The class of semiparametric or transformation models has been presented in the literature as a promising alternative for the analysis of lifetime data in the presence of covariates and censored data. This class of models generalizes the popular class of proportional hazards models proposed by Cox (J R Stat Soc: Ser B (Methodol) 34(2):187–202, 1972) where it is not needed to assume a parametric probability distribution for the survival times. In addition to our focus on semipametric models, we also explore the situation where the population of interest is a mixture of susceptible individuals, who experience the event of interest and non-susceptible individuals that will never experience the event of interest. These individuals are not at risk with respect to the event of interest and are considered immune, non-susceptible, or cured. In this study, we present a simple method to obtain inferences for the parameters of semiparametric or transformation models in the presence of censoring, covariates and cure fraction under a Bayesian approach assuming the unknown hazard rates as latent variables with a given probability distribution. The posterior summaries of interest are obtained using existing Markov Chain Monte Carlo (MCMC) simulation methods. Some applications with real medical survival data illustrate the proposed methodology.

半参数或变换模型类已在文献中提出，作为在存在协变量和审查数据的情况下分析寿命数据的有前途的替代方案。此类模型概括了 Cox 提出的流行的比例风险模型（J R Stat Soc: Ser B (Methodol) 34(2):187–202, 1972），其中不需要假设生存的参数概率分布次。除了我们关注半参数模型之外，我们还探讨了这样的情况：感兴趣的群体是经历感兴趣事件的易感个体和永远不会经历感兴趣事件的非易感个体的混合体。这些人对于感兴趣的事件没有风险，并且被认为是免疫的、不受影响的或已治愈的。在本研究中，我们提出了一种简单的方法，在贝叶斯方法下，假设未知危险率作为具有给定概率分布的潜在变量，在存在审查、协变量和治愈率的情况下获得半参数或变换模型参数的推论。使用现有的马尔可夫链蒙特卡罗 (MCMC) 模拟方法获得感兴趣的后验摘要。一些具有真实医疗生存数据的应用说明了所提出的方法。