  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.
