Adding Events to a Markov Model Using DICE Simulation

Background . Health care decisions are often made under uncertainty and modeling is used to inform the choices and possible consequences. State-transition (“Markov†) models are commonly used but they represent the problem solely in terms of states; events are not explicitly considered. Methods. Discretely integrated condition event (DICE) simulation provides for both aspects that persist over time (“conditions†) and for those happening at a point in time (“events†). A Markov model can be specified in DICE by representing states as conditions with a recurrent transition event processing transition probabilities, and other events added explicitly. Results. The DICE specification of a Markov model is compact because transitions are enumerated only once; it is very transparent, as these specifications are tabulated rather than programmed in code; and flexibility is enhanced by the ease with which alternative structures are specified. Events can be added to represent clinical occurrences, treatment features, health care activities, and any other relevant aspect of this type. They may coincide with the transition event or occur at their own times. Varying cycle times and structural sensitivity analyses are easy to implement. Limitations. Execution of a DICE simulation using a macro in spreadsheet software can be slow, especially for complex models requiring stochastic analyses replicated thousands of times. Modelers wishing to use other software can still use the tabular specification ideas to expand their Markov models, but the descriptions provided here may not be entirely applicable. Another limitation is the inability of these simulations to handle constrained resources or interactions among patients. Conclusions. With DICE simulation, it is possible to expand the Markov formulation to include explicitly many events occurring at various times.