Computationally efficient Bayesian inference for semi-parametric joint models of competing risks survival and skewed longitudinal data using integrated nested Laplace approximation.

Background: 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.

Methods: 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.

Results: 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.

Conclusion: 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.