Multistate models for the natural history of cancer progression

Multistate models can be effectively used to characterise the natural history of cancer. Inference from such models has previously been useful for setting screening policies. We introduce the basic elements of multistate models and the challenges of applying these models to cancer data. Through simulation studies, we examine (1) the impact of assuming time-homogeneous Markov transition intensities when the intensities depend on the time since entry to the current state (i.e., the process is time-inhomogenous semi-Markov) and (2) the effect on precancer risk estimation when observation times depend on an unmodelled intermediate disease state. In the settings we examined, we found that misspecifying a time-inhomogenous semi-Markov process as a time-homogeneous Markov process resulted in biased estimates of the mean sojourn times. When screen-detection of the intermediate disease leads to more frequent future screening assessments, there was minimal bias induced compared to when screen-detection of the intermediate disease leads to less frequent screening. Multistate models are useful for estimating parameters governing the process dynamics in cancer such as transition rates, sojourn time distributions, and absolute and relative risks. As with most statistical models, to avoid incorrect inference, care should be given to use the appropriate specifications and assumptions.