Motivation: In biomedicine, every molecular measurement is relative to a reference point, like a fixed aliquot of RNA extracted from a tissue, a defined number of blood cells, or a defined volume of biofluid. Reference points are often chosen for practical reasons. For example, we might want to assess the metabolome of a diseased organ but can only measure metabolites in blood or urine. In this case the observable data only indirectly reflects the disease state. The statistical implications of

more »

... hese discrepancies in reference points have not yet been discussed. Results: Here we show that reference point discrepancies compromise the performance of regression models like the LASSO. As an alternative, we suggest zero-sum regression for a reference point insensitive analysis. We show that zero-sum regression is superior to the LASSO in case of a poor choice of reference point both in simulations and in an application that integrates intestinal microbiome analysis with metabolomics. Moreover, we describe a novel coordinate descent based algorithm to fit zero-sum elastic nets. Availability: The R-package "zeroSum" can be downloaded at https://github.com/rehbergT/zeroSum. Moreover, we provide all R-scripts and data used to produce the results of this manuscript as supplementary material.