This R package provides an intuitive interface to simulate censored longitudinal multistate processes. The censored data are assumed to be observed at irregular time intervals (i.e., non-discrete time). The data generation is based on the continuous-time Markov/Semi-Markov chain framework.
The continuous-time Markov models have been studied for more than half of a century as of 2023. It has found many use cases in epidemiological studies, clinical trials, and public health surveillance. It is a useful tool to study the dynamic of a multistate process. It can also be extended in several directions. For example, the msm package has implementations of continous-time hidden Markov models (HMM), or the distribution assumptions can be relaxed to encompass more complex processes (e.g., semi-Markov models).
This package allows for data simulation from our extension of the CTMC model, latent class CTMC. In our study, we assumed individuals belong to one of
# use the 'devtools' package to directly install from GitHub
devtools::install_github("j-kuo/LCTMC.simulate")Here we demonstrate the simulation of a two-state process:
# set seed
set.seed(456)
# simulate
d = LCTMC.simulate::simulate_LCTMC(
N.indiv = 5,
N.obs_times = 5,
max.obs_times = 10,
fix.obs_times = FALSE,
true_param = LCTMC.simulate::gen_true_param(K_class = 3, M_state = 2),
alpha.include = TRUE,
beta.include = TRUE,
K = 3,
M = 2,
p1 = 2,
p2 = 2,
initS_p = c(0.5, 0.5),
death = NULL,
sojourn = list(dist = "gamma", gamma.shape = 2)
)This code simulates a two-state process with 3 latent clusters. Using the N.indiv = 5 argument, 5 independent CTMC processes were generated (one per person). Excluding the baseline, each person was observed at 5 irregular times (N.obs_times = 5).
The as.data.frame() function extracts/tidies the simulated data and returns the data as data.frame objects. In this example, we specify id = "BA000" to extract only this person's simulated data.
# coerce the "observed" data into a data frame
as.data.frame(sim_data, type = "obs", id = "BA000")
id obsTime state_at_obsTime x1 x2 w1 w2 latent_class
1 BA000 0.000000 1 0.04352429 1 -0.2349686 1 1
2 BA000 5.470254 2 0.04352429 1 -0.2349686 1 1
3 BA000 7.793661 1 0.04352429 1 -0.2349686 1 1
4 BA000 7.915950 1 0.04352429 1 -0.2349686 1 1
5 BA000 7.986747 1 0.04352429 1 -0.2349686 1 1
6 BA000 9.930836 1 0.04352429 1 -0.2349686 1 1
# coerce the "exact transition" data into a data frame
as.data.frame(sim_data, type = "exact", id = "BA000")
id transTime state_at_transTime x1 x2 w1 w2 latent_class
1 BA000 0.0000000 1 0.04352429 1 -0.2349686 1 1
2 BA000 0.6124992 2 0.04352429 1 -0.2349686 1 1
3 BA000 5.8285964 1 0.04352429 1 -0.2349686 1 1
4 BA000 12.6018292 2 0.04352429 1 -0.2349686 1 1To visualize the longitudinal process, we plot person BA000's data over time. The figure on the left shows the actual process.
# S3 method for plotting
plot(x = d, id = "BA000")
The left figure's interpretation is the following:
- This person begins by being in state 1 at time = 0
- The state then transitions to state 2 at approximately time = 0.6
- At roughly time = 5.8, the state transitions back to state 1
- At last, the state then jumps back to state 2 at around time = 12.6
The red dots in the figures indicate the times at which the data are being collected on this person (e.g., at a clinic visit). If the model does not properly adjust for censoring, we would be assuming the longitudinal process is the figure on the right.
However, in time-to-event analyses, making this assumption will almost surely lead to biased estimates. Since any changes that occur between observations are not accounted for. The CTMC model or other Markov-based models handle these unobserved in-between-observation changes by making some assumptions on the sojourn time (what is sojourn time). For more info see the Wiki section at the bottom of this page.
- Jacky Kuo - author, maintainer
- Wenyaw Chan, PhD - dissertation advisor