Handling deviating control values in concentration-response curves

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{20}$$\end{document} 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 concentration-response 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.