Gaussian variational approximate inference for joint models of longitudinal biomarkers and a survival outcome.

The shared random effects joint model is one of the most widely used approaches to study the associations between longitudinal biomarkers and a survival outcome and make dynamic risk predictions using the longitudinally measured biomarkers. Various types of joint models have been developed under different settings in the past decades. One major limitation of joint models is that they could be computationally expensive for complex models where the number of the shared random effects is large. Moreover, the inferential accuracy of joint models could also be diminished for complex models due to approximation errors. However, complex models are frequently needed in practice, for example, when the longitudinal biomarkers have nonlinear trajectories over time or the number of longitudinal biomarkers of interest is large. In this article, we propose a novel Gaussian variational approximate inference approach for fitting joint models, which significantly improves computational efficiency while maintaining inferential accuracy. We conduct extensive simulation studies to evaluate the performance of our proposed method and compare it to existing methods. The performance of our proposed method is further demonstrated on a dataset of patients with primary biliary cirrhosis.