Objective Bayesian Analysis Of Mixture Cure Model

In clinical trials,it is vital to study whether and when the endpoint events occur in the researches.With the progress of medical level and industrial technology,sometimes it can be found that some individuals will never experience the endpoint events in the observation period,and these individuals are called cured ones.Mixture cure model is a useful tool to study the problem of cure rate,and it is also a hotspot in the research fields of survival analysis and reliability analysis.However,most of the related researches are mainly based on the maximum likelihood methods and the subjective Bayesian methods,and the application of the objective Bayesian methods in the mixture cure model is still a blank in research.In this paper,we conduct objective Bayesian analysis for the mixture cure model based on the Weibull distribution with right-censored data.By introducing latent variables,the complete likelihood function of the model is given and from that the Fisher information matrix is obtained by approximation.We obtain the maximum likelihood estimates(MLEs)by EM algorithm,and derive objective priors including Jeffreys prior,reference priors and matching probability priors to carry out Bayesian estimation.A simulation study and a real data analysis illustrate the methods proposed in this paper,and show that the objective Bayesian method gives better performance under small sample sizes compared to maximum likelihood method.