A Method for Determining Dose-modification Factors

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 two such sets of observations when they are treated as if there were a common extrapolation number. The two straight lines are then described by three parameters, instead of the four 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 fourth parameter adds significantly to the goodness of fit; if the three 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 four-parameter and the three-parameter models; the “F-ratio”, used to test the adequacy of the three parameters; and confidence limits on slopes, extrapolation numbers and dose-modification factors.