Improved models of tumour cure

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Abstract
The standard mechanistic model for the probability of tumour cure (the 'Poisson model') is based on the assumption that the number of surviving clonogens at the end of treatment follows a Poisson distribution from tumour to tumour. This assumption is not correct, however, if proliferation of tumour clonogens occurs during treatment, as would be expected in general during a fractionated course of radiotherapy. In the present study, the possible magnitude of the error in the Poisson model was investigated for tumours treated with either conventional fractionation 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 errors in the Poisson model found in this study were for very small tumours (100 clonogens), but for larger tumours (106 clonogens), the Poisson model may still be highly inaccurate, predicting a cure rate that differs from the actual cure rate by as much as 40. Three new tumour-cure models are proposed (the GS, PS, and GS + models), and their accuracy is also investigated. Two of these (the GS and PS models) are better than the Poisson model for the clinically relevant cases tested here. The third model, the GS+ model, 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 perfectly accurate in all cases, since the cure rate depends on the details of the cell kinetics contributing to the effective doubling time.