Evaluating Trauma Patients: Addressing Missing Covariates with Joint Optimization

Missing values are a common problem when applying classification algorithms to real-world medical data. This is especially true for trauma patients, where the emergent nature of the cases makes it difficult to collect all of the relevant data for each patient. Standard methods for handling missingness first learn a model to estimate missing data values, and subsequently train and evaluate a classifier using data imputed with this model. Recently, several proposed methods have demonstrated the benefits of jointly estimating the imputation model and classifier parameters. However, these methods make assumptions that limit their utility with many real-world medical datasets. For example, the assumption that data elements are missing at random is often invalid.We address this situation by exploring a novel approach for jointly learning the imputation model and classifier. Unlike previous algorithms, our approach makes no assumptions about the missingness of the data, can be used with arbitrary probabilistic data models and classification loss functions, and can be used when both the training and testing data have missing values. We investigate the utility of this approach on the prediction of several patient outcomes in a large national registry of trauma patients, and find that it significantly outperforms standard sequential methods.

[1]  D. Rubin,et al.  Statistical Analysis with Missing Data. , 1989 .

[2]  E. DeLong,et al.  Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach. , 1988, Biometrics.

[3]  Michael I. Jordan,et al.  Supervised learning from incomplete data via an EM approach , 1993, NIPS.

[4]  Thomas Hofmann,et al.  Kernel Methods for Missing Variables , 2005, AISTATS.

[5]  Lawrence Carin,et al.  Incomplete-data classification using logistic regression , 2005, ICML.

[6]  E. Finkelstein,et al.  Incidence and Economic Burden of Injuries in the United States , 2006 .

[7]  Pieter Abbeel,et al.  Max-margin classification of incomplete data , 2006, NIPS.

[8]  Hui Li,et al.  Quadratically gated mixture of experts for incomplete data classification , 2007, ICML '07.

[9]  Lawrence Carin,et al.  On Classification with Incomplete Data , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Peter Haider,et al.  Learning from incomplete data with infinite imputations , 2008, ICML '08.

[11]  M. Pencina,et al.  Evaluating the added predictive ability of a new marker: From area under the ROC curve to reclassification and beyond , 2008, Statistics in medicine.

[12]  Aníbal R. Figueiras-Vidal,et al.  Pattern classification with missing data: a review , 2010, Neural Computing and Applications.

[13]  M. Kenward,et al.  Multiple imputation for missing data in epidemiological and clinical research: potential and pitfalls , 2009, BMJ : British Medical Journal.

[14]  David Grangier,et al.  Feature Set Embedding for Incomplete Data , 2010, NIPS.

[15]  David B. Dunson,et al.  Classification with Incomplete Data Using Dirichlet Process Priors , 2010, J. Mach. Learn. Res..

[16]  Stef van Buuren,et al.  MICE: Multivariate Imputation by Chained Equations in R , 2011 .