Discrete-state, continuous-time stochastic processes, with applications to HPV

Genital infection by human papillomavirus (HPV) is a common sexually transmitted disease, with an important public health consequence of potential cervical neoplasia development that can lead to cancer. Development of an HPV vaccine that is aimed at reducing cervical cancer is scientifically challenged by the multiple types of HPV and the need to target the persistent infections that would progress to cervical cancer, as opposed to the transient infections that are controlled by the host immune response. In addition to the lack of diagnostic tests that distinguish a persistent from a transient infection, research is challenged by the observations that are subject to misclassification errors in HPV detection and diagnosis of clinical symptoms and infrequent collection of the data—leading to panel data—where the exact times of state transitions are not known. The nonprogressive (bidirectional) state structure of the underlying process further complicates matters.; In Chapter 1, we address the challenges in modeling the natural history of HPV infections and cervical neoplasia as a semi-Markov process, where a longer infection would be more likely to progress to clinical symptoms than resolve to an infection-free state. We develop likelihood-based methods for panel data that are subject to misclassification, then apply these methods to fit the placebo data from a recently completed HPV clinical trial to make inference on the rate at which an infection clears or develops into clinical symptoms. In Chapter 2, we examine several operational definitions of HPV infection from the literature that are meant to preferentially detect persistent infections. We postulate an underlying model for the natural history of HPV as a multi-state process, then assess the performances of these candidates as an endpoint in an HPV vaccine trial. Our findings show that none of the candidates performs satisfactorily, thus raising concerns that clinical trials designed for only these infection endpoints will not be reliable. In Chapter 3, we synthesize what we have learned from previous chapters to evaluate the role of HPV vaccine in cervical cancer prevention and to outline some issues in the design and analysis of HPV vaccine trials.