A Simple Method for Fitting Curves to Dose-effect Data for Functional Damage

Summary

Dose–effect curves are used extensively to assess how tissues respond to radiation. One method of obtaining these is to fit a curve to the values of some measured effect plotted against dose using non-linear least-squares regression. This paper reports the use of a generalized (four-parameter) sigmoid equation fitted to all the individual data points, rather than to the mean values for each dose group, which eliminates the need to incorporate weighting of the data. The equation allows an analytical solution for values of isoeffect doses, which can be used, for example, to determine dose enhancement ratios, or equivalent remembered doses in top-up experiments. The regression approach can also determine both standard errors and 95% confidence limits on the mean predicted effect values from the fit to the data at all doses, and these define a uniform envelope of errors about the best-fit line, from which an error in an isoeffect dose can be assessed. This approach has been used to fit dose-effect data from a variety of normal tissues and tumours with highly satisfactory results.