Correlated measurement error hampers association network inference

Abstract

Modern chromatography-based metabolomics measurements generate large amounts of data in the form of abundances of metabolites. An increasingly popular way of representing and analyzing such data is by means of association networks. Ideally, such a network can be interpreted in terms of the underlying biology. A property of chromatography-based metabolomics data is that the measurement error structure is complex: apart from the usual (random) instrumental error there is also correlated measurement error. This is intrinsic to the way the samples are prepared and the analyses are performed and cannot be avoided. The impact of correlated measurement errors on (partial) correlation networks can be large and is not always predictable. The interplay between relative amounts of uncorrelated measurement error, correlated measurement error and biological variation defines this impact. Using chromatography-based time-resolved lipidomics data obtained from a human intervention study we show how partial correlation based association networks are influenced by correlated measurement error. We show how the effect of correlated measurement error on partial correlations is different for direct and indirect associations. For direct associations the correlated measurement error usually has no negative effect on the results, while for indirect associations, depending on the relative size of the correlated measurement error, results can become unreliable. The aim of this paper is to generate awareness of the existence of correlated measurement errors and their influence on association networks. Time series lipidomics data is used for this purpose, as it makes it possible to visually distinguish the correlated measurement error from a biological response. Underestimating the phenomenon of correlated measurement error will result in the suggestion of biologically meaningful results that in reality rest solely on complicated error structures. Using proper experimental designs that allow for the quantification of the size of correlated and uncorrelated errors, can help to identify suspicious connections in association networks constructed from (partial) correlations.

Keywords: Figures-of-merit; Measurement design; Measurement error; Metabolomics.