Meta回归模型的异常值识别及其修正

Outlier Detection and Accommodation in Meta-regression Model

基于异常值对异质性参数和回归系数估计同时影响的这一新视角下,文章利用方差加权异常值模型(variance-weight outlier model,VWOM)研究了随机效应Meta回归模型的多个异常值识别及其修正问题。首先,推导出Meta回归VWOM分别使用ML和REML估计方法的Score(SC)检验统计量,并考虑Meta回归VWOM的三种扰动方式,包括全局方差扰动,个体方差扰动和随机误差扰动,证明了三种方差扰动的SC检验统计量是等价的。其次,基于异常值对异质性参数和回归系数估计同时影响的考虑,提出了随机效应Meta回归方差加权异常值修正模型(variance-weight outlier modified model,VWOMM),并给出了VWOMM参数的ML和REML估计迭代算法并进行数值求解。此外,通过随机模拟分析验证了SC检验统计量的尺度和功效。最后,利用两个不同类型效应量异常值识别及其处理的实例分析结果,表明了Meta回归VWOM的SC检验统计量识别效果较为显著,VWOMM能有效改善模型拟合程度,为识别和处理复杂数据的异常值提供了一种新的思路和方法。

Based on the new perspective of the simultaneous infuence of outliers on the estimation of heterogeneity parameters and regression coefficients,the variance-weight outlier model(VWOM)is used to study the multiple outliers detection in the random effects meta-regression model and its accommodation in the paper.Firstly,the Score(SC)test statistics is derived for the meta-regression VWOM using ML and REML estimation methods respectively,furthermore,three perturbation methods of meta regression VWOM are taken into consideration including global variance perturbation,individual variance perturbation and random error perturbation,and moreover,the equivalence of SC test statistics for three kinds of variance perturbations is proved.Secondly,based on the consideration of the influence of outliers on the heterogeneity parameters and regression coefficient estimates simultaneously,random effect meta-regression variance-weighted outlier modified model(VWOMM)is proposed,and the ML and REML estimation iterative algorithms for VWOMM model parameters are derived by numerical method.In addition,the size and power of SC test statistics are verified by random simulation analysis.Finally,based on the analysis results of two different types of effect size outlier detection and accommodation examples,it shows that the meta-regression VWOM test statistics recognition effect is more significant,VWOMM can effectively improve the degree of model fitting,for identifying and processing complex data of outliers provide a new idea and method.