Inclusion of control data in fits to concentration-response curves improves estimates of half-maximal concentrations

Some data are just underappreciated. Maybe they look different or come from a different background than most other data. Maybe they don't fit neatly into common notions of what data on a ``curve'' should look like. Whatever the case, they are pigeonholed into a restricted role that limits their contributions. But if people would only give them the opportunity, they could improve the entire fit. This is the case for control data in concentration response curves. Concentration-response curves - in which the effect of varying the concentration on the response of an assay is measured - are widely used in pharmacology and toxicology to evaluate biological effects of chemical compounds. While National Center for Advancing Translational Sciences guidelines specify that readouts should be normalized by the controls, recommended statistical analyses do not explicitly fit to the control data. Here, we introduce a nonlinear regression procedure based on maximum likelihood estimation that determines parameters for the classical Hill equation by fitting the model to both the curve and control data. Simulations show that the proposed procedure provides more precise parameters compared to previously prescribed practices. Analysis of enzymatic inhibition data from the COVID Moonshot demonstrates that the proposed procedure yields a lower asymptotic standard error for estimated parameters. Benefits are most evident in the analysis of incomplete curves. We also find that Lenth's outlier detection method appears to determine parameters more precisely.