Simulation Method

A general approach to estimating a model's results by repeatedly running it computationally, rather than solving for results using closed-form equations.

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

A simulation method estimates a model's results by running it many times computationally rather than solving it with a formula. It becomes necessary when a model is too complex for a closed-form solution, as when outcomes depend on many interacting parts, chance events, or an individual's accumulated history. In such cases no equation gives the answer, but repeated computation can approximate it as closely as wanted. The cost is running time and a small residual sampling error. Its generality is why complex models rely on it. Briggs and colleagues (2006) contrast it with analytical methods.

Source: Briggs et al. 2006

A simulation method estimates results by repeatedly running the model with sampled values and summarising the outcomes, introducing some sampling variation, whereas an analytical method solves the model with closed-form equations, giving exact results directly. Analytical methods are faster and exact where available, but many complex models, with individual variation, interactions, or complex dynamics, cannot be solved in closed form and require simulation. So the two differ in approach and applicability: exact calculation for tractable models, and repeated computational running for complex ones.

Source: Briggs, Claxton & Sculpher 2006

A simulation method is used when a model is too complex for an analytical solution, for example when outcomes depend on individual histories and heterogeneity, when there are complex interactions or dynamics such as disease transmission, or when the quantities of interest arise from combining many uncertain inputs. In these cases, running the model repeatedly with sampled values estimates the results where closed-form equations are unavailable. Simulation is therefore the approach of choice for complex models, while analytical methods are preferred for simpler structures that can be solved exactly.

Source: Law & Kelton 2000

Types of simulation method include cohort simulation, which tracks the average movement of a hypothetical cohort through model states; individual-level, or microsimulation, which simulates individual patients one at a time, capturing heterogeneity and history; discrete-event simulation, which models events over time; and Monte Carlo simulation, which repeatedly samples to estimate quantities or propagate uncertainty. These differ in what they represent and how, from average cohort flows to detailed individual trajectories. The choice depends on the model's needs, such as whether individual variation and history must be captured.

Source: Briggs, Claxton & Sculpher 2006

Simulation methods introduce sampling variation, so their estimates carry Monte Carlo error that must be controlled by running enough iterations or replications, and they can be computationally intensive, especially individual-level simulations or nested schemes. Their results require checking for convergence and can be harder to interpret and verify than closed-form solutions. Complexity can also obscure errors. These limitations mean simulation methods are used where analytical solutions are unavailable, with attention to computational cost, Monte Carlo error, verification, and convergence to ensure reliable results.

Source: Briggs, Claxton & Sculpher 2006