Modelling the hazard of transition into the absorbing state in the illness-death model

The illness-death model is the simplest multistate model where the transition from an initial state 0 to an absorbing state 2 may involve also an intermediate state 1 (e.g. disease relapse). The impact of the transition into state 1 on the subsequent hazard of the absorbing state enables to increase the knowledge about the evolution of the disease. The approaches commonly applied to analyse illness-death data depend on the choice of the time scale(s) used to measure follow-up time after the transition to illness. In multistate literature, the original (or “clock forward”) time scale is commonly used to measure follow-up time for subjects in state 0 and can be considered also for those in state 1, since time from the initial state can be measured even after the transition to illness. The time to such transition can be included as covariate in models estimated on the entire set of subjects (full-sample models). The follow-up time after the transition to state 1 can be measured also in the “clock reset” scale, which uses the intermediate state as a new origin. In this case, models are commonly estimated only on the subjects who develop illness (sub-sample models) and the time of occurrence of the intermediate event can be included as a covariate. An approach proposed in literature consists in a model where the follow-up time after the transition into the intermediate state is measured in both scales and time to illness is included as a time-varying covariate. A further possibility is to measure the follow-up time in the clock forward scale before the transition into state 1 and in the clock reset scale after that transition. Through theoretical reasoning and simulation protocols we developed practical strategies a statistician can follow to: (a) validate the Markov, semi-Markov and extended semi-Markov properties of the illness-death process, from which the choice of the scale to measure time after illness, for the transition hazard into the absorbing state, depends; (b) estimate the impact of time to the intermediate event on the hazard from the illness state to the absorbing state, proposing also a novel modelling approach that ensures the interpretability of the model coefficient of the time to illness in case of non-Markov data; (c) quantify the impact that the transition into the intermediate state has on the hazard of the absorbing state.