Centre for Health Economics, University of York, UK.
Pharmacoeconomics. 2012 Dec 1;30(12):1101-17. doi: 10.2165/11599380-000000000-00000.
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.
决策分析模型在成本效益分析中的设计一直是讨论的主题。本研究通过指出，当需要明确建模时间时，我们需要表示连续时间中发生的现象，解决了这个问题。在连续时间中评估的模型可能没有闭式解，在这种情况下，可以使用两种近似方法：连续时间模拟模型和聚合水平离散化模型。建立了可以实施这两种近似方法的简化示例。这些示例旨在说明使用这两种近似方法的决定因素：周期长度和精度、离散化模型中连续性校正的使用以及速率离散化为概率。这些示例还用于探索近似方法不仅在绝对生存方面，而且在成本效益和增量比较方面的影响。如果使用较短的周期长度，离散化模型可以更好地近似连续时间的结果。连续时间模拟模型本质上是随机的，结果的精度取决于模拟样本量。在离散化模型中使用连续性校正可以使用更长的周期长度，不会因离散化而产生显著的偏差。对过程的离散化（将速率离散化为概率）是关键。结果表明，适当的离散化加上使用连续性校正可以产生对更高周期长度无偏差的结果。替代的离散化方法效率较低，即需要较短的周期长度才能获得无偏差的结果。所开发的工作表明，承认在估计成本效益方面存在偏差的重要性。当可以应用替代的近似方法时，我们认为实施队列离散化模型比在连续时间中实施模拟模型更为可取。然而，在实践中，可能无法通过任何传统定义的离散化模型来表示决策问题，在这种情况下，需要应用其他模型设计，例如模拟模型。
