Phase-type distribution in ageing process of the elder patients with skin cancer

In this article, we apply phase-type distributions (PH) to modelling physiological ageing process for the patients with skin cancer. Our model focus on physiological age rather than chronological age. The time spent in each physiological age has an exponential distribution in a Markov chain environment. The underlying continuous-time Markov chain, has one absorbing state (death) and nx (x is the age when the patient is diagnosed with cancer) transient states. Each transient-state represents a physiological age, and ageing is transition from one physiological age to the next physiological age and process reaches to its end as transition occurs from any other state to the absorbing state. For 70-90 age interval of the patients with skin cancer in United States, we estimate unknown parameters that can be useful for calculating survival probability via PH distributions. This ftting results are very satisfactory. For every group of ages we estimate physiological age parameters.