A Tutorial on Time-Dependent Cohort State-Transition Models in R using a Cost-Effectiveness Analysis Example

TL;DR

This paper provides a tutorial on implementing time-dependent cohort state-transition models in R, demonstrating how to incorporate time-varying transition probabilities and state residence times for cost-effectiveness analysis.

Contribution

It introduces methods for adding time-dependency to cSTMs in R, including simulation-time and state-residence time dependence, with practical R code examples.

Findings

Demonstrated how to model time-dependent transition probabilities.

Showed how to track state residence time using tunnel states.

Applied models to cost-effectiveness and sensitivity analyses.

Abstract

In an introductory tutorial, we illustrated building cohort state-transition models (cSTMs) in R, where the state transitions 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 two types of time-dependency 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.