In this article, 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 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 article, and show that the objective Bayesian method gives better performance under small sample sizes compared to maximum likelihood method.

在本文中，我们基于带有右删失数据的Weibull分布对混合固化模型进行客观的贝叶斯分析。通过引入潜在变量，给出了模型的完整似然函数，并通过近似获得了Fisher信息矩阵。我们通过EM算法获得最大似然估计，并得出客观先验，包括Jeffreys先验，参考先验和匹配概率先验以进行贝叶斯估计。仿真研究和真实数据分析说明了本文提出的方法，并表明与最大似然法相比，客观贝叶斯方法在小样本量下具有更好的性能。