用于诊断共享脆弱性模型的交叉验证Z-残差
Cross-validatory Z-Residual for Diagnosing Shared Frailty Models
摘要：
残差诊断方法在评估模型假设和检测统计建模中的异常值方面发挥着关键作用。在具有删失观察值的生存模型的背景下，Li等人（2021）引入了Z残差，其在真实模型下近似遵循正态分布。这个属性使得可以使用Z残差来诊断生存模型，其方式类似于Pearson残差在正态回归中的使用方式。然而，基于完整数据集计算残差可能会导致保守偏倚，从而降低检测模型错误指定的能力，因为相同的数据集用于模型拟合和验证。虽然交叉验证是解决这个问题的一种潜在方法，但由于计算上的挑战，它还没有被广泛用于残差诊断。在本文中，我们提出了一个交叉验证方法计算Z-残差的背景下，共享的脆弱性模型。具体来说，我们开发了一个通用函数，使用R中\texttt{survival}包中的\texttt{coxph}函数的输出计算交叉验证Z残差。我们的模拟研究表明，对于拟合优度检验和离群值检测，交叉验证Z残差比没有交叉验证的Z残差更强大，更具鉴别力。我们还比较了Z-残差的性能，以及在没有交叉验证的情况下，在对肾脏感染患者的复发时间进行建模的实际应用中识别离群值。我们的研究结果表明，交叉验证Z残差可以识别Z残差遗漏的离群值，而无需交叉验证。
英文摘要：
Residual diagnostic methods play a critical role in assessing model assumptions and detecting outliers in statistical modelling. In the context of survival models with censored observations, Li et al. (2021) introduced the Z-residual, which follows an approximately normal distribution under the true model. This property makes it possible to use Z-residuals for diagnosing survival models in a way similar to how Pearson residuals are used in normal regression. However, computing residuals based on the full dataset can result in a conservative bias that reduces the power of detecting model mis-specification, as the same dataset is used for both model fitting and validation. Although cross-validation is a potential solution to this problem, it has not been commonly used in residual diagnostics due to computational challenges. In this paper, we propose a cross-validation approach for computing Z-residuals in the context of shared frailty models. Specifically, we develop a general function that calculates cross-validatory Z-residuals using the output from the \texttt{coxph} function in the \texttt{survival} package in R.Our simulation studies demonstrate that, for goodness-of-fit tests and outlier detection, cross-validatory Z-residuals are significantly more powerful and more discriminative than Z-residuals without cross-validation. We also compare the performance of Z-residuals with and without cross-validation in identifying outliers in a real application that models the recurrence time of kidney infection patients. Our findings suggest that cross-validatory Z-residuals can identify outliers that are missed by Z-residuals without cross-validation.
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