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