Misclassified variables used in regression models, either as a covariate or as the response, may lead to biased estimators and incorrect inference. Even though Bayesian models to adjust for misclassification error exist, it has not been shown how these models can be implemented using integrated nested Laplace approximation (INLA), a popular framework for fitting Bayesian models due to its computational efficiency. Since INLA requires the latent field to be Gaussian, and the Bayesian models adjusting for covariate misclassification error necessarily introduce a latent categorical variable, it is not obvious how to fit these models in INLA. Here, we show how INLA can be combined with importance sampling to overcome this limitation. We also discuss how to account for a misclassified response variable using INLA directly without any additional sampling procedure. The proposed methods are illustrated through a number of simulations and applications to real-world data, and all examples are presented with detailed code in the supporting information.

翻译：回归模型中使用的误分类变量（无论是作为协变量还是响应变量）可能导致估计量偏倚与推断错误。尽管存在用于校正误分类误差的贝叶斯模型，但尚未有研究展示如何通过集成嵌套拉普拉斯近似（INLA）这一因其计算效率而被广泛采用的贝叶斯模型拟合框架来实现这些模型。由于INLA要求潜场为高斯分布，而校正协变量误分类误差的贝叶斯模型必然引入潜分类变量，因此如何通过INLA拟合此类模型并不明确。本文提出将INLA与重要性采样相结合以突破此限制的方法。同时探讨如何直接利用INLA处理响应变量误分类问题，无需额外采样步骤。通过多组仿真实验和实际数据应用展示了所提方法的有效性，所有案例均附有支持信息中的详细代码说明。