Cellwise outlier detection and biomarker identification in metabolomics based on pairwise log ratios

Abstract

Data outliers can carry very valuable information and might be most informative for the interpretation. Nevertheless, they are often neglected. An algorithm called cellwise outlier diagnostics using robust pairwise log ratios (cell-rPLR) for the identification of outliers in single cell of a data matrix is proposed. The algorithm is designed for metabolomic data, where due to the size effect, the measured values are not directly comparable. Pairwise log ratios between the variable values form the elemental information for the algorithm, and the aggregation of appropriate outlyingness values results in outlyingness information. A further feature of cell-rPLR is that it is useful for biomarker identification, particularly in the presence of cellwise outliers. Real data examples and simulation studies underline the good performance of this algorithm in comparison with alternative methods.

Multivariate Outlier Detection in Applied Data Analysis: Global, Local, Compositional and Cellwise Outliers

“…Subject matter knowledge is helpful for this step in order to determine the reasonability of irregularity. If they are kept (Walach et al 2019) as they are, it is recommended that robust statistical techniques be applied for subsequent analysis, since such methods automatically downweight outlying observations (according to the statistical model) due to their degree of outlyingness. The outlier detection methods employed here were based on the assumption that the data majority is originating from a multivariate normal distribution-after they have been expressed in coordinates in the case of compositional data.…”

“…As a result, identification of cellwise outlyingness requires modern approaches to multivariate outlier detection that are able to handle both cellwise and casewise (row-wise) outliers. Recent approaches to cellwise outlier detection are based on the adapted Stahel-Donoho estimator (Van Aelst 2016), the generalized S-estimator (Agostinelli et al 2015), cellwise prediction models (Rousseeuw and Bossche 2018), and the pairwise logratios of the variables (Walach et al 2019). Here, the focus is on the cellwise outlier detection techniques presented in Rousseeuw and Bossche (2018) and Walach et al (2019).…”

“…Sparse data sets might pose a problem as well. An alternative cellwise-outlier detection algorithm called cell-rPLR is presented by Walach et al (2019). Information regarding the cellwise outlyingness of an observation is obtained through the robustly centred and scaled logratio of pairs of its variables and the use of a weight function called the outlyingness function.…”

“…Note that the visualized colour scheme and outlier approach depends mainly on the chosen outlyingness function. In the simulation study described in Walach et al (2019), the DDC method and cell-rPLR were compared, and it was found that cell-rPLR had superior performance in terms of accuracy and misclassification of regular observations. However, it must be mentioned that DDC does not make use of grouping information, while cell-rPLR does.…”

“…It can be seen that in the area of Monchegorsk (distance zero), Cu is very dominant in the composition, and these values reach the background at a distance of about 100 km. The cellwise outlier procedure of Walach et al (2019) is applied, and the result is shown in Fig. 7.…”