ABSTRACT
This chapter demonstrates how intensity functions characterizing the instantaneous risks of transitions can be used to compute the probability of a sample path for a multistate process and outlines simulation of multistate processes. It highlights the close relation between the form of the resulting likelihoods and those for survival times subject to left truncation and right censoring. The chapter discusses marginal process features of common interest such as the entry time distribution for states, and the probability a particular state is occupied at a specified time. It describes some important types of multistate models and considers how process features such as transition probabilities and sojourn time distributions can be obtained. The chapter presents the more general problem of constructing the likelihood in the presence of possible time-dependent covariates and random censoring. Semi-Markov models play a useful role in settings where it is natural to focus on sojourn times in particular states.
