In recent years, mixture cure models have gained increasing popularity in survival analysis as an alternative to the Cox proportional hazards model, particularly in settings where a subset of patients is considered cured. The proportional hazards mixture cure model is especially advantageous when the presence of a cured fraction can be reasonably assumed, providing a more accurate representation of long-term survival dynamics. In this study, we propose a novel hierarchical Bayesian framework for the semiparametric mixture cure model, which accommodates both the inclusion and exclusion of a frailty component, allowing for greater flexibility in capturing unobserved heterogeneity among patients. Samples from the posterior distribution are obtained using a Markov chain Monte Carlo method, leveraging a hierarchical structure inspired by Bayesian Lasso. Comprehensive simulation studies are conducted across diverse scenarios to evaluate the performance and robustness of the proposed models. Bayesian model comparison and assessment are performed using various criteria. Finally, the proposed approaches are applied to two well-known datasets in the cure model literature: the E1690 melanoma trial and a colon cancer clinical trial.

翻译：近年来，混合治愈模型在生存分析中作为Cox比例风险模型的替代方案日益受到关注，特别是在部分患者被认为已治愈的研究场景中。当有理由假设存在治愈比例时，比例风险混合治愈模型尤其具有优势，能够更准确地刻画长期生存动态。本研究提出了一种新颖的分层贝叶斯框架，用于构建半参数混合治愈模型，该框架既可纳入也可排除脆弱性成分，从而在捕捉患者间未观测异质性方面具有更强的灵活性。通过采用受贝叶斯Lasso启发的分层结构，我们使用马尔可夫链蒙特卡罗方法从后验分布中获取样本。研究通过多种情境下的综合模拟实验，评估了所提模型的性能与稳健性。同时采用多种准则进行贝叶斯模型比较与评估。最后，将所提方法应用于治愈模型文献中两个经典数据集：E1690黑色素瘤试验和结肠癌临床试验。