TCP isoeffect analysis using a heterogeneous distribution of radiosensitivity.

A formula for the alpha/beta ratio is derived using the heterogeneous (population averaged) tumor control model. This formula is nearly identical to the formula obtained using the homogeneous (individual) tumor control model, but the new formula includes extra terms showing that the alpha/beta ratio, the ratio of the mean value of a divided by the mean value of beta that would be observed in a patient population, explicitly depends on the survival level and heterogeneity. The magnitude of this correction is estimated for prostate cancer, and this appears to raise the mean value of the ratio estimate by about 20%. The method also allows investigation of confidence limits for alpha/beta based on a population distribution of radiosensitivity. For a widely heterogeneous population, the upper 95% confidence interval for the alpha/beta ratio can be as high as 7.3 Gy, even though the population mean is between 2.3 and 2.6 Gy.