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.
Bibliographical noteFunding Information:
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Dr. Alarid-Escudero was supported by grants U01-CA199335, U01-CA253913, U01-CA265750, and U01-CA265729 from the National Cancer Institute (NCI) as part of the Cancer Intervention and Surveillance Modeling Network (CISNET), and a grant by the Gordon and Betty Moore Foundation. Miss Krijkamp was supported by the Society for Medical Decision Making fellowship through a grant by the Gordon and Betty Moore Foundation (GBMF7853). Dr. Enns was supported by a grant from the National Institute of Allergy and Infectious Diseases of the National Institutes of Health under award No. K25AI118476. Dr. Hunink received research funding from the American Diabetes Association, the Netherlands Organization for Health Research and Development, the German Innovation Fund, Netherlands Educational Grant (“Studie Voorschot Middelen”), and the Gordon and Betty Moore Foundation. Dr. Jalal was supported by a grant from the National Institute on Drug Abuse of the National Institute of Health under award No. K01DA048985 and U01-CA265750 from NCI as part of CISNET. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The funding agencies had no role in the design of the study, interpretation of results, or writing of the manuscript. The funding agreement ensured the authors’ independence in designing the study, interpreting the data, writing, and publishing the report.
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