  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.
