The impact of data transformations on concentration–response modeling

• Published in: Toxicology letters Vol. 213; no. 2; pp. 292 - 298
• Main Authors: Weimer, Marc, Jiang, Xiaoqi, Ponta, Oriana, Stanzel, Sven, Freyberger, Alexius, Kopp-Schneider, Annette
• Format: Journal Article
• Language: English
• Published: Shannon Elsevier Ireland Ltd 03-09-2012; Elsevier
• Subjects: Androgen Antagonists - pharmacology; Background correction; Biological and medical sciences; Computer Simulation; Concentration–response data; Data normalization; Dose-Response Relationship, Drug; EC50 estimation; Humans; Log-logistic model; Male; Medical sciences; Models, Statistical; Monte Carlo Method; Receptors, Androgen - metabolism; Regression Analysis; Toxicology; SC; Log-logistic model; EC50 estimation; Background correction; CI; NSB; Concentration–response data; Data normalization; CP; Activity concentration relation; Estimation; Concentration-response data; Logistic model; Modeling
• ISSN: 0378-4274; 1879-3169
• DOI: 10.1016/j.toxlet.2012.07.012

► Concentration–response data are often background corrected and normalized to control. ► A 4-parameter log-logistic function is often fitted to concentration–response data. ► EC50 estimate depends on the number of parameters in the log–logistic model. ► Parameters in the log-logistic model should be fixed only with compelling reason. ► Data transformation on does not affect EC50 estimate if the fitting function is kept.
Concentration–response studies are performed to investigate the potency of the substance under investigation. Data are typically evaluated using non-linear regression. A common model is the log-logistic model which includes parameters for lower and upper boundary of mean response, EC50 and Hill slope. Often, response and/or concentration data are transformed before proceeding with the analysis of their relationship. This is motivated by practical reasons, including comparability of results across different assays. We prove mathematically that a linear transformation of data will not change the EC50 and Hill slope estimates and only results in an identical transformation of the estimated parameters for lower and upper boundary of mean response. However, fixing some of the parameters may lead to erroneous estimates. This is of practical relevance when data are corrected for background signal and normalized by background corrected solvent control and a reduced model is used in which the response range is fixed between 100% and 0%. Computer simulations and a real data example are used to illustrate the impact of data transformations on parameter estimation. We further shed light on some common problems arising in the analysis of concentration–response data. Recommendations for practical implementation in concentration–response analysis are provided.