Mortality Modeling of Skin Cancer Patients with Actuarial Applications

In this article, the Markovian aging process is used to model mortality of patients with skin cancer. The time until death is assumed to have a phase-type distribution (which is defined in a Markov chain environment) with interpretable parameters. The underlying continuous-time Markov chain has one absorbing state (death) and nx +1 (x is the age when the patient is diagnosed with cancer) transient states. Each transient state represents a physiological age, and aging is a transition from one physiological age to the next until the process reaches its end. The transition can occur from any other state to the absorbing state. For patients with skin cancer in the United States, we estimate unknown parameters related to the aging process that can be useful for comparing the physiological aging processes of patients with cancer and healthy people. For different age intervals, we estimate physiological age parameters for both males and females. The index of conditional expected physiological age of the patients with skin cancer at given ages is calculated and compared with the total U.S. population. By using bootstrap techniques, confidence bands and confidence intervals are constructed for the estimated survival curves and aging process parameters, respectively. The fitting results have been used for pricing substandard annuities.