Effects of 'rogue' points on non-linear fitting.

Computers make it possible to fit data directly to curves such as a hyperbola or the Hill equation (sometimes called logistic equation), and remove the requirement of previously used methods to convert the data so as they fit a straight line (as in Scatchard or Hill plots). There are good reasons for abandoning these older procedures, but what are the problems with the new ones? Errors in points at either end of straight line have more effect on the slope and intercept than errors in the middle range, but what is to be expected with a direct fit to curves? In this article, Dick Barlow describes the effects of errors at particular points ('rogue' points) on the results of the analysis for the fit of data by equally-weighted least-squares to: (1) a single line that may represent the results obtained in ligand-binding experiments or the relationship between dose and pharmacological response; (2) two dose-response curves that may represent the results obtained with a competitive antagonist and are used to calculate dose ratios; and (3) two dose-response curves in which the second curve is flattened that may represent the results obtained with an irreversible antagonist and are used to calculate the EC50 (apparent equilibrium constant) for the interaction between an agonist and a receptor. The method used involves making the repeated analysis of theoretical data and can be extended to other relations, including those describing pharmacokinetics.