This paper considers biomedical problems in which a sample of subjects, for example clinical patients, is monitored through time for purposes of individual prediction. Emphasis is on situations in which the monitoring generates data both in the form of a time series and in the form of events (development of a disease, death, etc.) observed on each subject over specified intervals of time. A Bayesian approach to the combined modeling of both types of data for purposes of prediction is presented. The proposed method merges ideas of Bayesian hierarchical modeling, nonparametric smoothing of time series data, survival analysis, and forecasting into a unified framework. Emphasis is on flexible modeling of the time series data based on stochastic process theory. The use of Markov chain Monte Carlo simulation to calculate the predictions of interest is discussed. Conditional independence graphs are used throughout for a clear presentation of the models. An application in the monitoring of transplant patients is presented