Gamma Process-Based Models for Disease Progression

Abstract

Classic chronic diseases progression models are built by gauging the movement from the disease free state, to the preclinical (asymptomatic) one, in which the disease is there but has not manifested itself through clinical symptoms, after spending an amount of time the case then progresses to the symptomatic state. The progression is modelled by assuming that the time spent in the disease free and the asymptomatic states are random variables following specified distributions. Estimating the parameters of these random variables leads to better planning of screening programs as well as allowing the correction of the lead time bias (apparent increase in survival observed purely due to early detection). However, as classical approaches have shown to be sensitive to the chosen distributions and the underlying assumptions, we propose a new approach in which we model disease progression as a gamma degradation process with random starting point (onset). We derive the probabilities of cases getting detected by screens and minimize the distance between observed and calculated distributions to get estimates of the parameters of the gamma process, screening sensitivity, sojourn time and lead time. We investigate the properties of the proposed model by simulations.