Present research deals with the extension of the Cox model that allows for heterogeneity due to omitted covariates using frailty (random effect) approach, and thereby uses a more general class of mixed-modeling that estimates predictors via non-parametric regression. The basic motivation is to compare several approaches of frailty estimation methods: gamma shared frailty estimation by Nielsen et al. [1992] (EM algorithm approach, later approximated by Penalized Partial Likelihood solution [Therneau and Grambsch, 2000]), Gaussian shared frailty estimation by McGilchrist and Aisbett[1991] (REML estimation approach, later approximated by Penalized Partial Likelihood solution [Therneau and Grambsch, 2000]) and Ripatti and Palmgren [2000] (Approximate Marginal Likelihood approach). Judging against each other, the estimates obtained from these approaches, an attempt has been made to pinpoint situations in which the particular frailty estimation approaches are appropriate to apply. In order to do so, comparable simulated survival data have been generated (controlled with respect to sample size, its composition, amount of prevailing censoring, postulated frailty distribution and true frailty parameter - implementing all these in a self-written R program). It has been found that, for small sample sizes, frailty approaches have no precedence over conventional Cox Model [Cox, 1972], provided the mentioned heterogeneity is not unusually high. However, when the purpose of the study is to estimate regression coefficients as precisely as possible, approach of Nielsen et al. [1992] is found to be the supreme for moderate sample sizes. For large sample cases, estimates from McGilchrist and Aisbett [1991]'s approach has less mean squared error. But, if the principal objective is to obtain estimate of frailty parameter (heterogeneity parameter) closest to the true value, the approach of Ripatti and Palmgren [2000] is the best choice.