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.

Panel count data often occur in a long-term recurrent event study, where the exact occurrence time of the recurrent events is unknown, but only the occurrence count between any two adjacent observation time points is recorded. Most traditional methods only handle panel count data for a single type of event. In this paper, we propose a Bayesian semiparameteric approach to analyze panel count data for multiple types of events. For each type of recurrent event, the proportional mean model is adopted to model the mean count of the event, where its baseline mean function is approximated by monotone I-splines. The correlation between multiple types of events is modeled by common frailty terms and scale parameters. Unlike many frequentist estimating equation methods, our approach is based on the observed likelihood and makes no assumption on the relationship between the recurrent process and the observation process. Under the Poisson counting process assumption, we develop an efficient Gibbs sampler based on novel data augmentation for the Markov chain Monte Carlo sampling. Simulation studies show good estimation performance of the baseline mean functions and the regression coefficients; meanwhile, the importance of including the scale parameter to flexibly accommodate the correlation between events is also demonstrated. Finally, a skin cancer data example is fully analyzed to illustrate the proposed methods.

The diagnostic accuracy of a test or rater has a crucial impact on clinical decision making. The assessment of diagnostic accuracy for multiple tests or raters also merits much attention. A Bayesian hierarchical conditional independence latent class model for estimating sensitivities and specificities for a large group of tests or raters is proposed, which is applicable to both with-gold-standard and without-gold-standard situations. Through the hierarchical structure, not only are the sensitivities and specificities of individual tests estimated, but also the diagnostic performance of the whole group of tests. For a small group of tests or raters, the proposed model is further extended by introducing pairwise covariances between tests to improve the fitting and to allow for more modeling flexibility. Correlation residual analysis is applied to detect any significant covariance between multiple tests. Just Another Gibbs Sampler (JAGS) implementation is efficiently adopted for both models. Three real data sets from literature are analyzed to explicitly illustrate the proposed methods.

A model for multiple diagnostic tests, applied repeatedly over time on each subject, is proposed; gold standard data are not required. The model is identifiable with as few as three tests, and correlation among tests at each time point in the diseased and nondiseased populations, as well as across time points, is explicitly included. An efficient Markov chain Monte Carlo scheme allows for straightforward posterior inference; sample R code is available in the Supporting Web Materials for this paper. The proposed model is broadly illustrated via simulations and an analysis of scaphoid fracture data from a prospective study. In addition, omnibus tests constructed from individual tests in parallel and serial are considered.