Regularization in Accelerated Failure Time (AFT) models with frailty parameters

Variable selection is one of the standard ways of conducting model selection in large scale data-sets. It is used in many studies especially in large multi-center clinical trials. One of the prominent methods in variable selection is the penalized likelihood which is both consistent and efficient. However, penalized selection in mixed effects models is significantly challenging because of the influence of random covariates. It is even more complicated when there is involvement of censoring as such issues may cause the equations for the maximum likelihood to not converge. Therefore, we pro-posed the penalized quasi-likelihood (PQL) approach to estimate the maximum likelihood and thereby introduced a sparsity-inducing adaptive penalty function that makes the selection on both fixed and frailty effects in censored survival data. We used the parametric accelerated failure time (AFT) models with frailty parameters and left censoring mechanism to develop the predictive model. We also compared our penalty function with other established procedures via their performance on accurately choosing the correct co-efficients and shrinking the false estimates towards zero.