Continuous time simulation and discretized models for cost-effectiveness analysis.

The design of decision-analytic models for cost-effectiveness analysis has been the subject of discussion. The current work addresses this issue by noting that, when time is to be explicitly modelled, we need to represent phenomena occurring in continuous time. Models evaluated in continuous time may not have closed-form solutions, and in this case, two approximations can be used: simulation models in continuous time and discretized models at the aggregate level. Stylized examples were set up where both approximations could be implemented. These aimed to illustrate determinants of the use of the two approximations: cycle length and precision, the use of continuity corrections in discretized models and the discretization of rates into probabilities. The examples were also used to explore the impact of the approximations not only in terms of absolute survival but also cost effectiveness and incremental comparisons. Discretized models better approximate continuous time results if lower cycle lengths are used. Continuous time simulation models are inherently stochastic, and the precision of the results is determined by the simulation sample size. The use of continuity corrections in discretized models allows the use of greater cycle lengths, producing no significant bias from the discretization. How the process is discretized (the conversion of rates into probabilities) is key. Results show that appropriate discretization coupled with the use of a continuity correction produces results unbiased for higher cycle lengths. Alternative methods of discretization are less efficient, i.e. lower cycle lengths are needed to obtain unbiased results. The developed work showed the importance of acknowledging bias in estimating cost effectiveness. When the alternative approximations can be applied, we argue that it is preferable to implement a cohort discretized model rather than a simulation model in continuous time. In practice, however, it may not be possible to represent the decision problem by any conventionally defined discretized model, in which case other model designs need to be applied, e.g. a simulation model.