title: Continuous-Time Semi-Markov Models in Health Economic Decision Making: An Illustrative Example in Heart Failure Disease Management.
abstract: 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.
authors.affiliation: Department of Epidemiology, University of Groningen, University Medical Center Groningen, Groningen, the Netherlands (QC, EB, TF, HH, DP)
authors.forename: Qi
authors.initials: Q
authors.lastname: Cao
authors.affiliation: Department of Epidemiology, University of Groningen, University Medical Center Groningen, Groningen, the Netherlands (QC, EB, TF, HH, DP)
authors.forename: Erik
authors.initials: E
authors.lastname: Buskens
authors.affiliation: 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)
authors.forename: Talitha
authors.initials: T
authors.lastname: Feenstra
authors.affiliation: Department of Social and Welfare Studies, Faculty of Health Sciences, Linköping University, Linköping, Sweden (TJ)
authors.forename: Tiny
authors.initials: T
authors.lastname: Jaarsma
authors.affiliation: Department of Epidemiology, University of Groningen, University Medical Center Groningen, Groningen, the Netherlands (QC, EB, TF, HH, DP)|Department of Cardiology, University of Groningen, University Medical Center Groningen, Groningen, the Netherlands (HH)
authors.forename: Hans
authors.initials: H
authors.lastname: Hillege
authors.affiliation: Department of Epidemiology, University of Groningen, University Medical Center Groningen, Groningen, the Netherlands (QC, EB, TF, HH, DP)
authors.forename: Douwe
authors.initials: D
authors.lastname: Postmus
mesh_terms: D003362:Cost-Benefit Analysis / Q000379:methods*; D003657:Decision Making; D019468:Disease Management; D018450:Disease Progression; D006333:Heart Failure / Q000191:economics* / Q000628:therapy*; D006801:Humans; D008390:Markov Chains; D008962:Models, Theoretical
keywords: continuous-time semi-Markov model; heart failure disease management; vertical modeling