A comparative study of maximum likelihood and bayesian estimation approaches in estimating of gamma frailty mixture survival model parameters

Abstract

Frailty mixture survival models are survival models that allow for a cured fraction and frailty at the same time. This study applies Gamma frailty mixture survival model on time-to-recurrence data of leukaemia patients who received an autologous treatment. The model involves 4 unknown parameters including the long-term survivor parameter. The choice of estimation approaches is important, since the estimation of parameters will influent the accuracy and performance of the survival model. The estimation approaches that are often used in survival analysis are Maximum Likelihood (ML) and Bayesian estimation approaches. The study aims to compare the performance of Maximum Likelihood (ML) and Bayesian estimators of Gamma frailty mixture survival model in terms of their accuracy and efficiency by comparing their mean square error (MSE) and model fits using goodness of fit test. This study found that maximum likelihood estimators perform better than Bayesian estimators in obtaining the parameter of Gamma frailty mixture survival model of this study.