How Well Is the Probability of Tumor Cure after Fractionated Irradiation Described by Poisson Statistics?

The probability of tumor cure in a homogeneous population of tumors exposed to fractionated radiotherapy was modeled using numerical simulations and compared with the predictions of Poisson statistics, assuming exact knowledge of the relevant tumor parameters (clonogen number, radiosensitivity, and growth kinetics). The results show that although Poisson statistics (based on exact knowledge of all parameters) accurately describes the probability of tumor cure when no proliferation occurs during treatment, it underestimates the cure rate when proliferation does occur. In practice, however, the inaccuracy is not likely to be more than about 10%. When the tumor parameters are unknown and are estimated by fitting an empirical Poisson model to tumor-cure data from a homogeneous population of proliferative tumors, the resulting estimates of tumor growth rate and radiosensitivity accurately reflect the true values, but the estimate of initial clonogen number is biased downward. A new formula that is more accurate than Poisson statistics in predicting the probability of tumor cure when proliferation occurs during treatment is discussed.