Abstract
Multistate models are increasingly being used to model complex disease profiles. By modelling transitions between disease states, accounting for competing events at each transition, we can gain a much richer understanding of patient trajectories and how risk factors impact over the entire disease pathway. In this article, we concentrate on parametric multistate models, both Markov and semi-Markov, and develop a flexible framework where each transition can be specified by a variety of parametric models including exponential, Weibull, Gompertz, Royston-Parmar proportional hazards models or log-logistic, log-normal, generalised gamma accelerated failure time models, possibly sharing parameters across transitions. We also extend the framework to allow time-dependent effects. We then use an efficient and generalisable simulation method to calculate transition probabilities from any fitted multistate model, and show how it facilitates the simple calculation of clinically useful measures, such as expected length of stay in each state, and differences and ratios of proportion within each state as a function of time, for specific covariate patterns. We illustrate our methods using a dataset of patients with primary breast cancer. User-friendly Stata software is provided.
Highlights
Parametric survival models have a number of advantages, and we believe should be used more widely
By direct modelling of the baseline hazard function, we can gain more understanding of how complex disease processes evolve over time
Parametric survival models are of particular importance in the realm of health economic modelling [5]
Summary
Multi-state models allow rich insights into complex disease pathways, where a patient may experience many nonfatal/intermediate events, and we wish to investigate covariate effects for each specific transition between two states, not just for example, on the first event, or a terminal event [1]. Piecewise exponential multi-state models have been implemented in R by Jackson (2011) [9], with a focus on panel data This allows the convenience of the exponential distribution and can capture complex shapes; assuming a discontinuous baseline hazard function is often not biologically plausible, which has motivated other approaches [10]. We adopt the simulation approach to calculate transition probabilities and other quantities of interest [16, 17, 18, 7], using a general survival simulation algorithm which can be readily applied to any combination of transition specific distributions to simulate from the multi-state model [19].
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