OBJECTIVE: The memoryless property makes Markov models challenging to use when the risk of future events depends on time in a health state. Two common approaches for incorporating memory involve adding tunnel states to capture time in a health state or using a patient-level simulation model where history is recorded. We consider another option – extending the Markov model with sub-health states to reflect broad differences in event risks over time. In this model, movement to the next sub-health state is determined by the expected duration in a sub-state. This study investigates how the extended Markov model performs vis-à-vis the tunnel state and patient-level simulation models.

METHODS: We created a hypothetical four-state (mild, moderate, severe, death) Markov model using monthly cycles to estimate the cost-effectiveness of an intervention vs. control. Mortality risk decreased over time in the severe state: 0.007, 0.005 and 0.003 in months 1-12, 13-36, and 37+, respectively. A Markov model with 36 tunnel states was created to capture the actual time in the severe state. A patient-level simulation model was also developed. In the extended Markov model, three severe sub-health states were created where transition probabilities between sub-health states depended on the expected duration (e.g., 12 and 24 months). Comparison of the models focused on the estimated incremental costs, QALYs and ICERs.

RESULTS: The incremental costs (€931, €905, €915), incremental QALYs (0.1006, 0.1000, 0.0999) and ICERs (€9262, €9046, €9154 per QALY gained) were similar for the tunnel state, patient-level simulation and extended Markov models, respectively. However, patient-level simulation results were variable (95% CI for ICER: €1,886 to €16,206 per QALY).

CONCLUSIONS: The ICER based on the extended Markov model was similar to those from models capturing the exact health state duration. While promising, simulations under alternative scenarios are needed before broadly adopting the extended Markov model approach.