Gradient boosting-based discrete failure time model for selecting time-varying effects and interactions

Analyzing survival data from the National Cancer Institute's Surveillance, Epidemiology, and End Results (SEER) Program offers invaluable insight to guide cancer management. In these data the event times are recorded in units of months. In such datasets, it can be important to consider the selection of covariates, distinguish between time-varying and time-independent effects, and capture important interaction terms. However, variable selection is difficult to combine with the differentiation between time-varying and time-independent effects. Moreover, accurately selecting interaction terms is more challenging because of the hierarchy restriction that an interaction term should only enter a model if one or both associated main effects are also included. To resolve these issues, we develop a coordinate ascent-based gradient boosting procedure for discrete failure time models. This approach achieves variable selection in high-dimensional settings, differentiates between time-varying and time-independent variables, and selects important interaction terms under hierarchy restrictions. Traditional boosting stopping criteria are ad hoc, while preferable information-criteria-based rules necessitate defining degrees of freedom, a challenge in survival models. Our approach provides well-defined degrees of freedom and offers information-criteria-based stopping rules. Simulation studies show the proposed method achieves good selection performance. We apply the proposed method to SEER melanoma cancer data and select important risk factors, distinguish between time-varying and time-dependent effects and detect important two-way interactions.