Nonlinear model-based estimates of IC50 for studies involving continuous therapeutic dose–response data

We present statistical details for estimating an in vitro 50% inhibitory concentration (IC50), based on several models for continuous response data fit to bone-marrow endothelial cell lines replicated in vehicle and at several dose increments. Nonlinear models are fit via maximum likelihood assuming normal errors, and primary attention is given to exponential, Gompertz, and scaled logistic dose–response curves that admit increasing or decreasing monotonic and sigmoidal patterns. Careful consideration is given to dose axis scaling, comparative model fit via mean squared error and graphical assessment, analogues to weighted least squares analysis to address heterogeneity of variance across doses, and potential hormetic effects. Standard error estimation is discussed in detail, highlighting the advantage of reparameterizing dose–response models directly in terms of IC50. Specific results for two cell lines are provided, along with a sample commercial software-based program for implementing a selection of the methods discussed.