A proposal for estimating intensity functions in a three-state model in the presence of arbitrary censoring

Multi-state are useful tools to model the dynamics of recurring processes over time or some changing phenomenon over time. This paper presents a methodology to estimate time-dependent intensity functions in the presence of interval censoring and right-hand censoring when considering a three-state model like the disease-death one. The likelihood function is deduced mathematically, which incorporates information that has been collected longitudinally, as well as the different modes of censoring. This likelihood should be optimized numerically with the help of a Gauss quadrature since in that expression there is an integral which is related to censored units. A piecewise function-based method is explored through a simulation study to obtain an estimate of the intensities.