Importance of Shrinkage in Empirical Bayes Estimates for Diagnostics: Problems and Solutions
Importance of Shrinkage in Empirical Bayes Estimates for Diagnostics: Problems and Solutions
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DOI：
10.1208/s12248-009-9133-0
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发表时间：
2009-09-01
期刊：
影响因子：
4.5
通讯作者：
Karlsson, Mats O.
中科院分区：
文献类型：
--
作者：
Savic, Radojka M.;Karlsson, Mats O.
S的经验贝叶斯估计(EBE)为模型师提供了诊断：EBE本身、个体预测(IPRED)和残差(个体加权残差)。当数据在个人层面上没有提供信息时，EBE分布将缩小到零(ETA-收缩，量化为1-SD(ETA(EBE))/omega)，IPRED向相应的观测值缩小，IWRES向零(epsilon-收缩，量化为1-SD(IWRES))。这些诊断方法被广泛应用于药代动力学(PK)药效学(PD)建模；我们在此研究它们在存在收缩的情况下的有效性。从一系列PK PD模型模拟数据集，基于真实或错误指定的模型在非线性混合效应建模中估计EBE，并对期望的诊断进行定性和定量评估。ETA收缩对基于EBE的模型诊断的已识别后果包括EBE的非正态和/或不对称分布，其平均值(“ETABAR”)明显不同于零，即使对于正确指定的模型也是如此；EBE-EBE相关性和协变量关系可能被掩盖、错误地诱导或真实关系的形状被扭曲。误差收缩的后果包括IPRED和IWRES分别诊断结构误差和残差模型错误的能力较低。只要存在显著的ETA或Ep收缩(通常大于20%至30%)，应谨慎解释基于EBE的诊断。报告Eta和epsilon收缩的幅度将有助于知情使用和解释基于EBE的诊断。
Empirical Bayes ("post hoc") estimates (EBEs) of eta s provide modelers with diagnostics: the EBEs themselves, individual prediction (IPRED), and residual errors (individual weighted residual (IWRES)). When data are uninformative at the individual level, the EBE distribution will shrink towards zero (eta-shrinkage, quantified as 1-SD(eta (EBE))/omega), IPREDs towards the corresponding observations, and IWRES towards zero (epsilon-shrinkage, quantified as 1-SD(IWRES)). These diagnostics are widely used in pharmacokinetic (PK) pharmacodynamic (PD) modeling; we investigate here their usefulness in the presence of shrinkage. Datasets were simulated from a range of PK PD models, EBEs estimated in non-linear mixed effects modeling based on the true or a misspecified model, and desired diagnostics evaluated both qualitatively and quantitatively. Identified consequences of eta-shrinkage on EBE-based model diagnostics include non-normal and/or asymmetric distribution of EBEs with their mean values ("ETABAR") significantly different from zero, even for a correctly specified model; EBE-EBE correlations and covariate relationships may be masked, falsely induced, or the shape of the true relationship distorted. Consequences of epsilon-shrinkage included low power of IPRED and IWRES to diagnose structural and residual error model misspecification, respectively. EBE-based diagnostics should be interpreted with caution whenever substantial eta- or epsilon-shrinkage exists (usually greater than 20% to 30%). Reporting the magnitude of eta- and epsilon-shrinkage will facilitate the informed use and interpretation of EBE-based diagnostics.