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:
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 end of first semester until they drop out or the follow-up ends.
To fit a Time-Dependent Shared Frailty model, the following elements are required:
data.frame, e.g. data_dropouttime_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.
For full examples, refer to the
Examples/ReplicationCode.R script.
Additionally, for guidance on selecting model parameters such as
time_axis, categories_range_min and
categories_range_max, we recommend base these choices on
insights gained after fitting a Time-Unvarying Shared Frailty model. You
can find a relevant example in the
Examples/ReplicationCode.R, in the Appendix D Section.
Several built-in methods are available to analyze the results of the fitted model:
summary(), coef(),
coefse(), confint()plot_bas_hazard()frailty_sd() and
plot_frailty_sd()plot_post_frailty_est()survival() and
plot_survival()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.Alessandra Ragni (alessandra.ragni@polimi.it), Giulia Romani (giulia.romani@mail.polimi.it), Chiara Masci (chiara.masci@polimi.it).