Generalizations of the statistical flowgraph model framework

Statistical flowgraphs model multistate semi-Markov processes and provide a way to perform inference for these processes. This methodology provides powerful results that significantly impact the study of multistate semi-Markov processes. This dissertation extends previous work in several ways. First, by demonstrating how any "smooth" transition distribution can be incorporated into a statistical flowgraph model (SFGM), we provide a method to use popular distributions, such as the lognormal, that have not been used in the past. Next, we propose an alternate way to consider Bayesian SFGMs by showing how computation can be accomplished when the traditional methods of SFGMs fail to be computationally feasible. We demonstrate this method with a Bayesian non-parametric example. We extend flowgraph models to handle time-varying covariates using an accelerated failure time model. We also show how SFGMs can be used to make inference in multistate semi-Markov models to calculate exact likelihood functions when faced with incomplete data. Finally, we develop a goodness-of-fit criterion that is applicable to any continuous model and can be applied to SFGMs. This goodness-of-fit test criterion is general enough to be useful when dealing with censored and incomplete multistate data.