Applying the theory of Markov chains and point processes in the study of HPV viruses

Abstract

High-risk HPV (human papilloma virus) viruses uses such as HPV16 may lead to precancerous cell changes- cervical intraepithelial neoplasia (CIN) - which may ultimately cause cervical cancer. There are three pre-cancerous states: CIN1, CIN2 and CIN3; patients infected with HPV16 may progress randomly from one state to the other. Thus, the aim of this dissertation is to analyse the rate (sometimes called intensity) at which patients move from one state to another. The time spent in each state before moving to any other state will also be studied and in addition, a number of variables were found to influence not only the time spent in each state but also the intensity. The medical history of 50 females who were infected with an HPV16 was studied in detail and their CIN status was recorded over a three-year span, from October 2010 till December 2013. The transitions between one CIN status to another may be viewed as a marked point process since these transitions are being counted and marked/labelled at different time points. Markov chains are then used to model the transitions from one particular state to another. During the course of this dissertation, three estimation techniques are discussed: the non-parametric, semi-parametric and the parametric approach. The first comprises the Kaplan-Meier, Nelson-Aalen and Aalen-Johansen techniques. In the semi-parametric section, the Cox proportional hazard model is discussed together with some of its properties. The parametric approach includes the Weibull proportional hazard model and the Weibull accelerated failure time model. Covariates and fixed factors related to the patients are incorporated in the semi-parametric and parametric models to analyse their effects on the transitions from one CIN status to another. These techniques are used to estimate the intensity rate from one particular state to another, the cumulative intensity matrices and the survival time in a particular state before moving to another state. Such a study can help the general public understand the risks which are associated to the pre-cancerous cell changes. In addition, medical practitioners can use such studies as a means of further understanding the way this medical condition progresses and/or regresses.