Conference Agenda

The Cox proportional hazards model is a widely used method for analyzing clinical time-to-event data. In its standard form, the Cox model assumes the covariate effects on the hazard function to be constant over time. However, in many clinical settings, covariate effects may vary with time, and covariate interactions may significantly influence survival. Selecting interactions and time-varying effects within the Cox model framework may be challenging and often requires manual pre-screening followed by model selection steps. These selection steps are often carried out through automated stepwise procedures, which, however, can be unstable or even infeasible—particularly if a large number of potential effects is considered.

We introduce a linked-shrinkage adaptive elastic net procedure for selecting two-way interactions and time-varying effects in Cox regression models. The proposed approach integrates an adaptive elastic net with penalty weights derived from an initial ridge regression that includes main effects only. Time-varying effects are modeled as piecewise constant functions. Penalty weights for interactions and time-varying terms are specified using a linked-shrinkage strategy based on the pre-estimated main effects, such that these effects are penalized more strongly than the main effects. We assessed the proposed modeling approach through a simulation study based on Weibull-distributed survival times, incorporating various structures of time-varying covariate effects. Using a simulation study, we compared the proposed method with several established approaches, including the classical elastic net extended to the Cox regression model. Model performance was assessed in terms of the mean squared error (MSE) of the estimated survival probabilities and the accuracy of variable selection.

The proposed method reliably identified true time-varying and two-way interaction effects. The true positive rates ranged between 80%-90% depending on the scenario. Compared to standard regularized Cox regression models, the proposed method yielded better performance in terms of MSE and the ability to select informative main/interaction/timevarying effects in a more precise way. Furthermore, we illustrate the proposed approach by analyzing real-world data from the National Cancer Institute Surveillance, Epidemiology, and End Results (SEER) program.

By addressing the limitations of manual covariate selection and stepwise procedures, the proposed method extends penalized estimation techniques to Cox regression with time-varying coefficients. Further, it facilitates the simultaneous selection of relevant interaction terms and time-varying covariate effects.