混合硫化模型中用于贝叶斯推断的Laplacian-P-样条
Laplacian-P-splines for Bayesian inference in the mixture cure model
摘要：
用于分析生存数据的混合治愈模型的特征在于假设研究人群分为一组受试者，该组受试者将在有限的时间范围内发生关注事件，另一组治愈受试者无论随访持续时间如何都不会发生事件。当使用贝叶斯范式推断具有治愈分数的生存模型时，通常的做法是依靠马尔可夫链蒙特卡罗（MCMC）方法从后验分布中采样。虽然计算上可行，但MCMC的迭代性质通常意味着长采样时间来探索具有可能遭受缓慢收敛和不良混合的链的目标空间。本文提出了一种基于拉普拉斯近似和惩罚B样条的混合硫化模型快速、灵活的无采样贝叶斯推断方法。假设治愈比例为逻辑斯谛回归模型，并使用具有P样条近似基线风险的考克斯比例风险模型来指定易感受试者的条件生存函数。拉普拉斯近似的条件潜在向量是基于对数似然的梯度和海森的分析公式，从而大大加快了近似后验分布。在模拟研究中评估了所提出的拉普拉斯-P-样条混合曲线（LPSMC）模型的统计性能和计算效率。结果表明，LPSMC是一个有吸引力的替代经典MCMC近似贝叶斯推断在标准的混合硫化模型。最后，新的LPSMC方法说明了三个应用程序，涉及真正的生存数据。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
