Modeling 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 the initial state 0 to the absorbing state 2 may involve an intermediate state 1 (e.g., disease relapse). The impact of the transition into state 1 on the subsequent transition hazard to state 2 enables insight to be gained into the disease evolution. The standard approach of analysis is modeling the transition hazards from 0 to 2 and from 1 to 2, including time to illness as a time-varying covariate and measuring time from origin even after transition into state 1. The hazard from 1 to 2 can be also modeled separately using only patients in state 1, measuring time from illness and including time to illness as a fixed covariate. A recently proposed approach is a model where time after the transition into state 1 is measured in both scales and time to illness is included as a time-varying covariate. Another possibility is a model where time after transition into state 1 is measured only from illness and time to illness is included as a fixed covariate. Through theoretical reasoning and simulation protocols, we discuss the use of these models and we develop a practical strategy aiming to (a) validate the properties of the illness-death process, (b) estimate the impact of time to illness on the hazard from state 1 to 2, and (c) quantify the impact that the transition into state 1 has on the hazard of the absorbing state. The strategy is also applied to a literature dataset on diabetes.