Bayesian Analysis of Binary Diagnostic Tests and Panel Count Data

This dissertation mainly explores several challenging topics that arise in diagnostic tests and panel count data in the Bayesian framework. Binary diagnostic tests, particularly multiple diagnostic tests with repeated measures and diagnostic procedures with a large number of raters, are studied. For panel count data, most traditional methods only handle panel count data for a single type of recurrent event. In this dissertation, we primarily focus on the case with multiple types of recurrent events. In Chapter 1, an introduction to the binary diagnostic tests data and panel count data is presented and related literature works are briefly reviewed. To make the dissertation more coherent for the later chapters, some preliminary theories and algorithms, for instance the Metropolis Hastings algorithm, are presented. Finally, an outline of the dissertation organization is put forward. In Chapter 2, 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 non-diseased populations, as well as across time points is explicitly included. An efficient Markov chain Monte Carlo (MCMC) scheme allows for straightforward posterior inference. The proposed model is broadly illustrated via simulations and scaphoid fracture data from a prospective study (Duckworth et al., 2012) is analyzed. In addition, omnibus tests constructed from individual tests in parallel and serial are considered. In Chapter 3, a Bayesian hierarchical conditional independence latent class model for estimating sensitivities and specificities for a large group of tests or raters is v 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.. In Chapter 4, a Bayesian semiparameteric approach is proposed to analyze panel count data for multiple types of recurrent events. For each type of 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 (Ramsay et al., 1988). Correlation between multiple 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 processes and the observation process. Under the Poisson process assumption, an efficient Gibbs sampler based on a novel data augmentation is developed for the MCMC 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. In Chapter 5, a brief summary of the studies we have completed in the previous chapters is delivered and at the same time we put forward some ideas for future work in each topic covered