Methods of nonparametric inference are proposed for a process with two transient and three absorbing states. It is assumed that the times of transitions between the transient states are unobservable. One area of application is in epidemiology where the transient states. correspond to healthy and ill, while the absorbing states correspond to types of death. It is the time of onset of illness which is assumed unobservable. Here we use the martingale theory to make inference about the cumulative hazard rate of the onset of the disease. The assumption of equality of hazard rates from the other causes with or without the disease is not needed. Instead, an assumption of proportionality between the two rates is made. A simulation study is given to compare the suggested procedure and the Nelson-Aalen estimator which requires complete observation of process.