Multi-stage Markov analysis of progressive disease applied to melanoma

A fundamental research goal in clinical studies of progressive, multi-stage disease is to understand its natural history and its relationship with prognostic factors. Our current understanding of this topic is based on the use of two-stage methods for event-time analysis which neglect intermediate transition information. In contrast, a multi-stage model utilizes all available data and provides more accurate insight into disease progression. We specify a forward-flowing multi-stage Markov model based on the discrete clinical stages of disease. By assuming the process to be Markovian, we avoid unnecessary complications to our numerical estimation procedure. Due to noncontinuous patient monitoring and the chronic nature of progressive disease, heavy right- and interval-censoring exists in the transition data. We develop a modified ECM algorithm to numerically carry out the otherwise complicated parameter estimation for this process. We also identify significant prognostic factors relevant to each transition, along with the relative importance of each prognostic factor. The numerical estimation is stable, and the parameter estimates are maximum likelihood estimates (Meng, 1990). In general our forward-flowing multi-stage models provide a flexible framework for the study of the effects of prognostic factors on progression among several stages. We apply our Markov model to a dataset of malignant melanoma patients, and present an inferential discussion. Results from our multi-stage Markov model provide an improved understanding of melanoma progression.