A Multidimensional Array Representation of State-Transition Model Dynamics
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Abstract
Cost-effectiveness analyses often rely on cohort state-transition models (cSTMs). The cohort trace is the primary outcome of cSTMs, which captures the proportion of the cohort in each health state over time (state occupancy). However, the cohort trace is an aggregated measure that does not capture information about the specific transitions among health states (transition dynamics). In practice, these transition dynamics are crucial in many applications, such as incorporating transition rewards or computing various epidemiological outcomes that could be used for model calibration and validation (e.g., disease incidence and lifetime risk). In this article, we propose an alternative approach to compute and store cSTMs outcomes that capture both state occupancy and transition dynamics. This approach produces a multidimensional array from which both the state occupancy and the transition dynamics can be recovered. We highlight the advantages of the multidimensional array over the traditional cohort trace and provide potential applications of the proposed approach with an example coded in R to facilitate the implementation of our method.
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Obtaining information on transitions between health states with origin and destination is relatively straightforward in a cSTM and is described in detail by Krijkamp et al. (2020).
“However, obtaining this information is relatively straightforward in a cSTM and is described in detail by Krijkamp et al. (2020).”
From A Tutorial on Time-Dependent Cohort State-Transition Models in R Using a Cost-Effectiveness Analysis Example (2023) · cites this paper as Krijkamp et al. (2020)
Changing the core computation in a traditional cSTM from mtPt to diag(mt)Pt allows computation of the proportion of the cohort that transitions between any two states in a cycle t.
“Briefly, this approach involves changing the core computation in a traditional cSTM, from mtPt to diag(mt)Pt. This simple change allows us to compute the proportion of the cohort that transitions between any two states in a cycle t.”
From A Tutorial on Time-Dependent Cohort State-Transition Models in R Using a Cost-Effectiveness Analysis Example (2023) · cites this paper as Krijkamp et al. (2020)
Implementing transition rewards by calculating incurred rewards based on the proportion of the cohort making the relevant transition requires storing a cohort state-transition array in addition to the cohort trace.
“For implementation, this requires storing not just the cohort trace, which reflects how many individuals are in each state at a given cycle, but also a cohort state-transition array, which records how many individuals are making each possible transition at a given cycle.9”
From A Tutorial on Time-Dependent Cohort State-Transition Models in R Using a Cost-Effectiveness Analysis Example (2023) · cites this paper as [9]
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Cites
State-Transition Modeling: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-3
Siebert, U., Alagoz, O., Bayoumi, A. M., Jahn, B., Owens, D. K., Cohen, D. J., & Kuntz, K. M. (2012) · Value in Health · doi:10.1016/j.jval.2012.06.014 · Cited by 495 · see citing works
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Research works printed but not linked: 8
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Alarid-Escudero, F., Krijkamp, E., Enns, E. A., Yang, A., Hunink, M. G. M., Pechlivanoglou, P., & Jalal, H. (2023) · Medical Decision Making · doi:10.1177/0272989x221121747 · Cited by 5 · see citing works
“by applying Equation (9) to the expected outcomes accounting for transition rewards.”
MethodInfluentialSelf-citation
- Authors
- Krijkamp, E. M., Alarid-Escudero, F., Enns, E. A., Pechlivanoglou, P., Hunink, M. G. M., Yang, A., & Jalal, H. J.
- Affiliations
- Erasmus MC (NL)
- Drug Policy Program, Center for Research and Teaching in Economics, (CIDE)-CONACyT, Aguascalientes, Ags., Mexico
- University of Minnesota (US)
- University of Toronto (CA)
- Harvard University (US)
- Hospital for Sick Children (CA)
- University of Pittsburgh (US)
- ORCID
- Venue
- Medical Decision Making
- Publisher
- SAGE Publications
- Published
- 2020-01-28
- Volume
- 40
- Issue
- 2
- Pages
- 242-248
- ISSN
- 0272-989X (ISSN-L)
- 1552-681X
- PMC
- PMC7065927
- OpenAlex
- W3003342603
- Cited by
- 18
- References
- 1
- Citations by year
- 2026: 2 · 2025: 8 · 2024: 1 · 2023: 1 · 2022: 2 · 2021: 3 · 2019: 1
- FWCI
- 1.27
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Medical Decision Making (publishedVersion, cc-by-nc)
- PubMed (publishedVersion)
- EUR Research Repository (Erasmus University Rotterdam) (publishedVersion, other-oa)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- EUR Research Repository (Erasmus University Rotterdam) (submittedVersion, other-oa)
- RePub (Erasmus University Rotterdam) (submittedVersion, other-oa)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- National Cancer Institute (U01- CA-199335)
- National Institute of Allergy and Infectious Diseases (K25AI118476)
- national institutes of health (KL2 TR0001856)
- Topics
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Health Systems, Economic Evaluations, Quality of Life
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Decision Sciences › Management Science and Operations Research › Simulation Techniques and Applications
- Keywords
- multidimensional arrays, transition dynamics, model calibration and validation, disease incidence, lifetime risk, cost-effectiveness analysis
- MeSH terms
- Computer Simulation, Cost-Benefit Analysis, Decision Support Techniques, Epidemiologic Methods, Humans, Software, Models, Statistical, Cohort Studies
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