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.
"Nonparametric Inference for a Class of Semi-Markov Processes with Censored Observations." Ann. Statist. 12 (1) 142 - 160, March, 1984. https://doi.org/10.1214/aos/1176346398