Krijkamp E, Alarid-Escudero F, Enns EA, Pechlivanoglou P, Hunink MGM, Yang A, Jalal H. A Multidimensional Array Representation of State-transition Model Dynamics. Medical Decision Making, 2020;40(2):242-248. The accompanying R code can be downloaded here.
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Abstract
Background
Cost-effectiveness analyses often rely on cohort state-transition models (cSTMs). The cohort trace is the primary outcome of cSTMs, which captures the proportion of the cohort in each health state over time (state occupancy). However, the cohort trace is an aggregated measure that does not capture information about the specific transitions among health states (transition dynamics). In practice, these transition dynamics are crucial in many applications, such as incorporating transition rewards or computing various epidemiological outcomes that could be used for model calibration and validation (e.g., disease incidence and lifetime risk).
Methods
To overcome the limitations of the cohort trace, we propose a multidimensional array–based approach that serves as a full summary of cSTM dynamics that complements the already useful cohort trace. The proposed approach, called the dynamics-array approach, allows modelers to efficiently calculate all measures of interest that rely on transition dynamics and at the same time to aggregate all model dynamics into a standard cohort trace.
Results
The practical application of our approach involves adding a simple step to the traditional cohort trace approach that stores all transitions among health states over time in multidimensional array A. We described the multidimensional array approach for a general cSTM where transitions are allowed from any state to others within a cycle, but our approach can also be applied to models that only allow one-state transition in a cycle (i.e., where the \(p_{i,j,t}\) are 0 for those transitions that are not allowed).
Conclusions
In conclusion, structuring the output of cSTMs using the dynamics-array approach is an efficient, simple, and convenient method of summarizing the model dynamics. This simple structure allows applying state and transition rewards and obtaining epidemiological measures while still being able to obtain and display the conventional cohort trace.