具有错误分类结果的逻辑斯谛回归模型的全局可辨识性
On the global identifiability of logistic regression models with misclassified outcomes
摘要：
在过去的十年中，来自卫生系统的大数据（如电子健康记录）的二次利用在推进生物医学发现和改善临床决策方面显示出巨大的前景。然而，有一个越来越多的关注的偏见，在关联研究所造成的错误分类的二元结果来自电子健康记录。我们重新审视经典的逻辑斯谛回归模型与错误分类的结果。尽管在一些相关的设置中的局部识别条件已经建立，这种模式的全局识别仍然在很大程度上是未知的，是一个重要的问题还有待回答。我们得到了全局可识别的逻辑斯谛回归模型与错误分类的结果的必要和充分条件，使用一种新的方法称为子模型分析，和一种技术改编自皮卡德-Lindelöf存在定理在常微分方程。特别地，我们的结果适用于具有离散协变量的Logistic模型，这是生物医学研究中常见的情况，条件易于在实践中验证。除了模型的可识别性，我们提出了一个假设检验程序的回归系数在错误分类的逻辑斯谛回归模型时，模型是不可识别的空。
英文摘要：
In the last decade, the secondary use of large data from health systems, such as electronic health records, has demonstrated great promise in advancing biomedical discoveries and improving clinical decision making. However, there is an increasing concern about biases in association studies caused by misclassification in the binary outcomes derived from electronic health records. We revisit the classical logistic regression model with misclassified outcomes. Despite that local identification conditions in some related settings have been previously established, the global identification of such models remains largely unknown and is an important question yet to be answered. We derive necessary and sufficient conditions for global identifiability of logistic regression models with misclassified outcomes, using a novel approach termed as the submodel analysis, and a technique adapted from the Picard-Lindelöf existence theorem in ordinary differential equations. In particular, our results are applicable to logistic models with discrete covariates, which is a common situation in biomedical studies, The conditions are easy to verify in practice. In addition to model identifiability, we propose a hypothesis testing procedure for regression coefficients in the misclassified logistic regression model when the model is not identifiable under the null.
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