Abstract–Much literature has focused on statistical inference for misclassified response variables or misclassified covariates. However, misclassification in both the response variable and the covariate has received very limited attention within applied fields and the statistics community. In situations where the response variable and the covariate are simultaneously subject to misclassification errors, an assumption of independent misclassification errors is often used for convenience without justification. This article aims to show the harmful consequences of inappropriate adjustment for joint misclassification errors. In particular, we focus on the wrong adjustment by ignoring the dependence between the misclassification process of the response variable and the covariate. In this article, the dependence of misclassification in both variables is characterized by covariance-type parameters. We extend the original definition of dependence parameters to a more general setting. We discover a single quantity that governs the dependence of the two misclassification processes. Moreover, we propose likelihood ratio tests to check the nondifferential/independent misclassification assumption in main study/internal validation study designs. Our simulation studies indicate that ignoring the dependent error structure can be even worse than ignoring all the misclassification errors when the validation data size is relatively small. The methodology is illustrated by a real data example.

摘要- 许多文献都集中在对错误分类的响应变量或错误分类的协变量的统计推断上。然而，两者的错误分类响应变量和协变量在应用领域和统计界受到的关注非常有限。在响应变量和协变量同时受到错误分类错误的情况下，通常为了方便而使用独立错误分类错误的假设而没有正当理由。本文旨在展示对联合错误分类错误进行不当调整的有害后果。特别是，我们通过忽略响应变量的错误分类过程和协变量之间的依赖性来关注错误调整。在本文中，两个变量中错误分类的相关性由协方差类型参数表征。我们将依赖参数的原始定义扩展到更一般的设置。我们发现了一个控制两个错误分类过程依赖性的单一数量。此外，我们提出似然比检验来检查主要研究/内部验证研究设计中的非差异/独立错误分类假设。我们的模拟研究表明，当验证数据量相对较小时，忽略相关错误结构可能比忽略所有错误分类错误更糟糕。该方法通过一个真实的数据示例来说明。我们的模拟研究表明，当验证数据量相对较小时，忽略相关错误结构可能比忽略所有错误分类错误更糟糕。该方法通过一个真实的数据示例来说明。我们的模拟研究表明，当验证数据量相对较小时，忽略相关错误结构可能比忽略所有错误分类错误更糟糕。该方法通过一个真实的数据示例来说明。