Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat), Data Science Institute, Hasselt University, Hasselt, Belgium.
Centre for Health Economics Research and Modelling Infectious Diseases, Vaxinfectio, University of Antwerp, Antwerp, Belgium.
Stat Med. 2022 Jun 30;41(14):2602-2626. doi: 10.1002/sim.9373. Epub 2022 Mar 14.
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. Furthermore, extra efforts have to be invested in diagnostic checks to monitor the reliability of the generated posterior samples. A sampling-free strategy for fast and flexible Bayesian inference in the mixture cure model is suggested in this article 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 posterior 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 spline specification yields smooth estimates of survival curves and functions of latent variables together with their associated credible interval are estimated in seconds. A fully stochastic algorithm based on a Metropolis-Langevin-within-Gibbs sampler is also suggested as an alternative to the proposed Laplacian-P-splines mixture cure (LPSMC) methodology. The statistical performance and computational efficiency of LPSMC is assessed in a simulation study. Results show that LPSMC is an appealing alternative to MCMC for approximate Bayesian inference in standard mixture cure models. Finally, the novel LPSMC approach is illustrated on three applications involving real survival data.
混合治愈模型用于分析生存数据，其特点是假设研究人群分为两组：一组是在有限的时间内经历感兴趣事件的受试者，另一组是无论随访时间多长都不会经历事件的治愈受试者。在使用贝叶斯推断范式进行具有治愈分数的生存模型推断时，通常依赖于马尔可夫链蒙特卡罗（MCMC）方法从后验分布中采样。虽然在计算上是可行的，但 MCMC 的迭代性质通常意味着需要很长的采样时间来探索可能存在缓慢收敛和混合不良的链的目标空间。此外，需要额外的努力进行诊断检查，以监测生成的后验样本的可靠性。本文提出了一种在混合治愈模型中进行快速灵活的贝叶斯推断的无采样策略，该策略结合了拉普拉斯近似和惩罚 B 样条。假设治愈比例为逻辑回归模型，并使用 Cox 比例风险模型和 P 样条近似基线风险来指定易感受试者的条件生存函数。对后验条件潜在向量的拉普拉斯近似是基于对数似然的梯度和 Hessian 的解析公式，这导致在后验分布的近似中大大加快了速度。样条指定产生了生存曲线和潜在变量的函数的平滑估计，并且可以在几秒钟内估计它们的相关可信区间。还提出了一种基于 Metropolis-Langevin-within-Gibbs 采样器的完全随机算法作为对所提出的拉普拉斯-P 样条混合治愈（LPSMC）方法的替代方法。在模拟研究中评估了 LPSMC 的统计性能和计算效率。结果表明，LPSMC 是标准混合治愈模型中近似贝叶斯推断的 MCMC 的一种有吸引力的替代方法。最后，将新的 LPSMC 方法应用于三个涉及真实生存数据的应用。
