Quantitative characterization of hormone receptors.

Most workers characterize steroid (and other hormone) receptors by graphical analysis of Scatchard plots or by simple linear regression. Unfortunately, these methods are suboptimal from a statistical point of view. The Scatchard plot, B/F vs. [Bound], does not satisfy the assumptions underlying simple linear regression: both variables are subject to error, and these errors are intimately interdependent. Accordingly, nether B/F nor [Bound] is an appropriate independent variable. Furthermore, both variables (B/F and [Bound] show non-uniformity of variance. Thus, even when the Scatchard plot is liner, one should estimate the binding parameters (affinity, K, and binding capacity, R) by means of weighted nonlinear least-squares regression, using the Total ligand concentration as the independent variable, and either B/T or [Bound] as the dependent variable. In the case of a nonlinear Scatchard plot, one should also use weighted nonlinear least-squares curve fitting to estimate the K and R values for the high and low affinity classes of sites. Allowing the computer program to provide the best estimate of the nonspecific or nonsaturable binding is also desirable. The program should provide estimates of the standard errors and/or 95% confidence limits for the estimated parameters, and the joint 95% confidence limits for K and R. One should routinely attempt to fit several models of varying degrees of complexity (e.g., 1,2, or 3 classes of sites), provide estimates of the goodness-of-fit for each, and then select the best model by statistical criteria. Sometimes, we encounter Scatchard plots that are obviously nonlinear but provide insufficient information within any one experiment to permit reliable characterization of two or more classes of sites. In this case, we may employ any of several alternative techniques, including 1) use of the " limiting slopes" technique to obtain approximate estimates of parameters; 2) use of a Continuous Affinity Distribution, with consideration of only the receptors with an affinity above an arbitrarily selected cutoff value of k; 3) use of a Discrete Affinity Distribution, by assigning values to the affinities (K19 K2) based on prior information, and then estimating the binding capacities; 4) pooling information over several specimens within an assay or over several assays by use of normalizing or scaling factors. The best estimates of these scaling factors can be obtained by the use of a general least-squares method for pooling data from different specimens or experiments. A series of computer programs to perform these analyses has been developed. They have been applied successfully to analysis of steroid receptors in specimens from breast carcinoma.