Discrete Model

A model in which time advances in fixed, distinct steps, such as one-year cycles, rather than flowing continuously.

Source: Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006. doi:10.1093/oso/9780198526629.001.0001.

Advancing time in fixed steps, such as monthly or yearly cycles, suits health processes that are naturally reviewed at intervals and matches the way much clinical data are recorded. It also keeps the calculations tractable, since the model needs to update states only once per cycle rather than continuously. The step must be short enough that little of importance happens within a single cycle unnoticed, which is why the choice of cycle length is a modelling decision in its own right. Briggs and colleagues (2006) explain this design.

Source: Briggs et al. 2006

A discrete model represents time as a sequence of fixed steps, or cycles, updating the state at each. During a cycle, transitions between states occur according to per-cycle probabilities, and costs and effects are accrued, then the state is updated for the next cycle. Events within a cycle are treated as happening at defined points, such as the start, end, or middle. The choice of cycle length affects the model, since a shorter cycle represents timing more finely but requires more computation.

Source: Briggs, Claxton & Sculpher 2006

A discrete model advances time in fixed steps and updates the state at each, whereas a continuous model treats time as flowing smoothly, with change occurring at every instant, usually through differential equations. Discrete models are simpler to build and implement and suit processes represented adequately by cycles, while continuous models capture the timing of events more finely but are harder to formulate and solve. The choice depends on whether the fine timing of events matters for the results.

Source: Briggs, Claxton & Sculpher 2006

Cycle length determines how finely a discrete model represents the timing of events: a shorter cycle captures rapid changes and reduces the error from treating events as occurring only at cycle points, but requires more computation, while a longer cycle is simpler but may misrepresent processes that change quickly within it. The cycle should be short enough that events and transitions are well approximated. A correction, such as the half-cycle correction, is often applied to reduce the error from discrete timing.

Source: Briggs, Claxton & Sculpher 2006

A discrete model is simple to build, implement, and understand, since it advances in clear steps and updates the state at each, making its logic transparent and its computation straightforward. It suits processes that can be represented adequately by cycles, and it avoids the mathematical demands of continuous models. This simplicity, together with the wide use of Markov cohort models, makes discrete-time representation a standard and convenient choice in health economic modelling, provided the cycle length captures the timing adequately.

Source: Briggs, Claxton & Sculpher 2006