Celine Cunen: Non-Markovian parametric multi-state models for interval censored data

For many real-life phenomena one may assume that the units of observation, typically patients, transition through a set of discrete states on their way towards an absorbing state. The states often constitute various stages of a disease, from perfect health through various stages of dementia for example. Multi-state models are a class of statistical models which allow us to study the time spent in different states, the probability of transitioning between states, and the relationship between these quantities and covariates of interest. In many applications the transition times between states are not observed exactly; instead, the current state of the patients is queried at arbitrary times. The transition times are therefore interval censored, and this makes inference and modelling challenging. Most current approaches are based on the Markov assumption, for example the simplest parametric model available - the time-homogeneous Markov model. Here, we propose a new, general framework for parametric inference with interval censored multi-state data. Our models allow non-Markovian behaviour. I will present the framework and an algorithm for the automatic construction of the likelihood function, along with real-data examples. This talk is based on joint work with Marthe Aastveit and Nils Lid Hjort.