Likelihood for interval-censored observations from multi-state models

Abstract

We consider the mixed dicrete-continuous pattern of observation in a multi-state model; this is a classical pattern because very often clinical status is assessed at discrete visit times while time of death is observed exactly. The likelihood can easily be written heuristically for such models. However a formal proof is not easy in such observational patterns. We give a rigorous derivation of the likelihood for the illness-death model based on applying Jacod’s formula to an observed bivariate counting process.