Improving concentration–response analysis by handling outlier concentrations

Concentration–response curves model the relationship between a concentration of a compound and the response it elicits in a biological system, such as the viability of cells. A primary objective is to estimate an alert concentration, meaning the concentration at which a predefined effect level is reached. These values are typically derived from parametric models fitted to the data. Therefore, accurately modeling the concentration–response relationship is essential for understanding the safety and potency of compounds. However, due to errors or biological variability, it is often observed that measurements at individual concentration levels deviate from the typically assumed sigmoidal models. Such deviations in the data can compromise the accuracy of the estimation of alert concentrations. Due to the usually very low number of measured concentrations, identifying these deviations is challenging. Here, we simulated data for different scenarios of possible deviations at each individual concentration level. We propose several statistical methods that can mitigate the impact of such deviations. Two methods identify the deviations and eliminate the data of the corresponding concentrations from the curve fitting process. Three methods use different weighting approaches to assign lower weights to deviating values. All methods are compared with a baseline method that disregards deviations on how accurately they estimate the true E C 20 value. Methods that remove concentrations with deviations perform best on average, but they perform notably worse if correct data are mistakenly excluded.