A New Approach for Multivariate Data Analysis in Interlaboratory Comparisons Based on Multidimensional Scaling and Robust Confidence Ellipse

Interlaboratory comparisons (IC) present a challenge related to multivariate data analysis. ISO 13528:2015 is a reference document for interlaboratory comparisons. This standard does not provide descriptions of statistical methods for multivariate analysis and, according to our best knowledge, there is no practical guidance for the organizing and evaluation of multivariate data analysis for interlaboratory comparisons available. Due to this reason, some researchers have made efforts to develop methodologies that make it possible to analyze multivariate data in IC. Generally, these approaches are based on dimensionality-reduction methods like principal component analysis. This paper proposes a new approach to reduce the dimensionality of large data set and check the performance of laboratories based on multidimensional scaling (MDS) and robust confidence ellipse/ellipsoid (RCE). MDS is a multivariate analysis technique that allows grouping laboratories according to their similarity in a Euclidean space. On the other hand, RCE is a statistical method for outlier detection in a multivariate data set. In this work, it is proposed to combine MDS and RCE to evaluate laboratory proficiency in interlaboratory comparison. This methodology was compared with the multivariate z-score and both methodologies identified the same outlying laboratories. This preliminary result indicates that MDS/RCE is promising for classifying IC results.

实验室间比对（Interlaboratory Comparisons, IC）面临多变量数据分析相关的挑战。ISO 13528:2015是实验室间比对的参考标准文件，但该标准未提供多变量分析的统计方法相关描述；据我们所知，目前尚无适用于实验室间比对的多变量数据分析的组织与评估的实用指南。鉴于此，已有研究者致力于开发可用于实验室间比对场景下多变量数据分析的方法，这类方法通常以主成分分析（Principal Component Analysis）等降维技术为基础。本文提出一种全新方法：基于多维标度（Multidimensional Scaling, MDS）与稳健置信椭圆/椭球（Robust Confidence Ellipsoid, RCE）对大规模数据集进行降维，并以此评估实验室表现。其中，多维标度是一种多变量分析技术，可依据实验室间的相似性在欧氏空间中完成分组；而稳健置信椭圆/椭球则是用于多变量数据集异常值检测的统计方法。本研究提出将MDS与RCE相结合，以评估实验室间比对中的实验室能力。将该方法与多变量z评分法进行对比后发现，两种方法识别出的异常实验室完全一致。这一初步结果表明，MDS/RCE方法在实验室间比对结果分类方面具有良好的应用前景。