SU‐FF‐T‐344: On the Equivalency of the Population and Individual TCP Models

Abstract

Purpose: To demonstrate that the functional form of the population tumor control probability (TCP) model is well approximated by the individual TCP model. Method and Materials: Due to inter‐parameter relations, the parameters of the population based Poisson TCP model in the limit of large heterogeneity reduce to the geometric parameters D50 and γ50:1 . On the other hand the individual TCP model can also be written in the terms of the geometrical characteristics of the dose‐response relationship — D50 and γ50: . For typical clinical values2 of the parameters D50 and γ50, we evaluate and compare the individual and population‐based TCP models. Results: The two models are approximately equivalent for different values of D50 and γ50. When plotted, the individual and population‐based TCP models almost overlap over a wide range of doses for all D50 values and γ50 higher than 1. When γ50 is less than 1 both functions start to differ from one another. Conclusion: The equivalency between the individual and population TCP models is demonstrated. The individual TCP model has been observed to fit clinical datasets reasonably well, and this phenomenon may be attributed to the similarity of the models. When fitted to clinical data, the individual TCP model will produce parameter estimates completely emptied from their biological meaning and become purely phenomenological.