Bayesian nonparametric inference for panel count data with an informative observation process

In this paper, the panel count data analysis for recurrent events is considered. Such analysis is useful for studying tumor or infection recurrences in both clinical trial and observational studies. A bivariate Gaussian Cox process model is proposed to jointly model the observation process and the recurrent event process. Bayesian nonparametric inference is proposed for simultaneously estimating regression parameters, bivariate frailty effects, and baseline intensity functions. Inference is done through Markov chain Monte Carlo, with fully developed computational techniques. Predictive inference is also discussed under the Bayesian setting. The proposed method is shown to be efficient via simulation studies. A clinical trial dataset on skin cancer patients is analyzed to illustrate the proposed approach.