Background. In state-transition models (STMs), decision problems are conceptualized using health states and transitions among those health states after predefined time cycles. The naive, commonly applied method (C) for cycle length conversion transforms all transition probabilities separately. In STMs with more than 2 health states, this method is not accurate. Therefore, we aim to describe and compare the performance of method C with that of alternative matrix transformation methods. Design. We compare 2 alternative matrix transformation methods (Eigenvalue method [E], Schure-Padé method [SP]) to method C applied in an STM of 3 different treatment strategies for women with breast cancer. We convert the given annual transition matrix into a monthly-cycle matrix and evaluate induced transformation errors for the transition matrices and the long-term outcomes: life years, quality-adjusted life-years, costs and incremental cost-effectiveness ratios, and the performance related to the decisions. In addition, we applied these transformation methods to randomly generated annual transition matrices with 4, 7, 10, and 20 health states. Results. In theory, there is no generally applicable correct transformation method. Based on our simulations, SP resulted in the smallest transformation-induced discrepancies for generated annual transition matrices for 2 treatment strategies. E showed slightly smaller discrepancies than SP in the strategy, where one of the direct transitions between health states was excluded. For long-term outcomes, the largest discrepancy occurred for estimated costs applying method C. For higher dimensional models, E performs best. Conclusions. In our modeling examples, matrix transformations (E, SP) perform better than transforming all transition probabilities separately (C). Transition probabilities based on alternative conversion methods should therefore be applied in sensitivity analyses.
Keywords: conversion transition probability; cost-effectiveness analysis; markov model; markov transition matrix; state-transition model.