Analysing data from hormone-receptor assays

Assay results for hormone receptors in human breast cancer are generally plotted in the form of a Scatchard plot. Usually a line is fitted to the data points by least squares regression and thence the concentration of binding sites present in the cancer is calculated. The subsequent treatment of the patient with hormones depends on this value, so a good estimate of it is necessary. In this study, three methods of representing the data, namely the Scatchard plot, the reciprocal plot and the Woolf plot, were investigated, and three ways of fitting lines to the data points of each graph, namely least squares regression, an unweighted robust procedure and a weighted robust procedure, were examined. When the data were well-behaved all plots gave similar answers for the concentration of binding sites, irrespective of the regression technique used. However, when there were up to three outlying points, the Scatchard plot, particularly with least squares regression analysis, performed poorly. The robust regression analyses yielded more consistent results on all plots; in particular the hitherto mistrusted reciprocal scale seemed to perform well under robust regression, but other evidence indicated instability in the plot. It is concluded that the most reliable way of representing binding data in these experiments is by a Woolf plot, and that the subsequent line fitting is made resistant by an unweighted robust regression analysis.