Department of Biostatistics, Boston University, 801 Massachusetts Avenue, Boston, MA 02118, USA.
Stat Med. 2011 May 30;30(12):1410-8. doi: 10.1002/sim.4196. Epub 2011 Feb 21.
In this paper we investigate the addition of new variables to an existing risk prediction model and the subsequent impact on discrimination quantified by the area under the receiver operating characteristics curve (AUC of ROC). Based on practical experience, concerns have emerged that the significance of association of the variable under study with the outcome in the risk model does not correspond to the significance of the change in AUC: that is, often the variable is significant, but the change in AUC is not. This paper demonstrates that under the assumption of multivariate normality and employing linear discriminant analysis (LDA) to construct the risk prediction tool, statistical significance of the new predictor(s) is equivalent to the statistical significance of the increase in AUC. Under these assumptions the result extends asymptotically to logistic regression. We further show that equality of variance-covariance matrices of predictors within cases and non-cases is not necessary when LDA is used. However, our practical example from the Framingham Heart Study data suggests that the finding might be sensitive to the assumption of normality.
在本文中，我们研究了向现有风险预测模型中添加新变量以及随后对接收者操作特征曲线（ROC 曲线下面积，AUC of ROC）衡量的区分度的影响。基于实际经验，人们开始关注到，研究变量与风险模型中结局的关联的显著性并不对应 AUC 变化的显著性：也就是说，通常情况下变量是显著的，但 AUC 的变化并不显著。本文表明，在多元正态性的假设下，并采用线性判别分析（LDA）来构建风险预测工具，新预测因子的统计学显著性等同于 AUC 增加的统计学显著性。在这些假设下，该结果渐近地扩展到 logistic 回归。我们进一步表明，当使用 LDA 时，病例和非病例之间的预测因子的方差-协方差矩阵相等并不是必需的。然而，我们来自弗雷明汉心脏研究数据的实际示例表明，这一发现可能对正态性假设敏感。
