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Hierarchical Bayesian models can be especially useful in precision medicinesettings, where clinicians are interested in estimating the patient-levellatent variables associated with an individual's current health state and itstrajectory. Such models are often fit using batch Markov Chain Monte Carlo(MCMC). However, the slow speed of batch MCMC computation makes it difficult toimplement in clinical settings, where immediate latent variable estimates areoften desired in response to new patient data. In this report, we discuss howimportance sampling (IS) can instead be used to obtain fast, in-clinicestimates of patient-level latent variables. We apply IS to the hierarchicalmodel proposed in Coley et al (2015) for predicting an individual's underlyingprostate cancer state. We find that latent variable estimates via IS cantypically be obtained in 1-10 seconds per person and have high agreement withestimates coming from longer-running batch MCMC methods. Alternative optionsfor out-of-sample fitting and online updating are also discussed.

Fast Out-of-Sample Predictions for Bayesian Hierarchical Models of Latent Health States