Non parametric estimation of an illness death stochastic model with recovery state

An illness death model is a Multi-state model where subjects progress though three different states. An illness death model is a discrete space continuous time stochastic process, for a random process with a finite state space S = {1, 2 ... N}. Here, T = [0, τ], τ < ∞ is a time interval and the value of the process at time t the state occupied at that time. The states are either transient or absorbing. An absorbing state is a state from which further transitions cannot occur while a transient state allows transition to other states. This paper deals with the Non parametric estimation of an illness death model with a recovery state, in which the patients move among disease free  diseased, diseased  disease free, diseased  death and diseased free  death. A longitudinal failure time data is being employed to describe the Non parametric estimators, Nelson Aalen (1972), Aalen Johansen (1978), and Kaplan Meier (1958) to estimate cumulative intensities, transition probabilities, and survival probabilities respectively and to study their statistical properties. The evolution of multi state model, an illness death model with recovery state has achieved by the method of episode spiting.