Panel count data arise when recurrent events are observed periodically in a study. The response variable of interest is the number of recurrent events within different time windows instead of the exact onset times of the events. The gamma frailty Poisson process model has been proposed to accommodate the within-subject correlation and overdispersion in panel count data. Although the existing methods based on the gamma frailty Poisson process model have shown some robustness against frailty distribution misspecifications, they are also found to produce biased estimates in some other cases when the gamma frailty assumption is violated. In this paper, we generalize the gamma frailty Poisson process model to allow an unknown frailty distribution for analyzing panel count data. Specifically the frailty distribution is modeled nonparametrically by assigning a Dirichlet Process Gamma Mixture prior. An efficient Gibbs sampler is developed to facilitate the Bayesian computation. Extensive simulation results suggest that the proposed Bayesian approach has an excellent performance in estimating the regression parameters and the baseline mean function and outperforms the corresponding Bayesian method based on the gamma frailty Poisson model when the gamma frailty distribution is misspecified. The proposed method is applied to a skin cancer dataset for an illustration.

The semiparametric proportional odds (PO) model is a popular alternative to Cox's proportional hazards model for analyzing survival data. Although many approaches have been proposed for this topic in the literature, most of the existing approaches have been found computationally expensive and difficult to implement. In this article, a novel and easy-to-implement approach based on an expectation-maximization (EM) algorithm is proposed for analyzing right-censored data. The EM algorithm involves only solving a low-dimensional estimating equation for the regression parameters and then updating the spline coefficients in simple closed form at each iteration. Our method is robust to initial values, converges fast, and provides the variance estimates in closed form. Simulation studies suggest that the proposed method has excellent performance in estimating both regression parameters and the baseline survival function, even when the right censoring rate is very high. The method is applied to a large dataset about breast cancer survival extracted from the Surveillance, Epidemiology, and End Results (SEER) database maintained by the U.S. National Cancer Institute. This method is now available in R package regPOr for public use.

Both panel count data and interval-censored data arise commonly in real-life studies when subjects are examined at periodic follow-ups. Interval-censored data are studied when the exact times of the events are of interest and these exact times are not directly observed but are only known to fall within some intervals formed by the observation times. Panel count data are under investigation when the exact times of the recurrent events are not of interest but the counts of the recurrent events occurring within the time intervals are available and of interest. A novel unified Bayesian approach is developed for analyzing panel count data under the Gamma frailty Poisson process model and interval-censored data under Cox’s proportional hazards model and the proportional odds model. The baseline functions in these models share the same property of being nondecreasing positive functions and are modeled nonparametrically by assigning a Gamma process prior. Efficient Gibbs samplers are developed for the posterior computation under these three models for the two types of data. The proposed methods are evaluated in a simulation study and illustrated by three real-life data applications.

Arbitrarily censored data are referred to as the survival data that contain a mixture of exactly observed, left‐censored, interval‐censored, and right‐censored observations. Existing research work on regression analysis on arbitrarily censored data is relatively sparse and mainly focused on the proportional hazards model and the accelerated failure time model. This article studies the proportional odds (PO) model and proposes a novel estimation approach through an expectation‐maximization (EM) algorithm for analyzing such data. The proposed EM algorithm has many appealing properties such as being robust to initial values, easy to implement, converging fast, and providing the variance estimate of the regression parameter estimate in closed form. An informal diagnosis plot is developed for checking the PO model assumption. Our method has shown excellent performance in estimating the regression parameters as well as the baseline survival function in a simulation study. A real‐life dataset about metastatic colorectal cancer is analyzed for illustration. An R package regPO has been created for practitioners to implement our method.