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A novel extrapolation method is proposed for longitudinal forecasting. Ahierarchical Gaussian process model is used to combine nonlinear populationchange and individual memory of the past to make prediction. The predictionerror is minimized through the hierarchical design. The method is furtherextended to joint modeling of continuous measurements and survival events. Thebaseline hazard, covariate and joint effects are conveniently modeled in thishierarchical structure. The estimation and inference are implemented in fullyBayesian framework using the objective and shrinkage priors. In simulationstudies, this model shows robustness in latent estimation, correlationdetection and high accuracy in forecasting. The model is illustrated withmedical monitoring data from cystic fibrosis (CF) patients. Estimation andforecasts are obtained in the measurement of lung function and records of acuterespiratory events.  Keyword: Extrapolation, Joint Model, Longitudinal Model, HierarchicalGaussian Process, Cystic Fibrosis, Medical Monitoring

Joint Hierarchical Gaussian Process Model with Application to Forecast in Medical Monitoring