Penalized variable selection for accelerated failure time models with random effects

Accelerated failure time (AFT) models allowing for random effects are linear mixed models under the log-transformation of survival time with censoring and describe dependence in correlated survival data. It is well known that the AFT models are useful alternatives to frailty models. To the best of our knowledge, however, there is no literature on variable selection methods for such AFT models. In this paper, we propose a simple but unified variable-selection procedure of fixed effects in the AFT random-effect models using penalized h-likelihood (HL). We consider four penalty functions (ie, least absolute shrinkage and selection operator (LASSO), adaptive LASSO, smoothly clipped absolute deviation (SCAD), and HL). We show that the proposed method can be easily implemented via a slight modification to existing h-likelihood estimation procedures. We thus demonstrate that the proposed method can also be easily extended to AFT models with multilevel (or nested) structures. Simulation studies also show that the procedure using the adaptive LASSO, SCAD, or HL penalty performs well. In particular, we find via the simulation results that the variable selection method with HL penalty provides a higher probability of choosing the true model than other three methods. The usefulness of the new method is illustrated using two actual datasets from multicenter clinical trials.