Comparison of alpha/beta estimates from homogeneous (individual) and heterogeneous (population) tumor control models for early stage prostate cancer.

Radiobiological parameter estimates for prostate cancer are obtained from both a homogeneous (individual) and heterogeneous (population) tumor control model based on Poisson statistics and the linear quadratic model of cell survival. Parameter estimates for both models are highly correlated: statistically equivalent fits are achievable using either (1) linear quadratic (LQ) parameters with low numbers of radioresistant tumor stem cells, or (2) LQ parameters with corresponding larger number of radiosensitive tumor stem cells. A theoretical framework is developed to explain this correlation. A Monte Carlo error analysis based on binomial statistics is used to estimate confidence intervals for all parameter estimates. It was found that both the homogeneous and heterogeneous models produce approximately equivalent estimates of radiobiological parameters, including the alpha/beta ratio. However, the 95% confidence interval for the alpha/beta ratio derived from the heterogeneous model are considerably larger than those derived from the homogeneous model, which indicate the homogeneous model overestimates the statistical significance of the alpha/beta estimate.