Bayesian variable and hazard structure selection in the General Hazard model

The proportional hazards (PH) and accelerated failure time (AFT) models are the most widely used hazard structures for analysing time-to-event data. When the goal is to identify variables associated with event times, variable selection is typically performed within a single hazard structure, imposing strong assumptions on how covariates affect the hazard function. To allow simultaneous selection of relevant variables and the hazard structure itself, we develop a Bayesian variable selection approach within the general hazard (GH) model, which includes the PH, AFT, and other structures as special cases. We propose two types of g-priors for the regression coefficients that enable tractable computation and show that both lead to consistent model selection. We also introduce a hierarchical prior on the model space that accounts for multiplicity and penalises model complexity. To efficiently explore the GH model space, we extend the Add-Delete-Swap algorithm to jointly sample variable inclusion indicators and hazard structures. Simulation studies show accurate recovery of both the true hazard structure and active variables across different sample sizes and censoring levels. Two real-data applications are presented to illustrate the use of the proposed methodology and to compare it with existing variable selection methods.