A Method for Determining Dose-modification Factors

Abstract

Survival curves are often defined by the slope of the straight portion, on a semi-logarithmic plot, and the intercept which this portion of the curve makes on the zero-dose axis (i.e. the extrapolation number). When a modifying agent is used, its effectiveness can be expressed by a single number only when it is dose-modifying, in which case the extrapolation number is the same for survival curves in the presence and the absence of the agent. A method is here described for deriving the best fit to 2 such sets of observations when they are treated as if there were a common extrapolation number. The 2 straight lines are then described by 3 parameters, instead of the 4 which would be found by fitting the best line to each set of observations independently. A test must be carried out to see whether the 4th parameter adds significantly to the goodness of fit; if the 3 parameters are sufficient, there is a considerable gain in the precision with which both the extrapolation number and the dose-modification factor may be determined. A programme has been written for the Ferranti Mercury computer, to calculate the constants both for the 4-parameter and the 3-parameter models; the "F-ratio", used to test the adequacy of the 3 parameters; and confidence limits on slopes, extrapolation numbers and dose-modification factors.