In this article, we present a Bayesian hierarchical model for predicting a latent health state from longitudinal clinical measurements. Model development is motivated by the need to integrate multiple sources of data to improve clinical decisions about whether to remove or irradiate a patient's prostate cancer. Existing modeling approaches are extended to accommodate measurement error in cancer state determinations based on biopsied tissue, clinical measurements possibly not missing at random, and informative partial observation of the true state. The proposed model enables estimation of whether an individual's underlying prostate cancer is aggressive, requiring surgery and/or radiation, or indolent, permitting continued surveillance. These individualized predictions can then be communicated to clinicians and patients to inform decision-making. We demonstrate the model with data from a cohort of low-risk prostate cancer patients at Johns Hopkins University and assess predictive accuracy among a subset for whom true cancer state is observed. Simulation studies confirm model performance and explore the impact of adjusting for informative missingness on true state predictions. R code is provided in an online supplement and at http://github.com/rycoley/prediction-prostate-surveillance.