Handling deviating control values in concentration-response curves
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BIOINFORMATICS AND STATISTICS
Handling deviating control values in concentration‑response curves Franziska Kappenberg1 · Tim Brecklinghaus2 · Wiebke Albrecht2 · Jonathan Blum3 · Carola van der Wurp1 · Marcel Leist3 · Jan G. Hengstler2 · Jörg Rahnenführer1 Received: 28 May 2020 / Accepted: 14 September 2020 © The Author(s) 2020
Abstract In cell biology, pharmacology and toxicology dose-response and concentration-response curves are frequently fitted to data with statistical methods. Such fits are used to derive quantitative measures (e.g. EC20 values) describing the relationship between the concentration of a compound or the strength of an intervention applied to cells and its effect on viability or function of these cells. Often, a reference, called negative control (or solvent control), is used to normalize the data. The negative control data sometimes deviate from the values measured for low (ineffective) test compound concentrations. In such cases, normalization of the data with respect to control values leads to biased estimates of the parameters of the concentrationresponse curve. Low quality estimates of effective concentrations can be the consequence. In a literature study, we found that this problem occurs in a large percentage of toxicological publications. We propose different strategies to tackle the problem, including complete omission of the controls. Data from a controlled simulation study indicate the best-suited problem solution for different data structure scenarios. This was further exemplified by a real concentration-response study. We provide the following recommendations how to handle deviating controls: (1) The log-logistic 4pLL model is a good default option. (2) When there are at least two concentrations in the no-effect range, low variances of the replicate measurements, and deviating controls, control values should be omitted before fitting the model. (3) When data are missing in the no-effect range, the Brain-Cousens model sometimes leads to better results than the default model. Keywords Concentration-response curve · Dose-response curve · Viability assay · Deviating controls · 4pLL model · Simulation study
Introduction Concentration-response curves are often used to graphically describe the relationship between the concentration of a compound applied to cells and the resulting response. More general, any response of a cell or an organism to an Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00204-020-02913-0) contains supplementary material, which is available to authorized users. * Franziska Kappenberg [email protected]‑dortmund.de 1
Department of Statistics, TU Dortmund University, 44221 Dortmund, Germany
2
Leibniz Research Centre for Working Environment and Human Factors (IfADo), TU Dortmund University, 44139 Dortmund, Germany
3
Department of Biology, University of Konstanz, 78457 Constance, Germany
exposure or stimulus can be modeled as a function of exposure time or as a function of a concentration or dos
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