BAYESIAN ESTIMATION OF PARETO SURVIVAL MODEL WITH INFORMATIVE PRIOR ON CENSORED DATA

Abstract

This research conducts a case of the cancer patients in censored data using Bayesian methodology. There are three types of loss function in Bayesian estimation method such as squared error loss function (self), linear exponential loss function (lelf) and general entropy loss function (gelf). Pareto survival model is selected as presentation data. To construct a posterior distribution, framing a likelihood function of Pareto and a prior, requires the prior distribution. An exponential distribution is chosen as a prior that describes parameter character of the Pareto. The posterior distribution is used to discover estimators in three loss functions of Bayesian methods. There are estimators held down by Bayesian self , Bayesian lelf  and Bayesian gelf  which substance 3.79, 3.78 and 3.90 correspondingly. After getting those estimators, the hazard functions  ,  and  and survival functions   ,  and  can be determined. The result shows that all of survival values under Bayesian approaches are lower than the real survival value. It means the result is more trusted because as a prior, the parameter is defined more precisely than before. The hazard function confirmations a same shape in all approaches. The rates of hazard are decreasing along with survival values which show the same behavior. The curves are strictly dropping after first data. This occurrence because due to a heavy-tailed character of Pareto.  The result indicates that MSE of parameter estimation under the Bayesian self, lelf and gelf are 1.3x10^-2, 1.2x10^-2 and 0 respectively. The mse of survival estimation under the Bayesian self, lelf and gelf are 10^-4, 1.1x10^-4 and 3x10^-5 individually. It concludes that the Bayesian gelf  is the best approximation.