nonhomogeneous Poisson process, and we develop a simple and stable EM-type algorithm. We show that the resulting estimators of the regression parameters are consistent and asymptotically normal, with a covariance matrix that can be estimated consistently by a sandwich estimator. In addition, we develop a class of graphical and numerical methods for checking the adequacy of the fitted model. Finally, we evaluate the performance of the proposed methods through simulation studies and analysis of a skin cancer clinical trial.