Cure models in survival analysis deal with populations in which a part of the individuals cannot experience the event of interest. Mixture cure models consider the target population as a mixture of susceptible and non-susceptible individuals. The statistical analysis of these models focuses on examining the probability of cure (incidence model) and inferring on the time to event in the susceptible subpopulation (latency model). Bayesian inference for mixture cure models has typically relied upon Markov chain Monte Carlo (MCMC) methods. The integrated nested Laplace approximation (INLA) is a recent and attractive approach for doing Bayesian inference but in its natural definition cannot fit mixture models. This paper focuses on the implementation of a feasible INLA extension for fitting standard mixture cure models. Our proposal is based on an iterative algorithm which combines the use of INLA for estimating the process of interest in each of the subpopulations in the study, and Gibbs sampling for computing the posterior distribution of the cure latent indicator variable which classifies individuals to the susceptible or non-susceptible subpopulations. We illustrated our approach by means of the analysis of two paradigmatic datasets in the framework of clinical trials. Outputs provide closing estimates and a substantial reduction of computational time in relation to those using MCMC.

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混合固化模型的近似贝叶斯推断

生存分析中的治疗模型处理的是某些个体无法体验到感兴趣事件的人群。混合治愈模型将目标人群视为易感人群和不易感人群的混合体。这些模型的统计分析着重于检查治愈的可能性（发病率模型）并推断易感亚群中事件发生的时间（潜伏期模型）。混合固化模型的贝叶斯推断通常依赖于马尔可夫链蒙特卡洛（MCMC）方法。集成嵌套拉普拉斯逼近（INLA）是一种最新且有吸引力的方法，用于进行贝叶斯推理，但其自然定义无法拟合混合模型。本文着重于实施适用于标准混合物固化模型的INLA扩展。我们的建议基于一种迭代算法，该算法结合使用INLA来估计研究中每个亚群的关注过程，以及使用Gibbs采样来计算治愈潜伏指标变量的后验分布，该变量将个体分类为易感人群或易感人群。非敏感亚群。我们通过在临床试验框架内分析两个范例数据集来说明我们的方法。与使用MCMC的输出相比，输出提供了接近的估计并大大减少了计算时间。Gibbs抽样用于计算治愈潜伏指标变量的后验分布，该变量将个体分类为易感或不易感亚群。我们通过在临床试验框架内分析两个范例数据集来说明我们的方法。与使用MCMC的输出相比，输出提供了接近的估计并大大减少了计算时间。Gibbs抽样用于计算治愈潜伏指标变量的后验分布，该变量将个体分类为易感或不易感亚群。我们通过在临床试验框架内分析两个范例数据集来说明我们的方法。与使用MCMC的输出相比，输出提供了接近的估计并大大减少了计算时间。