TimeDepFrail: Time-Dependent Shared Frailty Cox Models in R

Abstract

This paper introduces TimeDepFrail, an R package designed to implement time-varying shared frailty models by extending the traditional shared frailty Cox model to allow the frailty term to evolve across time intervals. These models are particularly suited for survival analysis in clustered data where unobserved heterogeneity changes over time, providing greater flexibility in modeling time-to-event data. The package builds on the piecewise gamma frailty model originally proposed by Paik (1994) and refined by Wintrebert et al. (2004). Our key contributions include the integration of posterior frailty estimation, a reduction in computational complexity, the definition of a prediction framework and the efficient implementation of these models within an R package. As a practical application, we use TimeDepFrail to analyze dropout rates within a university, where high dropout rates are a known issue. By allowing frailty to vary over time, the package uncovers new insights into the unobserved factors influencing dropout. TimeDepFrail simplifies access to advanced time-varying frailty models, providing a practical and scalable alternative to more computationally demanding methods, making it highly applicable for large-scale datasets.