Prediction and Inference With Missing Data in Patient Alert Systems

We describe the Bedside Patient Rescue (BPR) project, the goal of which is risk prediction of adverse events for non-intensive care unit patients using ∼100 variables (vitals, lab results, assessments, etc.). 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. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

本研究对床边患者救援（Bedside Patient Rescue, BPR）项目进行详细介绍，该项目旨在利用约100项变量（生命体征、实验室检验结果、临床评估指标等），针对非重症监护病房（non-intensive care unit, 简称非ICU）患者开展不良事件风险预测。多数患者存在若干缺失的预测变量值，这在健康科学领域属于普遍常态，而非特例。本研究提出一种贝叶斯（Bayesian）方法，可有效解决传统缺失预测变量处理范式的诸多缺陷：(i) 在贝叶斯框架（Bayesian paradigm）下，可直接处理由缺失值插补带来的不确定性；(ii) 预测变量分布可通过搭载隐变量的无限正态混合模型（infinite normal mixture with latent variables）实现灵活建模，以显式适配离散型预测变量（即类似多元概率单位回归模型（multivariate probit regression models）的处理逻辑）；(iii) 针对部分非随机缺失（missing not at random）场景，可通过将缺失标识（indicator of missingness）纳入预测变量分布、仅用于推断缺失变量的分布，实现高效处理。所提方法还可输出预测结果的完整分布，涵盖插补过程本身固有的不确定性。据此可开展针对性探究：例如，某患者是否存在高风险，但因缺失过多有效信息而无法确诊？若获取某一特定缺失变量的观测值，可在多大程度上降低风险预测的不确定性？将该方法应用于BPR项目场景后，其在识别病情恶化患者方面展现出优异的预测性能。本文的补充材料（含可复现研究的标准化材料说明）可通过在线补充资源获取。