Cao Qi, Buskens Erik, Feenstra Talitha, Jaarsma Tiny, Hillege Hans, Postmus Douwe
Department of Epidemiology, University of Groningen, University Medical Center Groningen, Groningen, the Netherlands (QC, EB, TF, HH, DP)
Centre for Nutrition, Prevention, and Health Services, National Institute for Public Health and the Environment, Bilthoven, the Netherlands (TF)
Med Decis Making. 2016 Jan;36(1):59-71. doi: 10.1177/0272989X15593080. Epub 2015 Jul 14.
Continuous-time state transition models may end up having large unwieldy structures when trying to represent all relevant stages of clinical disease processes by means of a standard Markov model. In such situations, a more parsimonious, and therefore easier-to-grasp, model of a patient's disease progression can often be obtained by assuming that the future state transitions do not depend only on the present state (Markov assumption) but also on the past through time since entry in the present state. Despite that these so-called semi-Markov models are still relatively straightforward to specify and implement, they are not yet routinely applied in health economic evaluation to assess the cost-effectiveness of alternative interventions. To facilitate a better understanding of this type of model among applied health economic analysts, the first part of this article provides a detailed discussion of what the semi-Markov model entails and how such models can be specified in an intuitive way by adopting an approach called vertical modeling. In the second part of the article, we use this approach to construct a semi-Markov model for assessing the long-term cost-effectiveness of 3 disease management programs for heart failure. Compared with a standard Markov model with the same disease states, our proposed semi-Markov model fitted the observed data much better. When subsequently extrapolating beyond the clinical trial period, these relatively large differences in goodness-of-fit translated into almost a doubling in mean total cost and a 60-d decrease in mean survival time when using the Markov model instead of the semi-Markov model. For the disease process considered in our case study, the semi-Markov model thus provided a sensible balance between model parsimoniousness and computational complexity.
当试图通过标准马尔可夫模型来表示临床疾病过程的所有相关阶段时，连续时间状态转移模型最终可能会具有庞大且难以处理的结构。在这种情况下，通常可以通过假设未来状态转移不仅取决于当前状态（马尔可夫假设），还取决于自进入当前状态以来的过去时间，从而获得一个更简洁、更易于理解的患者疾病进展模型。尽管这些所谓的半马尔可夫模型在指定和实现方面仍然相对简单，但它们尚未在卫生经济评估中常规应用于评估替代干预措施的成本效益。为了便于应用卫生经济分析师更好地理解这类模型，本文的第一部分详细讨论了半马尔可夫模型的内涵，以及如何通过采用一种称为垂直建模的方法以直观的方式指定此类模型。在本文的第二部分，我们使用这种方法构建了一个半马尔可夫模型，用于评估三种心力衰竭疾病管理方案的长期成本效益。与具有相同疾病状态的标准马尔可夫模型相比，我们提出的半马尔可夫模型对观察数据的拟合效果要好得多。当随后外推到临床试验期之外时，在拟合优度方面这些相对较大的差异转化为使用马尔可夫模型而非半马尔可夫模型时平均总成本几乎翻倍，平均生存时间减少60天。对于我们案例研究中考虑的疾病过程，半马尔可夫模型因此在模型简洁性和计算复杂性之间提供了合理的平衡。
