IMPROVED MODELS OF TUMOR CURE

The standard mechanistic model for the probability of tumour cure (the 'Poisson model') is based on the assumption that the number of surviv ing clonogens at the end of treatment follows a Poisson distribution f rom tumour to tumour. This assumption is not correct, however, if prol iferation of tumour clonogens occurs during treatment, as would be exp ected in general during a fractionated course of radiotherapy. In the present study, the possible magnitude of the error in the Poisson mode l was investigated for tumours treated with either conventional fracti onation or split-course therapy. An example is presented in which the Poisson model has an absolute error of nearly 100%, predicting a cure rate of 0% when in fact the cure rate was close to 100%. The largest e rrors in the Poisson model found in this study were for very small tum ours (approximate to 100 clonogens), but for larger tumours (greater t han or equal to 10(6) clonogens), the Poisson model may still be highl y inaccurate, predicting a cure rate that differs from the actual cure rate by as much as 40%. Three new tumour-cure models are proposed (th e GS, PS, and GS+ models), and their accuracy is also investigated. Tw o of these (the GS and PS models) are better than the Poisson model fo r the clinically relevant cases tested here. The third model, the GSmodel, consistently produced the most accurate estimate of the tumour cure rate, but has more limited use than the GS and PS models because it is more highly parametrized. It is demonstrated here that no tumour -cure model based on the effective clonogen doubling time will be perf ectly accurate in all cases, since the cure rate depends on the detail s of the cell kinetics contributing to the effective doubling time.