This paper conducts a comprehensive analysis of information criteria such as Akaike's Information Criterion (AIC) and Bayesian Information Criterion (BIC) applied on survival analysis models, including the Cox Proportional Hazard Model, Linear Mixed Model (LMM), and Generalized Linear Mixed Model (GLMM). The aim is to identify the model that fits the data in the best way based on these criteria. The paper proposes the utilization of various survival models, including the Cox Proportional Hazard Model, LMM, and GLMM to handle non- linear data which leads to in accurate parameter estimates and comparing between them using the proposed criteria. The primary objective is to estimate the coefficients of these models using breast cancer data consisting of (96) patients. The models accuracy is assessed using two statistical criteria including AIC and BIC. The paper's findings demonstrate that, based on both AIC and BIC, the GLMM is the best fit for the application study with a value (120.4) for AIC and a value (179.1) for BIC. Also, the simulation study conducts that the best model fit at probabilities (0.2, 0.8) and sample size (50) is GLMM with (55.30) for AIC and (64.86) for BIC under exponential distribution, and the LMM under Weibull distribution with (61.61) for both AIC and BIC.