Assessing and relaxing the Markov assumption in the illness-death model

Multi-state survival analysis considers several potential events of interest along a disease pathway. Such analyses are crucial to model complex patient trajectories and are increasingly being used in epidemiological and health economic settings. Multi-state models often make the Markov assumption, whereby an individual's future trajectory is dependent only upon their present state, not their past. In reality, there may be transitional dependence upon either previous events and/or more than one timescale, for example time since entry to the current or previous state(s). The aim of this study was to develop an illness-death Weibull model allowing for multiple timescales to impact the future risk of death. Following this, we evaluated the performance of the multiple timescale model against a Markov illness-death model in a set of plausible simulation scenarios when the Markov assumption was violated. Guided by a study in breast cancer, data were simulated from Weibull baseline distributions, with hazard functions dependent on single and multiple timescales. Markov and non-Markov models were fitted to account for/ignore the underlying data structure. Ignoring the presence of multiple timescales led to bias in underlying transition rates between states and associated covariate effects, while transition probabilities and lengths of stay were fairly robustly estimated. Further work may be needed to evaluate different estimands or more complex multi-state models. Software implementations in Stata are also described for simulating and estimating multiple timescale multi-state models.