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TimeDepFrail is the ultimate R package for fitting and analyzing Time-Dependent Shared Frailty Cox Models. These models extend the traditional Shared (Gamma) Frailty Cox Models by incorporating a time-dependent frailty component, making it a robust tool for studying how unexplained heterogeneity in data evolves over time.
This package implements the methods discussed in “Centre-Effect on Survival After Bone Marrow Transplantation: Application of Time-Dependent Frailty Models” by C.M. Wintrebert et al. (2004).
You can install the development version of the package from
GitHub:
{r, eval=FALSE} devtools::install_github("alessandragni/TimeDepFrail")
data_dropoutThe data_dropout dataset is used to exemplify the
package. It tracks the academic progress of students enrolled in 2012
over three academic years (six semesters). This dataset aims to explore
the factors leading to student dropout.
The dataset is composed of four variables: - Gender:
Categorical covariate indicating gender (Male or Female). -
CFUP: Numeric covariate representing the standardized
number of credits or CFUs (Credito Formativo Universitario) passed by
the student in the first semester. - time_to_event: The
time (in semesters) when a student decides to drop out. A value greater
than 6.0 means the student did not drop out during the follow-up period.
- group: Categorical variable representing the student’s
course of study, with 16 levels from CosA to CosP.
Students are followed for a maximum of 6 semesters (3 academic years), from the start of lectures until they drop out or the follow-up ends.
To fit a Time-Dependent Shared Frailty model, the following elements
are required: - dataset as data.frame,
e.g. data_dropout - time_axis vector: The time
intervals for which the model is applied. For example, in the
data_dropout dataset, no events occur in the first
semester, so the time_axis starts at the end of the first
semester (t = 1) and ends at the end of the third year (t = 6). -
categories_range_min and categories_range_max
vectors: Provide minimum (categories_range_min) and maximum
(categories_range_max) bounds for each parameter category
to constrain the optimization. - formula object: Specify
the relationship between time-to-event, covariates, and group. For the
clustering variable (group), it must be provided as
cluster(group) in the formula.
Once these elements are prepared, you can call the desired model
using the AdPaikModel() function. While
PowParModel() and StocTimeDepModel() are also
available, they are secondary models with room for performance
improvements.
For full examples, refer to the
Examples/ModelsApplication.R script.
Additionally, for guidance on selecting model parameters such as
time_axis, categories_range_min and
categories_range_max, we recommend basing these choices on
insights gained after fitting a Time-Unvarying Shared Frailty model. You
can find a relevant example in the
ExamplesTimeUnvarying.R.
Several built-in methods are available to analyze the results of the
fitted model: - Baseline Hazard Step-Function:
plot_bas_hazard() - Frailty Standard Deviation/Variance:
plot_frailty_sd() - Posterior Frailty Estimates:
plot_post_frailty_est() - Model Summary:
summary()
These methods provide insightful visualizations and summaries to help you interpret your model results effectively.
Furthermore, also a support function suitable for the choice of the
range of parameters and analysis of the 1D log-likelihood is available,
AdPaik_1D().
AdPaikModel model is optimized for fast computation
although estimating certain coefficients (e.g., Male versus
Female) may vary slightly in computational time. Note that
changing the reference category (e.g., using Male as the
baseline) alters the coefficient estimates but not the overall
log-likelihood or model fit. Users should choose reference categories
based on interpretability rather than performance.PowParModel) is slower than the AdPaikModel,
but it produces coherent and expected results.StocTimeDepModel) is computationally heavy and may not
converge easily.Alessandra Ragni (alessandra.ragni@polimi.it), Giulia Romani (giulia.romani@mail.polimi.it), Chiara Masci (chiara.masci@polimi.it).
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.