Nonparametric Inference for a Class of Semi-Markov Processes with Censored Observations

A class of semi-Markov models, those which have proportional hazards and which are forward-going (if state j can be reached from i, then i cannot be reached from j), are shown to fit into the multiplicative intensity model of counting processes after suitable random time changes. Standard large-sample results for counting processes following this multiplicative model can therefore be used to make inferences on the above class of semi-Markov models, including the case where observations may be censored. Large-sample results for a four-state model used in clinical trials are presented.