Ferede Melkamu Molla, Nakhaei Rad Najmeh, Chen Ding-Geng
Department of Statistics, University of Gondar, Gondar, Ethiopia.
Department of Statistics, University of Pretoria, Pretoria, South Africa.
BMC Med Res Methodol. 2025 Sep 2;25(1):210. doi: 10.1186/s12874-025-02662-7.
Joint modeling is widely used in medical research to properly analyze longitudinal biomarkers and survival outcomes simultaneously and to guide appropriate interventions in public health. However, such models become increasingly complex and computationally intensive when accounting for multiple features of these outcomes. The need for computationally efficient methods in joint modeling of competing risks survival outcomes and longitudinal biomarkers is particularly critical in clinical and epidemiological settings, where prompt decision-making is essential. Moreover, there is very little literature on joint modeling of competing risks survival and skewed longitudinal data using Integrated Nested Laplace Approximations (INLA), despite its growing popularity in Bayesian inference. This paper presents a computationally efficient inference approach for modeling competing risks survival and skewed longitudinal data using INLA.
We propose cause-specific competing risks joint models with a semi-parametric mixed-effects longitudinal submodel and second-order random walk baseline hazards. The proposed models are reformulated as latent Gaussian models to enable efficient Bayesian inference using INLA. The INLA approach and its R packages are also presented. Various smoothing spline functions, distributions, and association structures were evaluated for both approaches. The INLAjoint and R2WinBUGS R packages were employed for the INLA and Markov-Chain Monte-Carlo (MCMC) approaches, respectively, to approximate the posterior marginals of the proposed joint models. Model comparisons and performance evaluations were performed using the deviance information criterion, relative bias, coverage probability, and root mean squared error.
We evaluated the computational efficiency and estimation performance of the INLA and MCMC approaches using real-world chronic kidney disease (CKD) follow-up data and an extensive confirmatory simulation study. We also conducted several model comparisons by considering different specifications related to smoothing spline approximations, non-Gaussian (skewed) distributions, and association structures to identify the best-fitting models for the CKD data and ensure robust statistical inference.
The application and simulation results revealed that both approaches provide accurate statistical estimation and inference. However, INLA significantly reduces the computational burden of the proposed joint models.
联合建模在医学研究中被广泛应用，以同时恰当地分析纵向生物标志物和生存结局，并指导公共卫生领域的适当干预措施。然而，当考虑这些结局的多个特征时，此类模型变得越来越复杂且计算量很大。在竞争风险生存结局和纵向生物标志物的联合建模中，对计算高效方法的需求在临床和流行病学环境中尤为关键，因为在这些环境中迅速做出决策至关重要。此外，尽管集成嵌套拉普拉斯近似法（INLA）在贝叶斯推断中越来越受欢迎，但关于使用该方法对竞争风险生存和偏态纵向数据进行联合建模的文献却非常少。本文提出了一种使用INLA对竞争风险生存和偏态纵向数据进行建模的计算高效的推断方法。
我们提出了特定病因的竞争风险联合模型，该模型具有半参数混合效应纵向子模型和二阶随机游走基线风险。所提出的模型被重新表述为潜在高斯模型，以便使用INLA进行高效的贝叶斯推断。还介绍了INLA方法及其R包。对两种方法都评估了各种平滑样条函数、分布和关联结构。分别使用INLAjoint和R2WinBUGS R包对INLA方法和马尔可夫链蒙特卡罗（MCMC）方法进行近似，以得到所提出联合模型的后验边缘分布。使用偏差信息准则、相对偏差、覆盖概率和均方根误差进行模型比较和性能评估。
我们使用真实世界的慢性肾脏病（CKD）随访数据和广泛的验证性模拟研究评估了INLA方法和MCMC方法的计算效率和估计性能。我们还通过考虑与平滑样条近似、非高斯（偏态）分布和关联结构相关的不同规格进行了几次模型比较，以确定CKD数据的最佳拟合模型，并确保稳健的统计推断。
应用和模拟结果表明，两种方法都能提供准确的统计估计和推断。然而，INLA显著降低了所提出联合模型的计算负担。
