Modelling survival functions and their critical points

Survival analysis has applications ranging across medicine, engineering and social sciences
where the main quantity of interest is time until an event. The methods in this project are applied to medical data where an 'event' will be defined as the death of a patient. There are a couple of models that are traditionally used by clinicians. The Kaplan Meier estimate can be used to determine whether a certain treatment has a significant effect on the survival time of a patient and the Cox proportional hazards model is used to identify individual factors that may contribute either positively or negatively to the prognosis of the patient.
This project uses a new method proposed by Bart et al. (2005) in which a survival function is determined by considering the underlying dynamics of the disease. This novel approach uses the opposing disease inhibiting and disease progressing factors. By estimating this disease progression function, the speed of disease progression and the period of the disease can be determined which allows the estimation of `critical points'. These critical points correspond to the best times that medical intervention should be applied to increase the length of survival of the patient. The aim of the project is to estimate these time points. The method is currently being applied to a small data set on acute pancreatitis (AP) , a serious inflammatory disease affecting around 37,000 people in the UK every year, with future plans to extend to a larger AP data set and other medical data sets that become available.