Prediction and Inference with Missing Data in Patient Alert Systems

Abstract:

We describe the Bed Side Patient Rescue (BPR) project, the goal of which is risk prediction of adverse events for non-ICU patients using ~150 variables (vital signs, 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 multiple imputation approach is presented that addresses many of the shortcomings to standard approaches to missing predictors: (i) treatment of multiple imputations is principled and straight-forward in the Bayesian paradigm, (ii) the predictor distribution is flexibly modeled as an infinite normal mixture via the Dirichlet process 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 (they are not included as part of the regression to maintain interpretability). This approach also has the major 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? Which missing predictor(s) would be the most beneficial to collect?