  A novel extrapolation method is proposed for longitudinal forecasting. A
hierarchical Gaussian process model is used to combine nonlinear population
change and individual memory of the past to make prediction. The prediction
error is minimized through the hierarchical design. The method is further
extended to joint modeling of continuous measurements and survival events. The
baseline hazard, covariate and joint effects are conveniently modeled in this
hierarchical structure. The estimation and inference are implemented in fully
Bayesian framework using the objective and shrinkage priors. In simulation
studies, this model shows robustness in latent estimation, correlation
detection and high accuracy in forecasting. The model is illustrated with
medical monitoring data from cystic fibrosis (CF) patients. Estimation and
forecasts are obtained in the measurement of lung function and records of acute
respiratory events.
  Keyword: Extrapolation, Joint Model, Longitudinal Model, Hierarchical
Gaussian Process, Cystic Fibrosis, Medical Monitoring
