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Modeling longitudinal and survival data jointly offers many advantages suchas addressing measurement error and missing data in the longitudinal processes,understanding and quantifying the association between the longitudinal markersand the survival events and predicting the risk of events based on thelongitudinal markers. A joint model involves multiple submodels (one for eachlongitudinal/survival outcome) usually linked together through correlated orshared random effects. Their estimation is computationally expensive(particularly due to a multidimensional integration of the likelihood over therandom effects distribution) so that inference methods become rapidlyintractable, and restricts applications of joint models to a small number oflongitudinal markers and/or random effects. We introduce a Bayesianapproximation based on the Integrated Nested Laplace Approximation algorithmimplemented in the R package R-INLA to alleviate the computational burden andallow the estimation of multivariate joint models with fewer restrictions. Oursimulation studies show that R-INLA substantially reduces the computation timeand the variability of the parameter estimates compared to alternativeestimation strategies. We further apply the methodology to analyze 5longitudinal markers (3 continuous, 1 count, 1 binary, and 16 random effects)and competing risks of death and transplantation in a clinical trial on primarybiliary cholangitis. R-INLA provides a fast and reliable inference techniquefor applying joint models to the complex multivariate data encountered inhealth research.

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