A Systematic Model Specification Procedure for an Illness-Death Model without Recovery

Multi-state models are a flexible tool for analyzing complex time-to-event problems with multiple endpoints. Compared to the Cox regression model with a single endpoint or a summarizing composite endpoint, they can provide a more detailed insight into the disease process. Furthermore, prognosis can be improved by including information from intermediate events occurring during the course of the disease. Different model variants, options and additional assumptions provide many possibilities, but at the same time complicate the implementation of multi-state techniques. So far, no guiding literature is available to specify a multi-state model systematically. The objective of this work was to set up a general specification procedure for an illness-death model that optimizes the model fit and predictive accuracy by stepwise reduction of the model. As an application example, we reanalyzed data from an observational study of 434 ovarian cancer patients with progression as intermediate and death as absorbing state. The technique is described in general terms and can be applied to other illness-death models without recovery. The clock-reset approach was used, implicating that the time was reset to zero after progression. The non-homogeneous semi-Markov characteristic stated that the present time as well as the time between surgery and progression influenced survival after progression. Covariate effects on transitions were estimated and proportionality of transition baseline hazards was tested. The finally developed model optimized the accuracy of predictions for two simulated patients. This stepwise procedure yields parsimonious but targeted multi-state models with well interpretable coefficients and optimized predictive ability, even for smaller data sets.