Alternative Conversion Methods for Transition Probabilities in State-Transition Models: Validity and Impact on Comparative Effectiveness and Cost-Effectiveness

Abstract

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.

Comparison of Decision Modeling Approaches for Health Technology and Policy Evaluation

“…In essence, an improperly-embedded discrete time model will rule out events and event sequences from occurring within a time step that would, with some probability, occur in continuous time. While this is certainly not a new observation (Jahn et al, 2019; Jones et al, 2017; O’Mahony et al, 2015; van Rosmalen et al, 2013; Welton and Ades, 2005), our results demonstrate that improper embedding can meaningfully affect decision outcomes.…”

“…Embedding errors arise because if not applied properly, standard conversion formulas do not separately accommodate more than one competing event (Jahn et al, 2019; Jones et al, 2017; O’Mahony et al, 2015; van Rosmalen et al, 2013; Welton and Ades, 2005). This observation is relevant because in many applications, the modeled process is conceptualised around multiple competing events or sequences of events occurring in continuous time (e.g., progression to or among various disease states or to an absorbing death state).…”

“…More technically, it means that the process may no longer be expressed in terms of an underlying generator matrix of continuous transition intensities (Iskandar, 2018). Specifying a transition matrix consistent with an underlying generator matrix is important not only for accurate modeling of the underlying continuous time process, but also for changing Markov cycle lengths (Chhatwal et al, 2016; Jahn et al, 2019). Otherwise, matrix transformation routines (e.g., based on unit roots from eigendecomposition of a specified transition probability matrix) can result in transformed transition matrices with negative probabilities and/or without unique solutions (Chhatwal et al, 2016; Jahn et al, 2019).…”

Comparison of Decision Modeling Approaches for Health Technology and Policy Evaluation

“…In essence, an improperly embedded discrete-time model will rule out events and event sequences from occurring within a time step that would, with some probability, occur in continuous time. While this is certainly not a new observation, 6,25–28 our results demonstrate that improper embedding can meaningfully affect decision outcomes.…”

“…25,30 Otherwise, matrix transformation routines (e.g., based on unit roots from eigendecomposition of a specified transition probability matrix) can result in transformed transition matrices with negative probabilities and/or without unique solutions. 25,30…”