The Impact of Data Transformations on Concentration-response Modeling

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.