  We describe the Bedside Patient Rescue (BPR) project, the goal of which is
risk prediction of adverse events for non-ICU patients using ~200 variables
(vitals, lab results, assessments, ...). There are several missing predictor
values for most patients, which in the health sciences is the norm, rather than
the exception. A Bayesian approach is presented that addresses many of the
shortcomings to standard approaches to missing predictors: (i) treatment of the
uncertainty due to imputation is straight-forward in the Bayesian paradigm,
(ii) the predictor distribution is flexibly modeled as an infinite normal
mixture with latent variables to explicitly account for discrete predictors
(i.e., as in multivariate probit regression models), and (iii) certain missing
not at random situations can be handled effectively by allowing the indicator
of missingness into the predictor distribution only to inform the distribution
of the missing variables. The proposed approach also has the benefit of
providing a distribution for the prediction, including the uncertainty inherent
in the imputation. Therefore, we can ask questions such as: is it possible this
individual is at high risk but we are missing too much information to know for
sure? How much would we reduce the uncertainty in our risk prediction by
obtaining a particular missing value? This approach is applied to the BPR
problem resulting in excellent predictive capability to identify deteriorating
patients.
