The mixture cure model for analyzing survival data is characterized by the assumption that the population under study is divided into a group of subjects who will experience the event of interest over some finite time horizon and another group of cured subjects who will never experience the event irrespective of the duration of follow-up. When using the Bayesian paradigm for inference in survival models with a cure fraction, it is common practice to rely on Markov chain Monte Carlo (MCMC) methods to sample from posterior distributions. Although computationally feasible, the iterative nature of MCMC often implies long sampling times to explore the target space with chains that may suffer from slow convergence and poor mixing. An alternative strategy for fast and flexible sampling-free Bayesian inference in the mixture cure model is suggested in this paper by combining Laplace approximations and penalized B-splines. A logistic regression model is assumed for the cure proportion and a Cox proportional hazards model with a P-spline approximated baseline hazard is used to specify the conditional survival function of susceptible subjects. Laplace approximations to the conditional latent vector are based on analytical formulas for the gradient and Hessian of the log-likelihood, resulting in a substantial speed-up in approximating posterior distributions. The statistical performance and computational efficiency of the proposed Laplacian-P-splines mixture cure (LPSMC) model is assessed in a simulation study. Results show that LPSMC is an appealing alternative to classic MCMC for approximate Bayesian inference in standard mixture cure models. Finally, the novel LPSMC approach is illustrated on three applications involving real survival data.
翻译:用于分析生存数据的混合治愈模型的特点是,假设研究中的人口被分成一组主题,在一定的时间跨度内会经历感兴趣的事件,而另一组被治愈的主体将经历感兴趣的事件,无论后续时间长短,都不会经历这种事件。在使用巴伊西亚模式在生存模型中用解药分数进行推断时,通常的做法是依靠Markov连锁Monte Carlo(MCMC)方法从后天分布样本进行取样。虽然计算上可行,但MCMC的迭代性质往往意味着要花很长的取样时间来探索目标空间,其链可能因缓慢趋同和混合不良而受到影响。本文建议采用另一种战略,在混合物治愈模型中采用快速和灵活无采样的巴伊斯推断,无论后续时间长短如何。如果使用巴伊西亚模式将拉贝近似和受惩罚的B-SP线结合起来,则通常采用一个物流回归模型,用于治疗比例的Cox比例危害模型,并使用一种P-spline基准危险模型来确定易感性对象的有条件生存功能。 Laple Pass对有条件的潜矢量矢量矢量矢量矢量是用于代和Hes make-Lsal-macal-Lsal-Lsal-Lsal-maxim sal-al-salal-al-sal-sal-simpal sal-s exalmaildal-s exalmadaldalisalisalisalisalmadalisaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldaldald