Variable selection has been administered in many studies of Biostatistics especially regarding large multi-center clinical trials that have high dimensional data points. The penalized likelihood is one of the most prominent methods for variable selection as it has shown a consistent and successful range of essential and necessary variables. Therefore, we aim to comparatively test these different penalty functions to conduct variable selection among parametric accelerated failure time (AFT) models with mixed effects (i.e., with a shared frailty parameter). The determination of the best estimates was done via mean sums of squares and the computational costs. We propose to use the penalized quasi-likelihood (PQL) approach with an induced penalty to our selection process. We used this method to compare with other penalty functions in mixed models and evaluated their performance under censoring.