Long before human-to-human transplantation was ever imagined by the public, scientists were conducting pioneering medical and surgical research that would eventually lead to today's transplantation successes. The Cox proportional hazards model has become the model of choice in the analysis of time to event data in survival analysis. It is evident that Cox proportional hazard model is not always appropriate and the Accelerated Failure Time (AFT) model provides a better alternative for variable selection in survival analysis. If the effects of treatment are to accelerate (or delay) the event of interest rather than having a longer term impact, in the context of the trial duration, on the occurrence of the event, then the accelerated failure time model should replace the proportional hazards model as the model of choice. For a detailed study refer to Kay and Kinnersley (2002). In this paper it is proposed to study the Cox’s Proportional Hazards and AFT Model for Heart Transplantation Data. Numerical examples are also provided.