Integrated nested Laplace approximation to combine multiple time-varying markers in joint model prediction of a bounded-range outcome

Music City Center 

Joint modelling is an attractive approach for prediction of longitudinally observed outcomes and causal inference, based on time-varying markers. Unfortunately, the application and development of this methodology is still hampered by speed and optimization problems in model estimation and above all in reaching sufficient scale for realistic practical application, especially through restrictions on the number of longitudinally recorded parameters which can be used for prediction of outcomes. Integrated nested Laplace approximations can address some of these problems by implementing a deterministic form of estimation which is both speedy and accurate, while still facilitating prediction application. We discuss application in a study on Duchenne muscular dystrophy at the Leiden University Medical Centre where multiple longitudinally tracked proteins must be combined to predict a bounded-range time-varying functional outcome score. A joint model is formulated which utilizes a beta-density outcome model for the time-dependent outcome, linked to the multiple protein predictors using the so-called scaled-predictor parametrization. Estimation through the integrated nested Laplace approach and results from a data analytic application are demonstrated.