Fast and flexible inference for joint models of multivariate longitudinal and survival data using Integrated Nested Laplace Approximations

TL;DR

This paper presents a fast Bayesian inference method using INLA for complex multivariate joint models of longitudinal and survival data, significantly reducing computation time and enabling more detailed health research analyses.

Contribution

The authors introduce an INLA-based approximation for joint models, allowing efficient estimation of multivariate data with multiple outcomes and random effects, overcoming previous computational limitations.

Findings

R-INLA reduces computation time significantly.

Parameter estimates show less variability with R-INLA.

Applied to clinical data with diverse markers and risks.

Abstract

Modeling longitudinal and survival data jointly offers many advantages such as addressing measurement error and missing data in the longitudinal processes, understanding and quantifying the association between the longitudinal markers and the survival events and predicting the risk of events based on the longitudinal markers. A joint model involves multiple submodels (one for each longitudinal/survival outcome) usually linked together through correlated or shared random effects. Their estimation is computationally expensive (particularly due to a multidimensional integration of the likelihood over the random effects distribution) so that inference methods become rapidly intractable, and restricts applications of joint models to a small number of longitudinal markers and/or random effects. We introduce a Bayesian approximation based on the Integrated Nested Laplace Approximation algorithm implemented in the R package R-INLA to alleviate the computational burden and allow the estimation of multivariate joint models with fewer restrictions. Our simulation studies show that R-INLA substantially reduces the computation time and the variability of the parameter estimates compared to alternative estimation strategies. We further apply the methodology to analyze 5 longitudinal markers (3 continuous, 1 count, 1 binary, and 16 random effects) and competing risks of death and transplantation in a clinical trial on primary biliary cholangitis. R-INLA provides a fast and reliable inference technique for applying joint models to the complex multivariate data encountered in health research.