This thesis focuses on two fundamental topics, specifically in medical statistics: the modelling of correlated survival datasets and the variable selection of the significant covariates and random effects. In particular, two types of survival data are considered: the classical survival datasets, where subjects are likely to experience only one type of event and the competing risks datasets, where subjects are likely to experience one of several types of event. In Chapter 2, among other topics, we highlight the importance of adding frailty terms on the proposed models in order to account for the association between the survival time and characteristics of subjects/groups.The main novelty of this thesis is to simultaneously select fixed effects and frailty terms through the proposed statistical models for each survival dataset. Chapter 3 covers the analysis of the classical survival dataset through the proposed Cox Proportional Hazard (PH) model. Utilizing a Cox PH frailty model, may increase the dimension of variable components and estimation of the unknown coefficients becomes very challenging. The method proposed for the analysis of classical survival datasets involves simultaneous variable selection on both fixed effects and frailty terms through penalty functions. The benefit of penalty functions is that they identify the non-significant parameters and set them to have a zero effect in the model. Hence, the idea is to ``doubly-penalize'' the partial likelihood of the Cox PH frailty model; one penalty for each term. Estimation and selection implemented through Newton-Raphson algorithms, whereas closed iterative forms for the estimation and selection of fixed effects and prediction of frailty terms were obtained. For the selection of frailty terms, penalties imposed on their variances since frailties are random effects. Based on the same idea, we further extend the simultaneous variable selection in the competing risks datasets in Chapter 4, using extended cause-specific frailty models. Two different scenarios are considered for frailty terms; in the first case we consider that frailty terms vary among different types of events (similar to the fixed effects) whereas in the second case we consider shared frailties over all the types of events. Moreover, our ``individual penalization'' approach allows for one covariate to be significant for some types of events, in contrast to the frequently used ``group-penalization'' where a covariate is entirely removed when it is not significant over all the events.For both proposed methods, simulation studies were conduced and showed that the proposed procedure followed for each analysis works well in simultaneously selecting and estimating significant fixed effects and frailty terms. The proposed methods are also applied to real datasets analysis; Kidney catheter infections, Diabetes Type 2 and Breast Cancer datasets. Association of the survival times and unmeasured characteristics of the subjects was studied as well as a variable selection for fixed effects and frailties implemented successfully.