标题： 二元结果预测规则的构建与评估：在存在缺失预测变量数据的情况下使用多重插补方法：理论视角与基于数据的评估 显示英文标题

标题： Construction and assessment of prediction rules for binary outcome in the presence of missing predictor data using multiple imputation: theoretical perspective and data-based evaluation

摘要： 我们研究在预测变量存在缺失值时，预后设计中预测规则的校准和评估问题。 我们的论文有两个关键目标，这两个目标是紧密交织在一起的。 第一个目标是研究如何将预测规则的校准与多重插补方法结合，以处理缺失的预测变量观测值。 第二个目标是提出可以使用当前多重插补软件实现的方法，同时允许通过在结果尚未可用的新观测值上进行验证来进行无偏预测评估。 为了明确方法论的定义，我们首先回顾多重插补作为模型估计方法的理论背景，而不是纯粹的算法描述。 我们特别对比了多重插补在参数（效应）估计中的应用与预测校准的应用。 基于这一回顾，形成了两种方法，其中第二种方法利用经典的Rubin规则进行参数估计，而第一种方法通过对单次插补拟合的模型计算概率，直接近似未来观测值的预测密度。 我们展示了使用当前软件的实现方式，这些软件允许对性能指标进行验证或交叉验证估计，以及在结果尚未观察到的未来数据中对预测变量的缺失数据进行插补。 我们始终限制讨论为二元结果和逻辑回归，尽管所讨论的原则通常适用。 我们提供了两个数据集作为我们常规咨询实践中的例子。 结果表明，对于准确性，不同方法之间的差异很小，但使用第一种方法时，校准概率的变异性有显著降低。 显示英文摘要

摘要： We investigate the problem of calibration and assessment of predictive rules in prognostic designs when missing values are present in the predictors. Our paper has two key objectives which are entwined. The first is to investigate how the calibration of the prediction rule can be combined with the use of multiple imputation to account for missing predictor observations. The second objective is to propose such methods that can be implemented with current multiple imputation software, while allowing for unbiased predictive assessment through validation on new observations for which outcome is not yet available. To inform the definition of methodology, we commence with a review of the theoretical background of multiple imputation as a model estimation approach as opposed to a purely algorithmic description. We specifically contrast application of multiple imputation for parameter (effect) estimation with predictive calibration. Based on this review, two approaches are formulated, of which the second utilizes application of the classical Rubin's rules for parameter estimation, while the first approach averages probabilities from models fitted on single imputations to directly approximate the predictive density for future observations. We present implementations using current software which allow for validatory or cross-validatory estimation of performance measures, as well as imputation of missing data in predictors on the future data where outcome is by definition as yet unobserved. We restrict discussion to binary outcome and logistic regression throughout, though the principles discussed are generally applicable. We present two data sets as examples from our regular consultative practice. Results show little difference between methods for accuracy but substantial reductions in variation of calibrated probabilities when using the first approach.