Radiation cancer risks are typically determined by the use of simple statistical descriptions of epidemiological data. It is important in risk assessment in general, however, to attempt to incorporate as much biological information into the risk models as possible. We illustrate this by presenting a biologically-based linear-quadratic-exponential (LQE) incidence rate model for radiation-induced chronic myeloid leukemia (CML). The model consists of a linear-quadratic dose-response for the induction of BCR-ABL, a waiting time distribution between BCR-ABL formation and detection of CML, and an exponential cell-killing term that multiplies both the background and induced incidence rates. Using data exclusive of the A-bomb survivor cohort, Bayesian priors are defined for each of the nine parameters in this LQE model. The priors are based on chromosomal translocations in lymphocytes, hematopoietic stem cell survival experiments, CML waiting times in women irradiated for benign disease, the background CML incidence rate in the U.S. population, and genomic DNA target sizes of BCR and ABL. Fixing three of the LQE model parameters to the means of their priors, maximum likelihood estimates of the remaining six parameters were obtained using A-bomb survivor incidence data for Hiroshima males. The likelihood estimates and the corresponding six prior distributions, both approximated as multivariate normal, were then used to form Bayesian posteriors for the six parameters not fixed. With these posteriors the LQE model yields Qgamma*=0.0042 Gy(-1) where Qgamma* is the upper 95% confidence bound of the lifetime CML risk per person-gray in the limit of low doses of gamma-rays. This value is slightly less than Qgamma*=0.0049 Gy(-1) obtained from likelihood estimates of the LQE parameters, and substantially less than Qgamma*=0.0158 Gy(-1) obtained for a simple statistical model linear in dose for kermas less than 4 Gy.