SURVIVAL MODELING USING COXIAN PHASE-TYPE DISTRIBUTION IN DISCRETE STATE-TRANSITION MODELS
Author(s)
Melanio U. Mauricio, III, BSc, MSc1, W.B. van den Hout, PhD2.
1PhD student, Leiden University Medical Center, Leiden, Netherlands, 2Leiden University Medical Center, Leiden, Netherlands.
1PhD student, Leiden University Medical Center, Leiden, Netherlands, 2Leiden University Medical Center, Leiden, Netherlands.
OBJECTIVES: State-transition models with time-dependence in non-initial states typically account for that time-dependence using tunnel states. However, this considerably increases the model size in case of long-term time-dependence. We used the Coxian phase-type distribution as an alternative approach, where patients progress stochastically through sequential phases, enabling long-term time-dependent transitions and rewards to be captured even with just a few phases. This study evaluates the feasibility and validity of using the Coxian phase-type distribution on cost and utility estimates compared with conventional approaches.
METHODS: We applied the Coxian and tunnel state approaches in a heart transplantation model, with monthly cycles. Hazard rates for the Coxian phase-type distribution were estimated through optimization and subsequently used to derive transition probabilities. We performed survival extrapolation using a three-phase Coxian distribution and compared fit with the tunnel-state approach. State rewards for each phase were calibrated to the time-dependent costs and utilities for each cycle. We compared approaches according to visual fit, and estimated lifetime costs and utilities associated with post-transplantation states.
RESULTS: The tunnel-state approach required a tunnel length of 13, while the Coxian approach only required 3 phases and provided better visual fit. The Coxian approach captured a non-monotonic hazard pattern, with the highest hazard occurring in the initial cycles, followed by a substantially lower intermediate hazard, and a modest increase in long-term hazard. Estimated lifetime costs are €13,876 using tunnel states and €14,108 using the Coxian phase-type distribution, while utilities are 22.61 in the 13-month tunnel-state approach and 22.60 with the Coxian approach.
CONCLUSIONS: The Coxian phase-type approach offers a flexible alternative to tunnel state for long-term extrapolation by avoiding limitations imposed by finite tunnel lengths. This approach can improve long-term fit in non-initial states while accounting for time-dependent hazards and rewards.
METHODS: We applied the Coxian and tunnel state approaches in a heart transplantation model, with monthly cycles. Hazard rates for the Coxian phase-type distribution were estimated through optimization and subsequently used to derive transition probabilities. We performed survival extrapolation using a three-phase Coxian distribution and compared fit with the tunnel-state approach. State rewards for each phase were calibrated to the time-dependent costs and utilities for each cycle. We compared approaches according to visual fit, and estimated lifetime costs and utilities associated with post-transplantation states.
RESULTS: The tunnel-state approach required a tunnel length of 13, while the Coxian approach only required 3 phases and provided better visual fit. The Coxian approach captured a non-monotonic hazard pattern, with the highest hazard occurring in the initial cycles, followed by a substantially lower intermediate hazard, and a modest increase in long-term hazard. Estimated lifetime costs are €13,876 using tunnel states and €14,108 using the Coxian phase-type distribution, while utilities are 22.61 in the 13-month tunnel-state approach and 22.60 with the Coxian approach.
CONCLUSIONS: The Coxian phase-type approach offers a flexible alternative to tunnel state for long-term extrapolation by avoiding limitations imposed by finite tunnel lengths. This approach can improve long-term fit in non-initial states while accounting for time-dependent hazards and rewards.
Conference/Value in Health Info
2026-11, ISPOR Europe 2026, Vienna, Austria
Value in Health, Volume 29, Issue 12S
Code
P59
Topic
Economic Evaluation, Methodological & Statistical Research, Study Approaches
Disease
Cardiovascular Disorders (including MI, Stroke, Circulatory)