Alarid-Escudero F, Krijkamp EM, Enns EA, Yang A, Hunink MGM, Pechlivanoglou P, Jalal H. A Tutorial on Time-Dependent Cohort State-Transition Models in R using a Cost-Effectiveness Analysis Example. Medical Decision Making, 2022;43(1):21-41. Download R code.
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Abstract
Background
In an introductory tutorial, we illustrated building cohort state-transition models (cSTMs) in R, where the state transition probabilities were constant over time. However, in practice, many cSTMs require transitions, rewards, or both to vary over time (time dependent). This tutorial illustrates adding 2 types of time dependence using a previously published cost-effectiveness analysis of multiple strategies as an example. The first is simulation-time dependence, which allows for the transition probabilities to vary as a function of time as measured since the start of the simulation (e.g., varying probability of death as the cohort ages). The second is state-residence time dependence, allowing for history by tracking the time spent in any particular health state using tunnel states. We use these time-dependent cSTMs to conduct cost-effectiveness and probabilistic sensitivity analyses. We also obtain various epidemiological outcomes of interest from the outputs generated from the cSTM, such as survival probability and disease prevalence, often used for model calibration and validation. We present the mathematical notation first, followed by the R code to execute the calculations. The full R code is provided in a public code repository for broader implementation.
Methods
We use base R to implement time-dependent cSTMs as the most transparent way to illustrate how to translate the mathematical specification of cSTMs into code. Using a base R implementation maximizes flexibility and customizability to model any disease that can be specified as a cSTM. However, there are R packages for building and running cSTMs and conducting CEAs, such as heemod and hesim, that are made such that they can support modeling arbitrary patient populations or many treatment strategies. Since much of the programming burden has already been done, these packages can reduce programming time. Users do not need to write functions themselves but instead need to call a series of prewritten functions. And in the case of hesim, all the memory preallocation and loops are made at the C++ level, making it more efficient than looping over base R but might require more RAM. Ultimately, it is up to the analyst to decide the most appropriate approach to implementing their cSTM-based CEAs.
Conclusions
This tutorial extends our conceptualization of time-independent cSTMs to allow for time dependence. It provides a step-by-step guide to implementing time-dependent cSTMs in R to generate epidemiological and economic outcomes, accounts for transition rewards, and conducts a CEA and a corresponding PSA. We hope that health decision scientists and health economists find this tutorial helpful in developing their cSTMs in a more flexible, efficient, and open-source manner. Ultimately, our goal is to facilitate R in health economic evaluations with the overall aim to increase model transparency and reproducibility.