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A mathematical approach for evaluating Markov models in continuous time without discrete-event simulation.
Joost van Rosmalen1,2, Mehlika Toy1,3, James F O'Mahony1,4
1Department of Public Health, Erasmus MC, University Medical Center, Rotterdam, the Netherlands (JVR, MT, JFO)
Summary
Continuous-time Markov models offer a more accurate analysis of health interventions than discrete-time models. This approach improves cost-effectiveness estimates by accounting for events occurring in real-time, unlike traditional cohort analysis.
Area of Science:
- Health economics
- Mathematical modeling
- Stochastic processes
Background:
- Markov models are widely used for health and economic evaluations of interventions.
- Discrete-time Markov models approximate continuous disease progression, potentially causing bias.
- Clinical events occur in continuous time, necessitating more accurate modeling.
Purpose of the Study:
- To present methods for evaluating Markov models in continuous time.
- To address the limitations of discrete-time approximations in Markov modeling.
- To provide a more accurate framework for cost-effectiveness analysis.
Main Methods:
- Utilizing mathematical results from stochastic process and control theory.
- Developing a mathematical solution for expected time spent in model states.
- Applying continuous-time Markov models to a chronic hepatitis B cost-effectiveness example.
Main Results:
- Continuous-time Markov models provide more accurate cost-effectiveness estimates.
- The proposed methods can incorporate age-dependent transitions and discounting.
- Tunnel states can model time-dependent transition rates effectively.
Conclusions:
- Continuous-time Markov models are a viable and advantageous alternative to discrete-time cohort analysis.
- These models offer theoretical and practical benefits for health economic evaluations.
- Implementation is feasible and computationally efficient.
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