USING A HIDDEN MULTI-STATE MARKOV MODEL TO CHARACTERIZE UNOBSERVABLE DISEASE NATURAL HISTORY: THE CASE OF COLORECTAL CANCER RECURRENCE

Purpose: The optimal frequency and intensity of post-treatment radiographic and laboratory surveillance in patients with early stage colorectal cancer is unknown. To inform clinical guidelines, we developed a non-homogenous (non-constant hazard) multi-state Markov model of the natural history of colorectal cancer (CRC) recurrence for use in a simulation model of post-treatment surveillance.

 

Methods: As a data source, we used a database from a completed large-scale, multicenter, prospective clinical trial containing periodic observations of recurrence status among curatively-treated colorectal cancer survivors.  A non-homogenous continuous-time multi-state Markov model was developed with states of “no known recurrence”, “detectable and resectable recurrence”, “detectable and non-resectable recurrence”, “death from CRC”, and “death from other causes”.  Movement through states was assumed to be unidirectional (no possibility of transitioning to an earlier state).  Parametric hazard functions were used to model transitions with non-zero probability.  Parameters for these hazard functions were estimated using maximum likelihood methods based on the interval-censored trial data.  As an extension, we developed a hidden Markov model to account for potential misclassification of states in the dataset due to false positive and false negative surveillance test results.

Results: Piecewise Weibull distributions provided the best fit for transition from no known recurrence to detectable resectable or non-resectable recurrence.  A decreasing Weibull distribution provided the best fit for the transition from resectable to non-resectable recurrence.  All other non-zero transitions were best modeled using constant hazards.  Plots of observed versus model-predicted survival were used to assess overall predictive ability of the model.  Furthermore, we constructed residual plots to assess the validity of distributions chosen to model intermediate transitions. 

Conclusions: If validated, this model may be used to guide development of clinical surveillance guidelines which may ultimately be tailored to individual patient clinical characteristics.  The modeling approach outlined here may prove useful in numerous scenarios where state transitions in disease natural history are unobservable and the potential for state misclassification exists.