A Bayesian approach for semiparametric regression analysis of panel count data

Panel count data commonly arise in epidemiological, social science, and medical studies, in which subjects have repeated measurements on the recurrent events of interest at different observation times. Since the subjects are not under continuous monitoring, the exact times of those recurrent events are not observed but the counts of such events within the adjacent observation times are known. A Bayesian semiparametric approach is proposed for analyzing panel count data under the proportional mean model. Specifically, a nonhomogeneous Poisson process is assumed to model the panel count response over time, and the baseline mean function is approximated by monotone I-splines of Ramsay (Stat Sci 3:425-461, 1988). Our approach allows to estimate the regression parameters and the baseline mean function jointly. The proposed Gibbs sampler is computationally efficient and easy to implement because all of the full conditional distributions either have closed form or are log-concave. Extensive simulations are conducted to evaluate the proposed method and to compare with two other bench methods. The proposed approach is also illustrated by an application to a famous bladder tumor data set (Byar, in: Pavone-Macaluso M, Smith PH, Edsmyn F (eds) Bladder tumors and other topics in urological oncology. Plenum, New York, 1980).