Stochastic Analysis

An analysis in which a model incorporates randomness explicitly, so repeated runs under the same inputs can produce different results, unlike a deterministic model.

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 stochastic analysis builds randomness into the model itself, so that events such as which patients have a complication are decided by chance draws, and each run uses different draws. Running the same model twice therefore yields somewhat different results, unlike a deterministic model that always returns the same answer. The variation between runs is not error but a representation of genuine chance, and it is summarised by averaging across many runs and reporting the spread. The randomness is intentional. Briggs and colleagues (2006) describe this.

Source: Briggs et al. 2006

Stochastic analysis incorporates randomness, so repeated runs with the same inputs can give different results, and outcomes are summarised by their distribution over many runs, whereas deterministic analysis uses fixed relationships and inputs, always producing the same result for given inputs. Stochastic models capture chance variation, such as individual-level randomness or random events, that deterministic models omit. The difference is the explicit role of randomness: present and generating variability in stochastic analysis, absent in deterministic analysis, which yields a single definite result per input set.

Source: Briggs, Claxton & Sculpher 2006

Stochastic analysis is used when randomness is an intrinsic feature of the process or uncertainty being modelled, such as individual-level variability in a patient-level simulation, random timing of events in a discrete-event model, or sampled parameter uncertainty in probabilistic analysis. In these cases, capturing the chance variation is necessary to represent the system or the uncertainty faithfully. Where outcomes depend only on fixed relationships and average values, a deterministic analysis suffices, so stochastic analysis is chosen when the variability itself matters to the question.

Source: Law & Kelton 2000

Results in stochastic analysis are summarised by running the model many times and characterising the distribution of the outcomes, reporting summaries such as the mean, which estimates the expected result, along with measures of spread and, where relevant, confidence intervals reflecting the variability across runs. Because each run gives a different result, enough runs are needed for stable estimates, and the Monte Carlo error is controlled. The distribution of outcomes conveys both the expected value and the variability, which is the information stochastic analysis is designed to provide.

Source: Briggs, Claxton & Sculpher 2006

Stochastic analysis introduces sampling variation, so its estimates carry Monte Carlo error requiring enough runs to control, and it can be computationally intensive, particularly for individual-level or nested models. Interpreting and verifying stochastic results is harder than for deterministic models, since outputs vary across runs, and distinguishing genuine effects from random noise needs care. These limitations mean stochastic analysis is used where randomness genuinely matters, with attention to the number of runs, Monte Carlo error, and verification, and deterministic analysis preferred where chance variation is not needed.

Source: Briggs, Claxton & Sculpher 2006